CHAPTER-12B OPTIONS - Shoundik Sinha & Co.

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CA-FINAL-SSFFMM

CHAPTER-12BOPTIONS

FCA RAJESH RITOLIA

8 YEARS TEACHING EXPERIENCE

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CHAPTER-12A OPTION DERIVATIVE 12A_A.1

HELPING HAND INSTITUTE| FCA, RAJESH RITOLIA| 9350171263, 8447824414| WEBSITE:CASSINHA.IN

12A.0 INDIAN CAPITAL MARKET

a) Broadly Indian Financial Market consists of Capital Market, Money Market and the Debt Market

b) The organized part of the Indian financial system can be classified from the point of view of regulatoryauthority as- RBI regulating Commercial Banks, Foreign Exchange Markets, Financial Institutions, NBFC etc.- SEBI regulating Primary Market, Secondary Market, Derivatives Market and market intermediaries likeMutual Funds, Brokers, Merchant Banks, depositories.

12A.0.1 INDIAN CAPITAL MARKET

(a) Role of Capital Market It is the indicator of the inherent strength of the economy. It is the largest source of funds with long and indefinite maturity for companies and thereby

enhances the capital formation in the country. It offers a number of investment avenues to investors. It helps in channeling the savings pool in the economy towards optimal allocation of capital in the

country.

12A.0.2 STOCK MARKET AND ITS OPERATIONS

1. Secondary markets are also referred to as Stock Exchange.

2. It is a place where the securities issued by the Government, public bodies and Joint Stock Companiesare traded.

3. There are 21 Stock Exchanges in the country.

List of recognized stock exchangehttp://www.rushabhinfosoft.com/Webpages/COMPANY%20LAWS/HTML/Appendix-87.htm

3. Leading Stock Exchanges in India: Bombay Stock Exchange (BSE) and National StockExchange (NSE).http://www.world-stock-exchanges.net/top10.html

12A.0.3 Functions of Stock Exchanges[T-1] [M11-6bi-4] Write short notes on Function of Stock Exchange

Functions of the stock exchanges can be summarized as follows:(a) Liquidity and Marketability of Securities: Investors can convert their securities into cash at any time

at the prevailing market price. Investors can change their portfolio as and when they want to change,i.e. they can at any time sell one security and purchase another.

(b) Fair Price Determination: This market is almost a perfectly competitive market as there are largenumber of buyers and sellers. Due to nearly perfect information, active bidding take place from bothsides. This ensures the fair price to be determined by demand and supply forces.

(c) Source for Long term Funds: Securities are traded and change hands from one investor to the otherwithout affecting the long-term availability of funds to the issuing companies.

(d) Helps in Capital Formation: There are the nexus between the savings and the investments of thecommunity.

Capital Market

Primary Market

A market where new securities are bought and sold for thefirst time is called the New Issues market or the IPO market

Secondary Market

It is a Market in which issued securities are sold andpurchased by investor. It is the stock exchanges and the over-

the-counter market.

(e)Reflects the General State of Economy: The performance of the stock markets reflects the boom anddepression in the economy. It indicates the general state of the economy to all those concerned, whocan take suitable steps in time.

12A.1 Derivatives[T-2] [M04-06] [M03-06] [PM-J17-17, 21] [PM-J15-17, 21] What is a “derivatives’? Briefly explainthe recommendation of the L C Gupta Committee on derivatives.[N07-5c-8](a) What are derivatives?(b) Who are the users and what are the purposes of use?(c) Enumerate the basic differences between cash and derivatives market.

[M11-7d-4] [RTP-M14-20d] [PM-J17-18] [PM-J15-18] What is the meaning of underlying in relationto a derivative instrument?

(a) Derivatives:It is a financial asset which derives its value from some specified underlying assets.Derivatives do not have any physical existence but emerges out of a contract between two parties.It does not have any value of its own but its value depends on the value of other physical assets.The underlying assets may be shares, debentures, tangible commodities etc.The parties to the contract of derivatives are the parties other than the issuer of the assets.The transactions in derivatives are settled by the offsetting in the same derivative. The difference invalue of the derivatives is settled in cash.There is no limit on number of units transacted in the derivative market because there is no physicalassets to be transacted.

(b) Users of Derivatives market: Hedgers ; Speculators; Arbitrages;

(c) Function of Derivatives MarketsThey help in transferring risk from risk averse people to risk oriented people.They help in discoveries of future prices.

Example-1Today date = 01/01/2012Today price of Flat = Rs 95000 = known as spot priceMr A wants to purchase flat on 31/03/2012, but he has fear that price of flat may go up, then how he canhedge himself from rising of prices.To hedge himself he can enter into contract on 01/01/2012 for purchase of flat on 31/03/2012Mr A has entered into Contract for purchase of flat with Mr B. Terms of the Contract are as follows

Type of Derivative

Commodity and Financial derivatives

Commodity DerivativesIt is a contract on differenttype of commodity such as

sugar, Jute, Gur etc.

Financial DerivativesIt is a contract on different

type of FinancialInstruments such as Shares,

Currencies etc.

Basic and Complex derivatives

Basic Derivatives:It is traded in Stock

ExchangeFutures and Options

Complex Derivative (OTC)It is not traded in stock

exchangeIt is a Contract between 2

partiesEx: Interest Swaps; Caps,Floor and Collar; Forward

Rate Agreement;Swaptions; Currency Swaps;

Forward Contracts;

Date of Contract = 01/01/2012Contract price of Flat = Rs.100000 [Strike Price or Contracted Price or Forward Price, Specified Price]Date of maturity = 31/03/2012 [Strike Date, Expiry date, Maturity Date, Specified Date]Benefit of ContractBy entering into contract Mr A has fixed its purchase price of Flat at Rs.1 lacs.Even if price of flat increases/decreases, Mr A has to pay Rs.1 lac.Now suppose,

Actual price of flat increase or decrease as follows

In case of Settlement (SpeculativeTransaction)

In case of Delivery (Hedging)

Date Actual price ofFlat

Long Position ofMr A

Short Position ofMr B

Purchase price forMr A

Sale price for MrB

05/01/2012 Rs.1.2 Lacs +0.2 -0.2 Rs.1 Lacs Rs.1 Lacs

15/03/2012 Rs.0.9 Lacs -0.1 +0.1 Rs.1 Lacs Rs.1 Lacs

Why this gain or loss arises to each party of contractThis is because of Contract between A and BThis contract is known as Derivative InstrumentGain or loss due to contract arises due to change in prices of flat [Under lying Assets]Hence contract derives its value from Flat [Underlying Assets]Value of the derivative instrument [Contract] is equal to gain or loss to each party.The same type of contract can be done for shares, debenture, etc through stock exchange.

12A.2 Option[T-3] [N02-03] [PM-J17-24] [PM-J15-24] Write short notes on the Option.[N97-05] Call and put option with reference to debentures.

(a) Options: Options are contracts which provide the holder the right to sell or buy a specified quantityof an underlying asset at a fixed price on or before the expiration of the option date.Options provide a right and not the obligation to buy or sell.The holder of the option can exercise the option at his discretion or may allow the option tolapse.

Option

Call Option (Right to Buy UA)

It provides to the holder a Right to Buy UA at stike price on orbefore strike date.

Holder - Buyer of Call OptionHe pays premium on call option.

He has right to buy UAMaximum Loss = Premium Paid

Maximum Gain - Unlimited

Writer - Seller of Call Option.He receives premium on call option.

He has obligation to sell UA on exercise of call option by holderMaximum Loss = Unlimited

Maximum Gain - Premium Gain

Put Option (Right to Sell UA)

It provides to the holder a Right to Sell UA at stike price on orbefore strike date.

Holder - Buyer of Put Option.He pays premium on put option.

He has right to sell UAMaximum Loss = Premium Paid

Writer - Seller of Put Option.He receives premium on put option

He has obligation to buy UA on exercise of put option byholder

Maximum Loss = UnlimitedMaximum Gain - Premium Gain

Excercie of Call Option at expiry date (Lower of Spot Price of UA and Strike Price)

If Spot Price of UA < Strike Price

Gain/(Loss) on settlement toHolder = NilWriter = Nil

Value of CO at Expiry = Nil

Status - Out of the Money

If Spot Price of UA = Strike Price

Status = At the Money

If Spot Price of UA > Strike Price

Exercise

Gain/(Loss) on settlement toHolder = Spot Price - Strike PriceWriter = Spot Price - Strike PriceValue of CO at Expiry = Gain on

Settlement

Status = In the Money

b) Strike or Exercise Price: The specified price at which the option can be exercised is known as theStrike Price.

c) Option Premium/Price:In options, the buyer pays option premium to seller.In case, the right is not exercised later, then the premium is not refunded by the option writer.

d) By buying Call option Holder fixes upper limit of its purchase price but does not fix lower limit ofpurchase price

f) Long and short position:Buyer of an option = long positionSeller of an option = short position

g) Today 01/09/2012

Excercie of Put Option at expiry date (Higher of Spot Price of UA and Strike Price)

Exercise

Gain/(Loss) on settlement toHolder = Strike Price - Spot PriceWriter = Strike Price - Spot PriceValue of PO at Expiry = Gain on

Settlement

Status - In the Money

Value of PO at Expiry = Nil

Status = Out of the Money

In Case of Hedging

Call Option

Holder

Purchase Price of UA = MP ofUA - Gain on Settlement

Writer

Sale Price of UA = MP of UA -Loss on Settlement

Put Option

Holder

Sale Price of UA = MP of UA +Gain on Settlement

Writer

Purchase Price of UA = MP ofUA + Loss on Settlement

Type of Option (Both)

American and European Option

American Option:It can be Exercised at anytimeon or before expiration date

European Option:It can be exercised only on

expiration date

Naked and Covered Option

Naked Option:Option is not covered by UA

Covered OptionOption is covered by UA

There will be maximum 3 Options on same underlying assets of 3 different maturity datesSep Call, Oct Call, Nov Call.Option is settled on last Thursday of month.

h) Option is distinguished by Underlying Assets, Maturity Date and Strike Price.Today Date = 10/09/2012CMP of Share of X Ltd = Rs.100Call Option on Share’s of X Ltd may be as follows for Sep monthSep Call 120, Sep Call 140, Sep Call 110 etc. All three Call options are different product.

Example-2*** [Understanding of Call Option]On 01/01/2012 Ram enters into contract with Shyam with following terms & Conditions(a) Ram has the right but not the obligation to buy 100 shares of A Ltd on 31/03/2012 @ Rs.50 per shares.(b) If Ram does not exercise the rights of purchase, then Shyam can not sell it to Ram.(c) It means ram has purchased the [Rights of Purchase] from Shyam.(d) Ram has to pay premium [Cost of Rights of Purchase] to Shyam say Rs.5 per share.

Spot price of Shares of A Ltd as on 01/01/2012 = Rs.45Price of Call Option as on 01/01/2012 = Rs.5What is the benefit and obligation of above contract to Ram and ShyamOn 31/03/2012Benefit/(Loss) of Call Option to Ram and Shyam

Actual Market price of share on 31/03/2012 Rs.35 Rs.43 Rs.50 Rs.60 Rs.70

Ram has Rights to Purchase share from Shyam at strike price Rs.50 Rs.50 Rs.50 Rs.50 Rs.50

Where from Ram should buy shares (Lower of above) Market Market Market orShyam

Shyam Shyam

Exercise of Call option by Ram No No No Yes Yes

Option-1 In case of Settlement/ Speculative Gain/Loss on maturity date

Gain to Ram due to exercise of Call Option 0 0 0 Rs.10 Rs.20

Loss to Shyam due to exercise of Call Option by Ram 0 0 0 Rs.10 Rs.20

Calculation of net gain/(Loss) = Gain on Maturity –Premium Paid

Net Gain/(Loss) to Ram -Rs.5 - Rs.5 - Rs.5 Rs.5 Rs.15

Net Gain or (Loss) to Shyam Rs.5 Rs.5 Rs.5 - Rs.5 -Rs.15

Status of Option Out Out At In In

Option 2 In case of Hedging/ Actual Delivery

Purchase price of Share to Ram (MP of UA – Gain on settlement) Rs.35 Rs.43 Rs.50 Rs.50 Rs.50

Sell price of Share to Shyam (MP of UA – Loss on settlement) Rs.35 Rs.43 Rs.50 Rs.50 Rs.50

Example-3*** [Understanding of Put Option]On 01/01/2012 Ram enters into contract with Shyam with following terms & Conditions(a) Ram has purchased (Right to Sell UA) (Put Option) right but not the obligation to sell 100 shares of A

Ltd on 31/03/2012 @ Rs.52 per shares.(b) If Ram does not exercise the rights of sale, then Shyam can not buy share from Ram.(c) It means Ram has purchased the [Rights of Sale UA] from Shyam. In other words, Ram has purchased

Put Option from Shyam(d) Ram has to pay premium [Cost of rights of sale] to Shyam say Rs.6 per share.

Say Spot price of Shares of A Ltd as on 01/01/2012 = Rs.45While spot price of Put Option [Right of Sale] as on 01/01/2012 = Rs.6What is the benefit and obligation of above contract to Ram and Shyam

On 31/03/2012

Spot Price of Share as on 31/03/2012 Rs.35 Rs.43 Rs.52 Rs.60 Rs.70

Ram has the rights to sell share to Shyam at StrikePrice

Rs.52 Rs.52 Rs.52 Rs.52 Rs.52

Where should Ram sell Shares[Ram should sell at higher of Spot and Strike]

Shyam Shyam Market Market Market

Exercise of Put option by Ram (Holder of Putoption)

Yes Yes No No No

Option-1 In case of Settlement/ Speculative Gain/Loss on maturity date

Gain to Ram due to exercise of Put Option 17 9 0 0 0

Loss to Shyam due to exercise of Put Option byRam

17 9 0 0 0

Calculation of net gain/(Loss) = Gain on Maturity – Premium Paid

Net Gain/(Loss) to Ram 11 3 -6 -6 -6

Net Gain or (Loss) to Shyam -11 -3 6 6 6

Status of Option In In At Out Out

Option-2 In case of Hedging/ Actual Delivery

Sale price of Share to Ram (MP of UA + Gain onSettlement)

52 52 52 60 70

Purchase price of Share to Shyam (MP of UA +Loss on Settlement)

52 52 52 60 70

12A.3 Calculation of Gain/(Loss) on Settlement of OptionQ No Exam PM-J15 PM-J16 PM-J17 RTP

1 M09-O-4a-10 50 54

1A M10-O-3a-4 51 55 N12-17

2 M06-5b-7 44 48

2A M16-1d-5

2B N08-2c-6, N09-O-5a-6, N11-6b-8, M10-1b-4 47 51

2C 42 45

Question-1 [M09-O-4a-10] [PM-J17-54] [PM-J15-50]The equity share of VCC Ltd is quoted at Rs.210. A 3-month call option is available at a premium of Rs.6 pershare and a 3-month put option is available at a premium of Rs. 5 per share.The strike price in both cases in Rs. 220; andThe share price on the exercise day is Rs.200, 210, 220, 230, 240.(a) Calculate purchase price/Sale Price of Holder in case of actual delivery. [Not part of Q](b) Calculate Gain/(Loss) of Holder in case of settlement. [Not part of Q](c) Ascertain the net payoffs to the option holder of a call option and a put option.(d) Ascertain the status of Option. [Not part of Q]

Also indicate the price range at which the call and the put options may be gainfully exercised.

Question-1A [M10-O-3a-4] [PM-J17-55] [PM-J15-51] [RTP-N12-17] [SP]A call and put exist on the same stock each of which is exercisable at Rs.60. They now trade for:

Market price of stock or stock index Rs.55

Market price of call Rs.9

Market price of put Re.1

Calculate the expiration date cash flow, Investment Value, and net profit from:(a) Buy 1 call(b) Write 1 call(c) Buy 1 put

(d) Write 1 putFor expiration date stock prices is Rs.50, Rs.55, Rs.65, Rs.70

Question-2 [M06-5b-7] [PM-J17-48] [PM-J15-44] [ICWA-J07]**The market received rumour about ABC corporation's tie-up with a multinational company. This has inducedthe market price to move up. If the rumour is false, the ABC corporation stock price will probably falldramatically. To protect from this an investor has bought the call and put options.He purchased one 3 months call with a striking price of Rs.42 for Rs.2 premium, and paid Re. 1 per sharepremium for a 3 months put with a striking price of Rs.40.(a) Determine the Investor's position if the tie up offer bids the price of ABC Corporation's stock up to Rs.43

in 3 months.(b) Determine the Investor's ending position, if the tie up programme fails and the price of the stocks falls

to Rs.36 in 3 months.

Question-2A [M16-1d-5] [SP]Fresh Bakery Ltd’s share price has suddenly started moving both upward and downward on a rumour thatthe company is going to have a collaboration agreement with a multinational company in bakery business. Ifthe rumour turns to be true, then the stock price will go up but if the rumours turn to be false, then stockprice will fo down. To protect from this an investor has purchased the following call and put option:(i) One 3 months call with s striking price of Rs.52 for Rs.2 premium per share.(ii) One 3 months put with s striking price of Rs.50 for Rs.1 premium per share.Assuming a lot size of 50 shares, determine the followings:(a) Determine the Investor's ending position, if the collaboration agreement push the share price of the

stocks to Rs.53 in 3 months.(b) Determine the Investor's ending position, if the collaboration agreement fails and the share price of the

stocks crashes to Rs.46 in 3 months.

Question-2B [N08-2c-6] [N09-O-5a-6] [N11-6b-8] [M10-1b-4] [PM-J17-51] [PM-J15-47] [SP]Mr. X established the following spread on the Delta Corporation's stock(i) Purchased one 3-month call option with a premium of Rs.30 and an exercise price of Rs.550.(ii) Purchased one 3-month put option with a premium of Rs. 5 and an exercise price of Rs.450.Delta Corporation's stock is currently selling at Rs.500. Determine profit or loss, if the price of DeltaCorporation's:(a) remains at Rs.500 after 3 months.(b) falls at Rs.350 after 3 months.(c) rises to Rs.600.Assume the size option is 100 shares of Delta Corporation.

Question-2C [PM-J17-45] [PM-J15-42] [SP]Mr. A purchased a 3 months call option for 100 shares in XYZ Ltd. at a premium of Rs.30 per share, with anexercise price of Rs.550. He also purchased a 3 month put option for 100 shares of the same company at apremium of Rs.5 per share with an exercise price of Rs.450. The market price of the share on the date ofMr. A’s purchase of options, is Rs.500. Calculate the profit or loss that Mr. A would make assuming that themarket price falls to Rs.350 at the end of 3 months.

Question-3 [ICWA-D08]**Rax Investments Ltd. deals in equity derivatives. Their current portfolio comprises of the followinginvestments.

Infosys Rs.1,400 Call expire December 2010 200 units bought at Rs.50 each (cost)

Infosys Rs.1,425 Call expire December 2010 3,000 units bought at Rs.33 each (cost)

Infosys Rs.1,350 Put expire December 2010 4,000 units bought at Rs.22 each (cost)

What will be the profit or loss to Rax Investments Ltd. in the following situations?

i) Infosys closes on the expiry day at Rs.1,550.

ii) Infosys closes on the expiry day at Rs.1,460.

iii) Infosys closes on the expiry day at Rs.1,280.

(Ignore transaction cost and taxation).

12A.4 Calculation of Value of Option/Intrinsic Value of Option at expirationQ No Exam PM-J15 PM-J16 PM-J17 RTP

4 N12-3a-8 49 53

4A N10-1c-5 48 52

Question-4 [N12-3a-8] [PM-J17-53] [PM-J15-49]***You as an investor has purchased a 4 month call option on the equity shares of X Ltd of Rs.10, of which thecurrent market price is Rs.132 and the exercise price Rs.150. You expect the price to range between Rs.120to Rs.190. The expected share price of X Ltd and related probability is given below:

Market price 120 140 160 180 190

Probability 0.05 0.20 0.50 0.10 0.15

Compute the following:(a) What is the expected value of share price 4 month hence? [Ans: Rs.160.50](b) Value of call option at the end of 4 months, if the exercise price prevails. [Rs.10.50](c) What is the expected value of option price at expiration. Assuming that the option is held to this time.

Question-4A [N10-1c-5] [PM-J17-52] [PM-J15-48] [SP]Equity share of PQR Ltd. is presently quoted at Rs.320. The market price of the share 6 months has thefollowing probability distribution:

Market price 180 260 280 320 400

Probability 0.1 0.2 0.5 0.1 0.1

(a) A put option with a strike price of Rs.300 can be written.(b) You are required to find out expected value of option at (i.e. 6 months) [Ans: Rs.30]

12A.5 Factors affecting value of OptionQ No Exam PM-J15 PM-J16 PM-J17 RTP

T-4 M14-7b-4 30 31

[T-4] [M14-7b-4] [PM-J17-31] [PM-J15-30] Factors affecting value of an option

The valuation of an option depends upon a number of factors relating to the underlying asset and thefinancial market. Some of these factors are:a) Current value of the Underlying Asset.b) Future Price: The future price level is a major determinant of the option premium.c) Strike price of the option: The exercise of the option depends upon the difference between the strike

price and the actual price of the underlying asset. In case of call option, the value of option will decline

Calculation of Value of Option at Expiration date

If only one Spot of Price of UA is given

TVCO = Max[(Spot Price – Strike Price),0] TVPO = Max[(Strike Price – Spot Price),0]

If more than one Spot of Price of UA isgiven with Probability

EVOExpiry = VO1P1 + VO2P2 + VO3P3 +VO4P4

Where VO is value of Option at eachprice of UA

as the strike price increases, and in case of put option, the value of the option will increases as thestrike price increases.

d) Expiration time of Option: The longer the time to expiry, higher would be the value of the option.e) Rate of Interest: The option holder has to pay the option premium up front, i.e., in advance to buy

the option. So, there is always an opportunity cost of this premium. Increase in interest rate willincrease the value of the call option but will reduce the value of the put option.

f) Income from Underlying Asset: During the life of the option, there may arise interest or dividendincome on the underlying assets. The value of the asset will decrease, as the interest or dividend ispaid. So, the value of the call option decreases and the value of the put option increases as more andmore interest and dividends are paid on the underlying assets.

Summary of effect of various factors on value of option

Factor Call Option Value Put Option Value

Increase in value of Underlying Asset Increases Decreases

Extent of Volatility in Value of Asset Increases Increase

Increase in Strike Price Decreases Increases

Longer Expiration Time Increases Increases

Increase in Rate of Interest Increases Decreases

Increase in Income from Asset Decreases Increases

Question-5Assume that TIC Ltd. equity is currently at Rs.500. It is now July 1. Three Call Options are quoted

TIC (550) Rs.10 Exp. Date 29.11.2002

TIC (500) Rs.50 Exp. Date 29.11.2002

TIC (450) Rs.100 Exp .Date..:..31.1.2003 (Ignore Commissions)

(a) Why the premium on January call (450) is so much higher than the premium on the November (500)call.

(b) Suppose that you purchased 100 shares of TIC on June 1 at a cost of Rs.475 per share. You wrote (sold)one contract TIC (450) 31.01.2003 on July 1. Suppose that on 31.1.2003 TIC was at Rs.525.(i) Would the holder January Call (450) benefit from exercising the call? Why?(ii) If the call were exercised what is your tax status?

(c) Suppose you do not own TIC shares. You simultaneously write one November (550) and buy oneNovember (500) call. What is your annualized rate of return if TIC stock closes in November at Rs.575.(Ignore commissions & dividends).

12A.6 Uses of OptionQ No Exam PM-J15 PM-J16 PM-J17 RTP

8 N15-1d-5 39

10 M07-2a-8

11 M10-O-4b-8

13 N13-2b-8 36 43

(a) Hedging: If Holder of Option buys option for actual delivery, then such transaction is known ashedging. In this case, only Sale/Purchase is to be done through option

(b) Speculative Transaction: If any person buys or sells option only for earning profit not for actualdelivery, then such transaction is known as speculative transaction. Such transaction involves risk. Itinvolves, both sale and purchase are to be done.

(c) Arbitrage Profit: If any person buys or sells option to earn risk less profit on the basis of fair valueand actual value of option. Such transaction does not involve any risk. It involves, both sale andpurchase are to be done.

Question-6 [ICWA-J04]***A portfolio manager purchased 1000 equity share's of Reliance Industries Ltd. @ Rs.510 per share. Hewants to hedge the position by writing an April call with a strike price of Rs.530 and call premium Rs.10.Alternatively, he wants to hedge by buying put option of strike price Rs.530 and premium of Rs.10.(a) Find out his profit or loss if the share price goes up to Rs.560 or Rs.540 or 525 or 490.(b) Does the strategy of buying a stock and writing a call manage his risk effectively?(c) Under which circumstance should the portfolio manager buy a put option?

12A.6.1 Hedging of Foreign Exchange receivable/ Payable through Option

Question-7***UK exporter is to receive $ 10000 in 3 Months. He wants hedging through option. How he can do so.Case-1 Strike Rate £ 1 = $ 1.5Calculate £ receivable if Spot Rate in 3 months; £ 1 = $ 1.7; £ 1 = $ 1.3

Case-2 Strike Rate $ 1 = £ 0.667Calculate £ receivable if Spot Rate in 3 months; $ 1 = £ 0.6; $ 1 = £ 0.8

Question-8 [N15-1d-5] [PM-J17-39-FOREX]***XYZ an Indian Firm, will need to pay Yen 500000 on 30th June. In order to hedge the risk involved inForeign Currency Transaction, the firm is considering two alternative methods, i.e. Forward Market Coverand Currency Option Contract.On 1st April, following quotations JY/INR are as follows:

Spot 3 months Forward

1.9516/1.9711 1.9726/1.9923

The prices for forex currency option on purchase are as follows:

Strike Price JY 2.125

Call Option (June) JY 0.047

Put Option (June) JY 0.098

For excess or balance of JY covered, the firm would use Forward rate as future spot rate.You are required to recommend the cheaper hedging alternative for XYZ

Question-9***A company has a receivable of $ 100 million in 3 months. A bank has offered him a put option with exerciseprice Rs.37/$. The premium payable is Rs. 1 per $. The probability of exchange rate after 3 months is

Probability 0.20 0.30 0.30 0.20

Exchange rate (Rs.1 per $) 35.00 35.50 36.00 36.50

In your opinion, should the company purchase put option? [Ans: Rs.0.25]

Hedging of Forex risk through Option

If LHC-Sale-Buy Put Option If LHC-Buy-Buy Call Option

Question-10 [M07-2a-8] [SP]**XYZ Ltd. a US firm will need £3,00,000 in 180 days. In this connection, the following information isavailable:Spot rate 1 £ = $ 2.00180 days forward rate of £ as of today = $1.96Interest rates are as follows:

U.K. US180 days deposit rate 4.5% 5%180 days borrowing rate 5% 5.5%A call option on £ that expires in 180 days has an exercise price of $ 1.97 and a premium of $ 0.04.XYZ Ltd. has forecasted the spot rates 180 days hence as below:Future rate Probability$ 1.91 25%$ 1.95 60%$ 2.05 15%Which of the following strategies would be most preferable to XYZ Ltd.?(a) a forward contract(b) a money market hedge(c) an option contract [Ans: $594900](d) no hedgingShow calculations in each case.

Question-11 [M10-O-4b-8]***A Ltd of U K has imported some chemical worth of USD 3,64,897 from one of the US suppliers. The amountis payable in six months time. The relevant spot and forward rates are:Spot Rate USD 1.5617 – 1.56736 months Forward Rate USD 1.5455 – 1.5609The borrowing rates in UK and US are 7% and 6% respectively and the deposit rates are 5.5% and 4.5%respectively.Currency options are available under which one option contract is for GBP 12,500. The option premium forGBP at a strike price of USD 1.70/GBP is USD 0.037 (call option) and USD 0.096 (put option) for 6 monthsperiodThe company has three choices:

(i) Forward Cover [Ans: GBP 236102.89](ii) Money Market Cover; and [Ans: GBP 236510.10](iii) Currency Option [Ans: GBP 227923.00]

Which of the alternatives is preferable by the company?

Question-12A London based firm has supplied a nuclear machine to a New York based firm for $120m, payment due in 4months time. The current spot rate is 1 £ = $ 1.58. The London firm has apprehensions that USD maydecline against British Pound. The London firm is considering the proposal of buying a put option, 4 monthsmaturity, strike Price 1 £ = $ 1.60. The option premium is $0.0002 per £. Explain the position of the Londonfirm on maturity if the Spot price of $ on maturity is £0.625; £0.65; £0.615. Also Calculate Premium Paid byLondon based firm.

Question-13 [N13-2b-8] [PM-J17-43-FOREX] [PM-J15-36-FOREX]An American firm is under obligation to pay interest of Can$ 1010000 and Can$ 705000 on 31st July and30th Sep respectively. The firm is risk averse and its policy is to hedge the risks involved in all foreigncurrency transactions. The finance manager of the firm is thinking of hedging the risk considering twomethods i.e. Fixed Forward or Option Contracts.It is now June 30. Following quotations regarding rates of exchange, US$ per Can$, from the firm’s bankwere obtained.Spot Rate Can$ 1 = US$0.9284 – 0.92881 Month Forward Rate Can$ 1 = US$0.9301

3 Months Forward Rate Can$ 1 = US$0.9356Price for a Can$/US$ option on a US Stock exchange (cents per Can$, payable on purchase of the option,contract size Can$ 50000) are as follows:

Strike Price (US$/Can$) Calls Puts

July Sep July Sep

0.93 1.56 2.56 0.88 1.75

0.94 1.02 NA NA NA

0.95 0.65 1.64 1.92 2.34

According to the suggestion of finance manager if option are to be used, one month option should be boughtat a strike price of 94 cents and three months option at a strike price of 95 cents and for the remainderuncovered by the options the firm would bear the risk itself. For this, it would use forward rate as the bestestimate of spot. Transaction cost are ignored. Recommended, which of the above two methods would beappropriate for the American firm to hedge its foreign exchange risk on the two interest payments.

12A.7 Breakeven Point for Call or Put OptionQ No Exam PM-J15 PM-J16 PM-J17 RTP

(a) Breakeven Point for Call Option = Strike Price + Premium Paid

(b) Breakeven Point for Put Option = Strike Price - Premium Paid

Question-14 [ICWA-D03]Current stock prices is Rs.100, strike price of call option Rs.100, option premium Rs.5. Find out break evenprice at which there will be no loss no profit for a call buyer.

12A.8 Calculation of Value of Option at beginning

(a) The value of option is the price at which it can be purchased or sold. Premium payable on option isalso known as value of option.

12A.9 Calculation of Value of Option at beginning by Expected Gain ApproachQ No Exam PM-J15 PM-J16 PM-J17 RTP

Calculation of Value of Option (TFVO) at Beginning

Expected Gain Approach Price Differencial Approach Binomial Model/RiskNeutralisation Method Black Scholes Model

Expected Gain Appraoch

Calculate Value of Option at expiration as given in Point 12A.4TVCO = Max[(Spot Price – Strike Price),0]TVPO = Max[(Strike Price – Spot Price),0]

If interest rate is Simple Coumpounding

TFVO today = Value of Option at expiration*PVF

If Interest Rate is Continuous Compounding

TFVO today = Value of Option at expiration*e-rt

Question-15***A six month call option for a share has the exercise price of Rs.38 along with probabilities and price atexpiration date as below:

Probabilities 0.10 0.25 0.30 0.25 0.10

Price of share 30 36 40 44 50

(a) What is the expected price of the share after six months? [Ans: Rs.40](b) What is the value of option at expiration? [Ans: Rs.3.30](c) What is the value of option at beginning assuming interest rate to be 12% p.a.? [Ans: Rs.3.11](d) What is the value of option at beginning assuming interest rate to be 12% p.a. continuously

compounding. [Ans: Rs.3.107]

12A.10 Calculation of Value of Option by Price Differential ApproachQ No Exam PM-J15 PM-J16 PM-J17 RTP

a) Under price differential approach, the value of option is taken as equal to difference between PV ofStrike Price and Spot Price on the valuation date.

Calculation of Value of Option under Price Differencetial Approach

TFVCO = Spot Price of UAtoday – PV of Strike Price TFVPO = PV of Strike Price - Spot Price of UAtoday

Whether Arbitrage Profit under PDA is possible or not

Call Option

If CMP of CO < TFVCO,then arbitrage profit is

possible

If CMP of CO > TFVCO,then arbitrage profit is not

possible

Put Option

If CMP of PO < TFVPO,then arbitrage profit is

possible

If CMP of PO > TFVPO,then arbitrage profit is not

possible

Steps for Arbitrage Profit

Call Option

Today1. Buy CO at CMP = a2. Assuming we have one Share, and sell it at CMP = b3. Investment (c) = (b – a) at interest rate given

At Maturity date4. Gain on Settlement of CO = (d)5. Purchase of Share from Market = (e)6. Realization of Investment (f) = (c)*(1+PIR) or (c)*ert

7. Arbitrage Profit = (d) + (f) – (e)

Put Option

Today1. Buy PO at CMP = a2. Buy one Share at CMP = b3. Borrow (c) = (a + b) at interest rate given

At Maturity Date4. Gain on Settlement of Put Option = (d)5. Sale of Share in Market = (e)6. Repayment of Borrowing (f) = (c)*(1+PIR) or (c)*ert

7. Arbitrage Profit = (d) + (e) – (f)

Question-16***Given the following data

Strike Price = Rs.90

Current stock Price = Rs.100

- Risk free rate of interest = 10% p.a. (not continuous compounding)

(a) Calculate theoretical current (fair) price of a European call option expiring after one year. [Ans:Rs.18.19]

(b) If the price of the call option is Rs.15, then how can arbitrageur make profit. [Ans: Min Arbitrage Profitis Rs.3.50]

Question-16A [SP]Given the following data

Current Price of one share = Rs.200

- Risk free rate of interest = 10% p.a. (Continuous compounding)

(a) Calculate theoretical current (fair) price of a European call option expiring after one year. [Ans:Rs.37.13]

(b) If price of the call option is Rs.30, then how can an arbitrageur make profit.

Question-17**Given the following data

Current stock Price = Rs.185

Time until expiration = 6 months.

- Risk free rate of interest = 5% p.a. (not continuous compounding)

(a) Calculate theoretical current (fair) price of a European put option expiring after six months.(b) If European put option price is Rs.5, then how can an arbitrageur make profit.

Question-17A [SP]Given the following dataStrike Price = Rs.400Current stock Price = Rs.370Time until expiration = 6 months- Risk free rate of interest = 5% p.a. (Continuous Compounding)

(a) Calculate theoretical current (fair) price of a European put option expiring after six months.

(b) If European put option price is Rs.10, then how can an arbitrageur make profit.

12A.11 Calculation of Value of Option by Binomial Model Tree or Risk NeutralisationMethodQ No Exam PM-J15 PM-J16 PM-J17 RTP

19 M11-1b-5 46 50 M13-16

19A M12-6a-8 43 46

20 N15-1c-5 47

21 M13-1c-5 42

26 M09-1a-8 45 49

a) Assumption of BM: CMP of the share is S and it can take two possible values at maturity, S1 or S2such that S1 > S > S2.

b) The investor can borrow or lend an amount (B) at risk free rate of interest 'r'

c) The strike price, K, is given

d) Hedge Ratio is known as delta. It refers to the number of units of stock one should hold for each optionsold to create a risk-free hedge.

e) The BM is based on the concept of Replicating Portfolio, which refers to a portfolio consisting of theunderlying asset and a riskless asset, which generates the same cash flow as a specified call/putoption.

Replicating Portfolio = Borrowing + Δ number of units of the underlying asset

Calculation of TFVCO under BM

Calculate Value of Option at expiration at S1

Calculate Hedge Ratio =

Calculate Borrowing

TFVCO under BM =

C1 = Max((S1-K),0)

C2 = Max((S2-K),0)

Δ = (C1 - C2) /(S1- S2)

Borrowing = Δ*S2/(1+r) OR (Δ*S1-nC1)/(1+r)

Δ*CMP of Share – Borrowing

Whether Arbitrage Profit under Binomial Model is possible or not

Call Option

If CMP of CO > TFVCO, then arbitrage profit is possible

Today1. Sell Call Option at CMPBuy Replicating Portfolio2. Buy Δ no of shares at CMP3. Borrow at interest rate given

At Maturity date4. Loss on settlement of Call option (Writer)Settlement of Replicating Portfolio5. Sell Δ no of shares at Market Price6. Repayment of Borrowing

If CMP of CO < TFVCO, then arbitrage profit is possible

Today1. Buy Call Option at CMPSell Replicating Portfolio2. Sell Δ no of shares at CMP3. Deposit at interest rate given

At maturity Date4. Gain on settlement of Call option (Holder)Settlement of Replicating Portfolio5. Buy Δ no of shares at Market Price6. Realisation of Deposit

Question-18***The CMP of share is Rs.50. It may be either Rs.60 or Rs.40 after a year. A call option with a strike price ofRs.50 is available. The rate of interest is 12%.(a) Calculate value of Call Option.(b) Show Holding Position after a year.

(c) If Actual price of Call Option is Rs.5 or Rs.8, whether arbitrage profit is possible under BM

Question-18A [CS-J04] [SP]The CMP of share of BB Ltd is Rs.190. It may be either Rs.250 or Rs.140 after a year. A call option with astrike price of Rs.180 is available. The rate of interest is 9%. Rahul wants to create a replicating portfolio inorder to maintain his pay off on the Call Option for 100 shares.Find out (i) Hedge ratio (ii) Amount of borrowing (iii) fair value of call (iv) his cash flow position after a year.

(f) Limitation of BM

Basic assumption that there are only two possibilities for share price in future is impractical andhypothetical. Such a strategy may not work because there are more and more possibilities of shareprice.

12A.11.1 Risk Neutralisation Method

(a) The current price of the share is S and it can take two possible values at maturity, S1 or S2 such thatS1 > S > S2.

Question-19 [M11-1b-5] [PM-J15-50] [PM-J15-46] [RTP-M13-16]***The CMP of an equity share of Pranchant Ltd Rs.420. Within a period of 3 months, the maximum andminimum price of it is expected to be Rs.500 and Rs.400 respectively. If the risk free rate of interest be 8%p.a. What should be the value of a 3 month call option under ‘Risk Neutral Method’ at the strike price ofRs.450. Given e0.02 = 1.0202

b) Calculation of Probability in alternative way

P1 for S1 = [SP x (1+r)/SP – LP/SP]/[HP/SP – LP/SP] = [1+r – d/u – d]

Where r = PIR; u = S1/S; d = S2/S

u = S1/S = 500/420 = 1.1904d = S2/S = 400/420 = 0.9523r = 0.05P1 = (ert – d)/(u – d) = (1.0202 – 0.9523)/(1.1904-0.9523) = 0.2851

Calculation of TFVO under RNM

Calculate Probability of S1 (P1) =

Calcualte Value of Option at expiration =

TFV of Option today =

(CMP of Share*(1+PIR) – S2)/(S1 – S2)

1 – P1

C1P1 + C2P2

Value of Option at expiration*PVF ORValue of Option at expiration* e-rt

Question-19A [M12-6a-8] [PM-J17-46] [PM-J15-43] [SP]Sumana wanted to buy shares of EIL which has a range of Rs.411 to Rs.592 a month later. The presentprice per share is Rs.421. Her broker informs her that the price of these shares can store up to Rs.522within a month, so she should buy a one month CALL of EIL. In order to be prudent in buying the call, theshare price should be more than or at least Rs.522 the assurance of which could not be given by her broker.Though she understands the uncertainly of the market, she wants to know the probability of attaining theshare price Rs.592 so that buying of a one month CALL of EIL at the executing price of Rs.522 is justified.Advice her. Take the risk free interest to be 3.60% and e0.036 =1.037.

Question–19B [SP]Find the value of one year European Call Option using:Spot Price = Rs.200; u = 1.4; d = 0.90; Exercise Price = Rs.220; r = 0.15Note: Value of u indicates possible higher price; value of d indicates possible lower price

Question-20 [N15-1c-5] [PM-J17-47]**Mr Dayal is interest in purchasing Equity Shares of ABC Ltd which are currently selling at Rs.600 each. Heexpects that price of share may go upto Rs.780 or may go down to Rs.480 in 3 months. The chances ofoccurring such variations are 60% and 40% respectively. A call option on the shares of ABC Ltd can beexercised at the end of 3 months with strike price of Rs.630.(i) What combination of share and option should Mr Dayal select if he wants a Perfect hedge?(ii) What should be the value of option today (Risk Free rate is 10% p.a.)?(iii) What is the expected Rate of Return on the option?

Question-21 [M13-1c-5] [PM-J15-42-CB]*Ramesh owns a plot of land on which he intends to construct apartment units for sale. No. of apartmentunits to be constructed may be either 10 or 15. Total construction costs for these alternatives are estimatedto be Rs.600 lakhs or Rs.1025 lakhs respectively. Current market price for each apartment unit is Rs.80lakhs. The market price after a year for apartment units will depend upon the conditions of market. If themarket is buoyant, each apartment unit will be sold for Rs.91 lakhs, if it is sluggish, the sale price for thesame will be Rs.75 lakhs. Determine the current value of vacant plot of land. Should Ramesh startconstruction now or keep the land vacant? The yearly rental per apartment unit is Rs.7 lakhs and the riskfree interest rate is 10% p.a.Assume that the construction cost will remain unchanged.

12A.11.2 Calculation of S1 or S2 if TFV of Option is givenQuestion-22 [SP]*Spot Price Rs.60. A one year European call Option is being quoted in the market at option premium of Rs.15with exercise price of Rs.55. Risk-free return = 12% p.a (NCC). The stock can either rise or fall after a year.It can fall by 30% by what % can it rise.

12A.11.3 Calculation of TFVPO under RNMQuestion-23**Spot price of Share Euro 500. After six months either 450 or 550. Find the value of European put opinionwith a strike price of Euro 510, if risk free rate is 14% p.a. Use Risk neutral method.

12A.11.4 Value of Option for foreign currency under RNM

a) In case of Foreign exchange transaction, interest rate is given for LHC and RHC.

b) P1 = (CMP of Share*(1+PIRHC) - S2*(1+PILHC))/(S1*(1+PILHC) - S2*(1+PILHC))

Question-24***From the following data calculate price of a call option expiring after one year:

Let spot exchange rate = Rs.50 per $

Strike rate = Rs.60 per $

Risk free interest rate for Rupees = 10% p.a.

Risk free interest rate for Dollars = 15% p.a.

Expected range of (Maximum and Minimum) spot rate on maturity of option afterone year

= Rs.70 - Rs.40 per$.

Question-24A [SP]From the following data calculate price of a call option expiring after one year.

Let spot exchange rate = Rs.60 per pound.

Exercise/Strike rate = Rs.64 per pound.

Risk free interest rate for Rupees = 15% p.a.

Risk free interest rate for pound = 20% p.a.

Expected range of (Maximum and Minimum) spot rate on maturity of optionafter one year

= Rs. 76.25 – Rs.45 perpound.

12A.11.5 Value of Option under BM or RNM if Dividend is paid

Question-25***The equity share of Madhav Ltd. is quoted at Rs.100 on spot. The company will pay a dividend of Rs.5 pershare after 2 months from today. After three months the price of the equity share will be either Rs.140 orRs.80. Assuming risk free rate of interest to be 12% p.a., find the option premium of three months ECOconsidering the risk strike to be Rs.110.

12A.11.6 Two Stage binomial method

In this case, we will apply movements of price for two periods.

(a) Calculation of 2 prices of UA at the end of 1st periodS1 = S*d1

S2 = S*u1

(b) Calculation of 4 prices of UA at the end of 2nd period as followsS3 = S*d1*d2 Or S1*d2

S4 = S*d1*u2 Or S1*u2

S5 = S*u1*d2 Or S2*d2

S6 = S* u1*u2 Or S2*u2

(c) Calculation of Probabilities for S1 and S2P1 = (S*(1+PIR) – S2)/(S1 – S2)P2 = 1 – P1

(d) Calculation of Probabilities for S3, S4 from S1 and Probabilities of S5, S6 from S2P3 = (S1*(1+PIR) – S4)/(S3 – S4)P4 = 1 – P3

P5 = (S2*(1+PIR) – S6)/(S5 – S6)P6 = 1 – P3

TFVO under BM/RNM if dividend is paid

TFVCO = Δ*(CMP of UA - PV of Dividend) – Borrowing

P1 = [CMP of UA*(1+PIR) - FV of Dividend] – S2)/(S1 – S2)

(e) Calculation of Join Probabilities S3, S4, S5, S6 from SJP1 of S3 = P1*P3

JP2 of S4 = P1*P4

JP3 of S5 = P2*P5

JP4 of S6 = P2*P6

(f) Calculate Value of Option at Maturity at S3, S4, S5 and S6

Expected value of ECO at maturity = JP1*S3 + JP2*S4 + JP3*S5 + JP4*S6

(g) TFV of Option today = PV of ECO at maturity

(h) Calculation of ACO (American Call Option)

Question-26 [M09-1a-8] [PM-J15-49] [PM-J15-45]***Consider a two year American call option with a strike price of Rs.50 on a stock the current price of which isalso Rs.50. Assume that there are two time periods of one year and in each year the stock price can moveup or down by equal percentage of 20%. The risk free interest rate is 6%. Using binominal option model,calculate the probability of price moving up and down. Also draw a two step binomial tree showing pricesand payoffs at each node.

Question-26A [SP]Current price of a share is Rs.100. Over each of next six months periods, it is expected to go up by 10% orto go down by 10%. Risk free rate is 8% p.a. cc. What is the value of 1 year ECO with a strike price ofRs.100. Use RNM.

Question-27 [SP]The equity share of Murari Ltd. is currently selling at Rs.100. Find the value of 6 months maturity putoption, strike price Rs.101, risk free rate of interest 12% p.a. Over 3 months period, it is expected to go upby 10% or go down by 10%. Over next 3 months period, it is expected to go up by 8% or go down by 6%.

12A.12 Black Scholes ModelsQ No Exam PM-J15 PM-J16 PM-J17 RTP

T-5 M15-7c-4 26

28 N06-4a-8 52 3 56

28A N08-1a-12 53 57

[T-5] [M15-7c-04] [PM-J17-56] [PM-J15-52] State any four assumptions of Black Scholes Model

(a) The Black-Scholes model is used to calculate a theoretical price of an Option.

Note K*e-rt*N(d2) represents this borrowing which is equivalent to the present value of the exercise pricetimes an adjustment factor of N(d2)

b) The market price of the share will go down after the payment of the dividend. The value of call optionwill decrease and the value of the put option will increase as more and more dividends are paid.

Basis and assumption for calculation of TFVO under BSM

It is based on 5 function

The model is based on thefollowing assumptions

1. CMP of Share (S)2. Strike Price (K)3. Time to expiry (t)4. Interest rate (r) = It is always Continues Compounding5. Volatility of the underlying assets (σ) = SD of continuously compounded return of the asset

1. The option is the European option;2. The underlying shares do not pay any dividend during the option period;3. There are no taxes and the transaction cost;4. Share prices move randomly in continuous time;5. The short term risk free interest rate is known and is constant during option period6. The short selling in share is permitted without penalty.

Steps for calculation of TFVO under BSM

Calculation d1

Calculate d2

Calculate N(d1) and N(d2) from Table

TFVCO =

TFVPO =

d1 = [In([S - PV of Dividend]/K) + (r + 0.5 σ2)t]/σ√tIn = Natural Log i.e. log to the base e.

d2 = d1 - σ√t

It represents the hedge ratio of shares to Options necessary to maintain a fully hedgeposition.

= (S - PV of Dividend)*N(d1) – K*e-rt xN(d2)

= K*e-rt *[1-N(d2)] – (S-PV of Dividend)*[1-N(d1)]

Question-28 [N06-4a-8] [PM-J17-56] [PM-J15-52] [ICWA – J07]***From the following data for certain stock, find the value of a call option:Price of stock now = Rs.80Exercise price = Rs.75Standard deviation of continuously compounded annual return = 0.40Maturity period = 6 monthsAnnual interest rate = 12%Givene0.12x0.5 = 1.062In 1.0667 = 0.0645

Question-28A [N08-1a-12] [PM-53] [SP]following information is available for X company and call option:

Current share price Rs.185

Option exercise price Rs.170

Risk free interest rate 7%

Time of the expiry of option 3 years

Standard deviation 0.18

Calculate the value of option using black scholes formula.

12A.12.1 The BSM and the dividend PaymentQuestion-29 [ICWA-D06]The share of E Ltd is trading at Rs.408 and the call option exercisable in three months time has an exerciseprice of Rs.400. SD is estimated to be 22% per year. The annualized Treasury Bill rate is 5%. The companyis going to declare a dividend of Rs.10 and is expected to be paid in two months time.What is the value of call option.

12A.12.2 Value of Put Option under BSMQuestion-30 [ICWA-D08] [SP]The share of A Ltd is trading at Rs.120 and the put option exercisable in three months time has an exerciseprice of Rs.112. SD is estimated to be 30% per year. The annualized Treasury Bill rate is 7%. What is thevalue of Put option.

12A.13 Different Type of Strategy for earning profit through OptionQ No Exam PM-J15 PM-J16 PM-J17 RTP

34 M09-4b-8 47 57

38A M12-7

By adopting following strategy, we may earn certain profit in option

12A.13.1 Strangle

a) Buy a put and a call option with the same expiration date but with different exercise prices

b) Strike Price of the Put (K1)< Strike Price of Call (K2)

c) Expiry date of Put = Expiry date of Call

d) On Maturity date

(i) CMP of UA > K2, Call Option will be exercised

(ii) CMP of UA < K1, Put Option will be exercised

(iii) K1 < CMP of UA < K2, both option will be lapsed

e) Strangle is purchased when there is strong move in the market which may be up or down.

Question-31What will be the payoff profile of a trader who adopts strangle strategy under following details:

Option Strike Price Premium

Put Rs.60 Rs.3

Call Rs.65 Rs.2

Question-32A person purchased a call with an exercise of Rs.190 at a premium of Rs.5. He also purchased a put with anexercise price of Rs.185 at a premium of Rs.6. Both the options have same expiration date. At what price(s) will the strangle break-even?

12A.13.2 Straddle

a) Buy/Sell a put and a call option with the same expiration date and same exercise prices

b) Strike Price of the Put (K) = Strike Price of Call (K)

c) Exercise price of Put = Exercise Price of Call

c) On Maturity date

(i) CMP of UA > K, Call Option will be exercised

(ii) CMP of UA < K, Put Option will be exercised

(iii) CMP of UA = K, both option will be lapsed

d) Straddle is purchased/sold when there is strong move in the market which may be up or down.

Question-33Equity shares of Casio Ltd. are being currently sold for Rs.90 per share. Both the call option and the putoption for a 3 month period are available for a strike price of Rs.97 at a premium of Rs.3 per share and Rs.2per share respectively. An investor wants to create a straddle position in this share. Find out his net payoffat the expiration of the option period; if the share price on that day happens to be Rs.90 or Rs.105 orRs.97.

Question-33AMr.X purchased 3-months call as well 3-months put, both at strike price of CHF 75. Premium of Call CHF 3:Premium of put- CHF 2. Prepare a table and draw a graph to show pay-offs of Mr. X if expiration prices are60,65,70,71,72,73,74,…..80,85, or 90. Do the same exercise for Y as well. Find whether the maximumamount of loss to Mr. X is equal to call premium plus put premium.

Question-34 [M09-4b-8] [PM-J17-57-FOREX] [PM-J15-47-FOREX]On 19h April following are the spot ratesSpot rate Euro 1 = $1.20; $ 1 = Rs.44.80Following are the quotes of European Options:

Currency Pair Call/Put Strike Price Premium Expiry Date

EUR/USD Call 1.20 $0.035 July 19

EUR/USD Put 1.20 $0.04 July 19

USD/INR Call 44.80 Rs.0.12 Sep.19

USD/INR Put 44.80 Rs.0.04 Sep.19

(a) A trader sells an at-the-money spot straddle expiring at three months (July 19). Calculate gain or loss ifthree months later the spot rate is Euro 1 = $1.2900

(b) Which strategy gives a profit to the dealer if five months later (Sep. 19) expected spot rate is $1 =Rs.45.00. Also calculate profit for a transaction USD 1.5 million.

12A.13.3 Strips

i) Buy one Call + Buy 2 Puts all with the same exercise price and date of expiration.

ii) Strike Price of the Put (K) = Strike Price of Call (K)

iii) Expiry Date of Call = Expiry date of Put

iv) On Maturity date

(1) CMP of UA > K, Call Option will be exercised

(2) CMP of UA < K, 2 Put Option will be exercised

(3) CMP of UA = K, both option will be lapsed

Strips is purchased when investor feels that decrease in the stock price is more likely than an increase.

Question-35Mr. A purchases a call of 1 shares of A Ltd with 3 months expiration at a strike price of Rs.60. Call PremiumRs.1 per share. At the same time he purchases put of 2 shares of same company with same expiration,same strike price, same option premium per share. Find his pay off if the spot price on maturity is 55, 56,….65.

12A.13.4 Straps

a) Buy 2 Call + Buy 1 Puts all with the same exercise price and date of expiration.

b) Strike Price of the Put (K) = Strike Price of Call (K)

c) Expiry Date of Call = Expiry date of Put

d) On Maturity date

(i) CMP of UA > K, 2 Call Option will be exercised

(ii) CMP of UA < K, 1 Put Option will be exercised

(iii) CMP of UA = K, both option will be lapsed

Strap is purchased when investor feels that increase in the stock price is more likely than decrease.

12A.13.5 Butter Flies

a) It involves positions in options with three different strikes prices.

b) Buying a Call at relatively low strike price = K1Buying a Call at relatively High strike price = K2Selling 2 Calls at average of K1 and K2 [K3 = (K1+K2)/2]

c) Expiry Date of all Calls are equal

d) It is adopted by those who expect insignificant movements in the market price.

e) This strategy has limited risk and limited profit.

f) A butterfly can be created using put option

Question-36Current Spot Price of Share Rs.61. Call options in the market:

Strike price Premium

Rs.55 Rs.10

Rs.60 Rs.7

Rs.65 Rs.5

Mr. X buys one call at strike price 55 and one call at strike price 65. He sells 2 calls with strike price 60.Give pay-offs if spot price on expiry on 51, 52…70

12A.13.6 Condor Spread

a) It is similar to the butterfly spread but involves 4 strike prices instead of 3 strike prices, resulting in awinder profitable range. The strategy can be either call based or put based (but never with calls andputs used together in the same trade).

b) Buying 1 Call Option with K1 < SSelling 1 Call Option with K = SSelling 1 Call Option with K2 > SBuying 1 Call Option K3 > K2

c) Expiry Date of all Calls are equal

d) This strategy is adopted by those operators who expect insignificant movements in the market price ofunderlying asset. This strategy may result in small amount of profit with limited loss.

Question-37Suppose spot price is Rs.100

A) Buy call at a strike price of Rs.97 Call premium Rs.2 per share

B) Sell call at a strike price of Rs.100 Call premium Rs.1.50 per share

C) Sell call at a strike price of Rs.102 Call premium Rs.1 per share

D) Buy call at a strike price of Rs.103 Call premium Rs.0.70 per share

12A.13.7 BULL SPREADS

(a) Bull Spread This strategy is used by those who expect that the market price of the underlying assetwill go up. This trading strategy can be accomplished with either puts or calls.

(b) Bull Call Spread

(i) Buy 1 Call at K1 + Sell 1 Call at K2 with the same date of expiration.

(ii) K1 < K2

Question-38Call market data

Strike price Call premium

Note: Lower the strike price, higher the call premium.100 5

Question-38A [RTP-M12-7]The current spot price of share of ABC Ltd is Rs.121 with strike price of Rs.125 and Rs.130 are trading at apremium of Rs.3.30 and Rs.1.80 respectively. Mr X a speculator is bullish about the share price over nextsix months. However, he is also of belief that share price could also go down. He approaches to you foradvice, you are required to:(a) Suggest a strategy that Mr X can adopt which puts limit on his gain and loss.(b) How much is maximum possible profit.(c) Draw out a rough diagram of the strategy adopted.(d) What will be break-even price of the share?[Assume – No brokerage fees and interest cost/gains]

(c) Bull Put Spread

(i) Buy 1 Put at K1 + Sell 1 Put at K2 with the same date of expiration.

(ii) K1 < K2

(iii) The options trader employing this strategy hopes that the price of the underlying securities goes up

Question-39 Put market data

Strike price Put premium

Note: Lower the strike price, lower the put premium.105 1

115 10

12A.13.8 Bear spread

(a) It is entered by the operators who expect that the prices of underlying asset will decline.

(b) Bear Call Spread

(i) Buy 1 Call at K1 + Sell 1 Call at K2 with the same date of expiration.

(ii) K1 > K2

Question-40 Call market data

Strike price Call premium

Note: Lower the strike price, higher the call premium.95 8

(c) Bear Put Spread

(i) Buy 1 Put at K1 + Sell 1 Put at K2 with the same date of expiration.

(ii) K1 > K2

Question-41 Put market data

Strike price Put premium

Note: Lower the strike price, higher the put premium.95 2

12A.13.9 CALENDER SPREAD

(a) Bull calendar spread- The strategy is used by those who expect a bullish tendency in the prices. Inthis strategy the options have the same strike price but different dates of maturities. The strategy canbe either call based or put based (but never with calls and puts used together in the same trade.)

(b) Call based strategy:, the operator buys call which long maturity period and sells the call with shortmaturity period on the same underlying asset with same strike price. Generally the option premium ofthe long term call is more than of short term call; the strategy generally requires an initial investment.

(i) Buy 1 Call at K + Sell 1 Call at K with different date of expiration.

(ii) Maturity Period of Call 1 > Maturity Period of Call 2

Example: Spot price of a share is Rs.40. Mr. X purchases call option maturity 3 months at a premium ofRs.2 per share strike price Rs.45. He writes a call maturity 1 month at a premium of Re. 1 per share strikeprice Rs.45. The net cost of the strategy Re.1. Suppose the spot price on one month maturity call is Rs.42.The call is not exercised. Mr. X does not have to pay anything. Now suppose the spot price on the 3 monthsmaturity call is Rs.47. Net profit Re.1 per share.

(c) A bear calendar Spread is used by option traders who believe that the price of the underlyingsecurity will remain stable in the near term but will eventually fall in the long term. In this case, theoperator buys put with long maturity period and sells the put with short maturity period on the sameunderlying asset with same strike price.

(i) Buy 1 Put at K + Sell 1 Put at K with different date of expiration.

(ii) Maturity Period of Put 1 > Maturity Period of Put 2

Summary of above StrategiesSl Strategies Option Option Maturity Date Strike Price

1 Strangle Buy 1 Call Buy 1 Put Same K of the Put < K of Call

2 Straddle Buy 1 Call Buy 1 Put Same K of the Put = K of Call

3 Strips Buy 1 Call Buy 2 Put Same K of the Put = K of Call

4 Straps Buy 2 Call Buy 1 Put Same K of the Put = K of Call

5 Butter Flies Buy 1 Call at K1Buy 1 Call at K2

Sell 2 Call at K3 Same K1 > K2 andK3 = (K1+K2)/2

6 Condor Spread Buy 1 Call at K1Buy 1 Call at K3

Sell 1 Call at KSell 1 Call at K2

Same K1 < S; K = SK2 > S; K3 > K2

7 Bull Call Spread Buy 1 Call at K1 Sell 1 Call at K2 Same K1 < K2

8 Bear Call Spread Buy 1 Call at K1 Sell 1 Call at K2 Same K1 > K2

9 Bull Put Spread Buy 1 Put at K1 Sell 1 Put at K2 Same K1 < K2

10 Bear Put Spread Buy 1 Put at K1 Sell 1 Put at K2 Same K1 > K2

11 Bull Calendar Spread Buy 1 Call1 at K Sell 1 Call1 at K MP of Call1 > MP of Call2 Same

12 Bear Calendar Spread Buy 1 Put1 at K Sell 1 Put1 at K MP of Put1 > MP of Put2 Same

12A.14 TheoryQ No Exam PM-J15 PM-J16 PM-J17 RTP

T-6 N04-5c-4, M06-2b-4

[T-6] [N04-5c-4] Explain the term ‘intrinsic value of an option’ and the ‘time value of an option.[M06-2b-4] Distinguish between Intrinsic value and time value of an option.

(a) Intrinsic value is the value that any given option would have if it were exercised today.

Intrinsic Value of an Option at any dayIntrinsic value of Call option (to Holder) at expiration = Max [(Spot Price - Strike Price), or 0]Intrinsic value of put option (to Holder) at expiration = Max [(Strike Price - Spot Price), or 0]

(b) Time Value: This is the second component of an option’s price. It is defined as any value of an optionother than the intrinsic value. From the above example, if Wipro is trading at Rs.105 and the Wipro100 call option is trading at Rs.7, then we would conclude that this option has Rs.2 of time value (Rs.7option price – Rs.5 intrinsic value = Rs.2 time value). Options that have zero intrinsic value are

comprised entirely of time value.Time value is basically the risk premium that the seller requires to provide the option buyer with theright to buy/sell the stock upto the expiration date. This component may be regarded as the Insurancepremium of the option. This is also known as “Extrinsic value.” Time value decays over time.

12A.15 Compounding concepts of Interest

1 Calculation of PV of any shares, Bonds etc. from FV, if interest rate is compounding yearly

PV = FV/(1+PIR)

PV = FV*PVF(1 Period, PIR)

PIR is interest rate of 1 period

Example-1FV of Share at the end of 6 months =Rs.110Period = 6 monthsInterest Rate = 12% p.a. [Compounding Yearly]PIR of 6 months = 6%PV of Share at t0 = FV/(1+PIR of 6 months) = 110/1.06 = Rs.103.77 ORPV of Share at t0 = FV*PVF(1 Period, 6%) = Rs.110*0.943 = Rs.103.73

2 Calculation of PV of any shares, Bonds etc. from FV, if interest rate is compounding periodically

Period, Future Value and Interest Rate should be given with period of compounding

PV = FV/(1+PIR)n

PV = FV*PVF(n Period, PIR)

PIR is interest rate for each compounding period

n = No of Compounding in Period Given

Example-2FV of Share at the end of 6 months =Rs.110Period = 6 monthsInterest Rate = 12% p.a. [Compounding Half Yearly, Quarterly, Monnthly]

Compounding Half yearly Quarterly Monthly

PIR 6% for 6 months 3% for 3 months 1% for 1 month

No of Compounding in Year 1 2 6

PV of Share at t0 FV/(1+PIR of 6 months)n FV/(1+PIR of 3 months)n FV/(1+PIR of 1 months)n

PV of Share at t0 Rs.110/1.06 110/(1.03)2 110/(1.01)6

PV of Share at t0 Rs.103.77 Rs.103.68 Rs.103.625

Alternative

PV of Share at t0 FV*PVF(1 Period, 6%) FV*PVF(2 Period, 3%) FV*PVF(6 Period, 1%)

PV of Share at t0 Rs.110*0.943 Rs.110*0.9425 Rs.110*0.9420

PV of Share at t0 Rs.103.73 Rs.103.675 Rs.103.62

4 Calculation of PV of any shares, Bonds etc. from FV, if interest rate is compounding continuously

Period, Future Value and Interest Rate should be given

PV = FV/ert

PV = FV*e-rt

t = Period in Months /12 or Period in days/365

Example-3FV of Share at the end of 6 months =Rs.110Period = 6 monthsInterest Rate (r) = 12% p.a. [Continuously Compounding]t = 6/12 = 0.5 yearsPV of Share at t0 = FV/ert = 110/e0.12*0.5 = Rs.110/e0.06 = Rs.110/1.0618 = Rs.103.5977 ORPV of Share at t0 = FV*e-rt = Rs.110*e-0.12*0.5 = Rs.110*e-0.06 = Rs.110*0.9417 = Rs.103.587

5 Calculation of FV of any shares, Bonds etc. from PV, if interest rate is compounding yearly

Period, Current Value and Interest Rate should be given

FV = CV*(1+PIR)

FV = CV/PVF(1 Period, PIR)

PIR is interest rate of 1 period

Example-4CV of Share = Rs.105Period = 6 monthsInterest Rate = 12% p.a. [Compounding Yearly]PIR of 6 months = 6%FV of Share at end of 6 months = CV*(1+PIR of 6 months) = 105*1.06 = Rs.111.30 ORFV of Share at end of 6 months = CV/FVF(1 Period, 6%) = Rs.105/0.9433 = Rs.111.31

6 Calculation of FV of any shares, Bonds etc. from CV, if interest rate is compounding periodically

Period, Current Value and Interest Rate should be given with period of compounding

FV = CV*(1+PIR)n

FV = CV/PVF(n Period, PIR)

PIR is interest rate for each compounding period

n = No of Compounding in Period Given

Example-5CV of Share = Rs.105Period = 6 monthsInterest Rate = 12% p.a. [Compounding Half Yearly, Quarterly, Monthly]

Compounding Half yearly Quarterly Monthly

PIR 6% for 6 months 3% for 3 months 1% for 1 month

No of Compounding in Year 1 2 6

FV of Share at six months CV*(1+PIR of 6 months)n CV*(1+PIR of 3 months)n CV*(1+PIR of 1 months)n

FV of Share at six months Rs.105*1.06 105*(1.03)2 105*(1.01)6

FV of Share at six months Rs.111.30 Rs.111.39 Rs.111.45

Alternative

FV of Share at six months CV/PVF(1 Period, 6%) CV/PVF(2 Period, 3%) CV/PVF(6 Period, 1%)

FV of Share at six months Rs.105/0.943 Rs.105/0.9425 Rs.105/0.9420

FV of Share at six months Rs.111.31 Rs.111.40 Rs.111.465

7 Calculation of FV of any shares, Bonds etc. from CV, if interest rate is compounding continuously

Period, Future Value and Interest Rate should be given

FV = CV*ert

FV = CV/e-rt

t = Period in Months /12 or Period in days/365

Example-6CV of Share = Rs.105Period = 6 monthsInterest Rate (r) = 12% p.a. [Continuously Compounding]t = 6/12 = 0.5 yearsFV of Share at end of 6 months = CV*ert = 105*e0.12*0.5 = Rs.105*e0.06 = Rs.105*1.0618 = Rs.111.489ORFV of Share at end of 6 months = CV/e-rt = Rs.105/e-0.12*0.5 = Rs.105/e-0.06 = Rs.105/0.9417 = Rs.111.5005

Summary of above

Particulars Calculation of PV Calculation of FV

IR is Compounding Yearly PV = FV/(1+PIR) FV = CV*(1+PIR)

PV = FV*PVF(1 Period, PIR) FV = CV/PVF(1 Period, PIR)

IR is Compounding Periodically PV = FV/(1+PIR)n FV = CV*(1+PIR)n

PV = FV*PVF(n Period, PIR) FV = CV/PVF(n Period, PIR)

IR is Continuously Compounding PV = FV/ert FV = CV*ert

PV = FV*e-rt FV = CV/e-rt

CHAPTER-12A OPTION DERIVATIVE - SOLUTION 12A_B.1

Solution-1Call Option

Share price on the exercise date Rs.200 Rs.210 Rs.220 Rs.230 Rs.240

Strike Price of call Option Rs.220 Rs.220 Rs.220 Rs.220 Rs.220

Where from Holder should buy shares [Lower] From Market From Market From Market From Writer From Writer

Whether Holder would exercise Call option No No No Yes Yes

(a) Purchase of Share to Holder Rs.200 Rs.210 Rs.220 Rs.220 Rs.220

(b) Gain to Holder due to Call Option 0 0 0 Rs.10 Rs.20

Maximum loss to Holder is premium paid -Rs.6 -Rs.6 -Rs.6 -Rs.6 -Rs.6

(c) Net Gain or (Loss) to Holder -Rs.6 - Rs.6 - Rs.6 Rs.4 Rs.14

(d) Status of Option Out Out At In In

Put Option

Share price on the exercise date Rs.200 Rs.210 Rs.220 Rs.230 Rs.240

Strike Price Rs.220 Rs.220 Rs.220 Rs.220 Rs.220

Where should holder sell shares [Higher] To Writer To Writer To Market To Market To Market

Whether holder would exercise Put option Yes Yes No No No

(a) Sale Price of Share to Holder Rs.220 Rs.220 Rs.220 Rs.230 Rs.240

(b) Gain to Holder due to Put Option Rs.20 Rs.10 0 0 0

Maximum loss to Holder is premium paid -Rs.5 -Rs.5 -Rs.5 -Rs.5 -Rs.5

(c) Net Gain or (Loss) to Holder Rs.15 Rs.5 - Rs.5 - Rs.5 - Rs.5

(d) Status of Option In In At Out Out

(ii) price range at which the call and the put options may be gainfully exercised.In case of Call Option, If Share Price on exercise date is more than Rs.220In case of Put Option, If Share Price on exercise date is Less than Rs.220

Solution-1APremium of call option = Rs.9Premium of put option = Rs.1

(i) Expiration date cash flows [Means purchase price or sale price on Exercise of Option]

Stock prices Rs.50 Rs.55 Rs.60 Rs.65 Rs.70

Buy 1 Call [Purchase price for Holder on Exercise of Call Option i.e [Lower] 0 0 0 Rs.60 Rs.60

Write 1 Call [Sale price for Writer on Exercise of Call Option by Holder] 0 0 0 Rs.60 Rs.60

Buy 1 Put [Sale price for Holder on Exercise of Put Option] [Higher] Rs.60 Rs.60 0 0 0

Write 1 Put [Purchase price for writer on Exercise of Put Option] Rs.60 Rs.60 0 0 0

(ii) Investment value = Expiration value of Option = Gain on exercise of Option

Buy 1 Call [Gain to Holder of Call Option] = Value of Call Option 0 0 0 5 10

Write 1 Call [Loss to Writer of Call Option] 0 0 0 -5 -10

Buy 1 Put [Gain to Holder of Put Option] = Value of Put Option 10 5 0 0 0

Write 1 Put [Loss to Writer of Put Option] -10 -5 0 0 0

(iii) Calculation of net profit/ Loss

Buy 1 call [Gain/(Loss) – Premium Paid] -9 -9 -9 -4 1

Write 1 call [Gain/(Loss) – Premium Paid] 9 9 9 4 -1

Buy 1 put [Gain/(Loss) – Premium Paid] 9 4 -1 -1 -1

Write 1 put [Gain/(Loss) – Premium Paid] -9 -4 1 1 1

Solution-2(a) If share price goes to Rs.43 at expiry

Particulars Call Option Put Option Total

Investor Buy 1 1

Premium Paid Rs.2 Rs.1 Rs.3

Strike Price Rs.42 Rs.40

If market Price of share at expiry Rs.43 Rs.43

Exercise of Option Yes No

Value of Option Rs.1 Nil

Gain 1 0 1

Premium Paid -2 -1 -3

Net Gain/ (Loss) -1 -1 -2

(c) If share price goes to Rs.36 at expiry

Investor Buy 1 1

Exercise of Option No Yes

Value of Option 0 4

Gain 0 4 4

Net Gain/ (Loss) -2 3 1

This can be done with 100 shares

Solution-2A(a) If share price goes to Rs.53 at expiry

Investor Buy 1 1

Exercise of Option Yes No

Value of Option Rs.1 Nil

Gain 1 0 1

No of Shares 50 50

Total -50 -50 -100

(c) If share price goes to Rs.36 at expiry

Investor Buy 1 1

Value of Option 0 4

Gain 0 4 4

Net Gain/ (Loss) -2 3 1

No of Share 50 50

Total Gain/(Loss) -100 +150 50

This can be done with 100 shares

Solution-2B(a) If share price = Rs.500 at expiry

Mr X Buy 1 1

Premium Paid Rs.30 Rs.5

No of Shares in One Option 100 100

Total Premium Paid Rs.3000 Rs.500 Rs.3500

Exercise of Option by Mr X No No

Value of Option 0 0

Gain 0 0 0

Premium Paid - 3000 - 500 - 3500

Net Gain/ (Loss) - 3000 - 500 - 3500

(b) If share price = Rs.350 at expiry

Mr X Buy 1 1

Exercise of Option by Mr X No Yes

Value of Option 0 100*100 = Rs.10000 Rs.10000

Gain 0 10000 10000

Premium Paid - 3000 - 500 - 3500

Net Gain/ (Loss) - 3000 9500 6500

(c) If share price = Rs.600 at expiry

Mr X Buy 1 1

Exercise of Option by Mr X Yes No

Value of Option Rs.50*100 = Rs.5000 0

Gain 5000 0 5000

Premium Paid - 3000 - 500 - 3500

Net Gain/ (Loss) 2000 -500 1500

Solution-2C(a) If share price goes to Rs.350 at expiry

Particulars Call Option Put Option Share Total

Investor Buy 1 for 100 shares 1 for 100 shares

Premium Paid Rs.30*100 Rs.5*100 Rs.3500

Value of Option 0 100*100 = 10000 10000

Gain 0 10000 10000

Premium Paid 3000 500 3500

Net Gain/ (Loss) -3000 9500 6500

Solution-3(a) If share price = Rs.1550 at expiry

Particulars Call 1400 Option Call 1425 Option Put 1350 Option Total

Investor Buy 200 3000 4000

Premium Paid Rs.50*200 = 10000 Rs.33*3000 = 99000 Rs.22*4000 = 88000 197000

Strike Price Rs.1400 Rs.1425 Rs.1350

Expiry Date Dec, 2010 Dec, 2010 Dec, 2010

If market Price of share at Expiry Rs.1550 Rs.1550 Rs.1550

Exercise of Option by Holder Yes Yes No

Value of Option 150*200 = 30000 125*3000 = 375000 0 405000

Gain 30000 375000 0 405000

Premium Paid -10000 -99000 -88000 -197000

Net Gain/ (Loss) 20000 276000 -88000 208000

(b) If share price = Rs.1460 at expiry

Particulars Call Option Call Option Put Option Total

Exercise of Option by Holder Yes Yes No

Value of Option 60*200 = 12000 35*3000 = 105000 0 117000

Gain 12000 105000 0 117000

Premium Paid -10000 -99000 -88000 -197000

Net Gain/ (Loss) 2000 6000 -88000 -80000

(c) If share price = Rs.1280 at expiry

Particulars Call Option Call Option Put Option Total

Exercise of Option by Holder No No Yes

Value of Option 0 0 70*4000 = 280000 280000

Gain 0 0 280000 280000

Premium Paid -10000 -99000 -88000 -197000

Net Gain/ (Loss) -10000 -99000 192000 83000

Solution-4(a) Expected price of share at expiry date = 120*0.05 + 140*0.2+160*0.5+180*0.1+190*0.15 = Rs.160.50

(b) If price of shares is equal to exercise price i.e. Rs.150 prevails on expiration date than the value of call option atexpiration= Max [(Spot Price of ShareAt Expiry – Strike Price), 0] = [(150–150),0] = Rs.0

(c) Expected value of option at expiration

MKT price at expiration Exercise price (MP – EP) Value of Option Prob. Expected value of Option

120 150 120 – 150 = -30 0 0.05 0

140 150 140 – 150 = -10 0 0.20 0

160 150 160 – 150 = 10 10 0.50 5

180 150 180 – 150 = 30 30 0.10 3

190 150 190 – 150 = 40 40 0.15 6

Expected value of option 14

Solution-4A(a) Expected price of share at expiry date = 180*0.1 + 260*0.2 + 280*0.5 + 320*0.1 + 400*0.1 = Rs.282

(b) Expected value of put option at expiration

Share Price Strike Price Value of Put Option Prob Expected Value of Option

180 300 120 0.1 12

260 300 40 0.2 8

280 300 20 0.5 10

320 300 0 0.1 0

400 300 0 0.1 0

Expected Value of Put Option at expiration = Rs.30

Solution-5(a) Premium on Nov call is less than premium on Jan Call because of 2 reasons(i) Greater the time to expiration, premium would be more. Time period of Jan Call is more than Nov call hence Premiumof Jan Call is more than Nov Call.(ii) In case of Call Option, lower the strike price of option, option premium would be more. In case of Jan Call, Strike priceis less than Nov call hence premium of Jan Call is more than Nov Call.

(b)(i) Position of Holder of Jan Call 450Exercise price of Jan Call = Rs.450Premium paid = Rs.100On expiration date 31/01/2003 the mkt. price is 525. It is more than the exercise price. Hence, the Holder of Call Optionwould exercise the call option.Value of option to Holder = Market Price of Share – Exercise Price = 525 – 450 = Rs.75Premium paid by Holder of Call option = Rs.100Net gain/(Loss) to Buyer = Rs.75 – Rs.100 = - Rs.25

(ii) Tax Status of Writer from Jan Call

Loss to Writer on settlement of Jan Call - Rs.75

Premium received by Writer + Rs.100

Net Gain to Writer on Settlement of Jan + Rs.25

Profit/ Loss on Sale of Shares

Sale Price of Share at Market + Rs.525

Less: Purchase of Share Rs.475

Profit on Sale of Shares + Rs.50

Total Profit to Writer = Gain on Settlement of Option + Profit on sale of Share = Rs.25 + Rs.50 = Rs.75

(c) If we does not own any shares

Particulars Nov Call (550) Nov Call (500) Total

Position Write Hold

Premium +10 -50 -40

Exercise of Option by Holder Yes Yes

Gain/Loss -25 +75

Premium +10 -50 -40

Net Gain/ (Loss) -15 +25 +10

Period of investment = July to Nov = 5 months% Annualized Return = Profit*100/Initial Investment = 10*100/40x12/5 =60%

Solution-6Alternative 1: For Hedging of sale price, he is writing Call OptionManager writes call option means he is writer of call Option. He is under obligation to sell shares. [For Understanding]Calculation of Profit & loss on Call Option from Writers Point of View

Share price on the exercise date Rs.560 Rs.540 Rs.525 Rs.490

Strike Price of call Option Rs.530 Rs.530 Rs.530 Rs.530

Where from Holder should buy shares [Lower of Two] From Writer From Writer From Market From Market

Exercise of Call option by Holder Yes Yes No No

Purchase price for Holder in case of deliver Rs.530 Rs.530 Rs.525 Rs.490

Sale price for Writer Rs.530 Rs.530 Rs.525 Rs.490

Purchase price for Writer Rs.510 Rs.510 Rs.510 Rs.510

Gain/(Loss) to Writer Rs.20 Rs.20 Rs.15 -Rs.20

Premium received by Writer Rs.10 Rs.10 Rs.10 Rs.10

Net Gain or (Loss) to Writer Rs.30 Rs.30 Rs.25 -Rs.10

Conclusion: Selling a call option for hedging of sale price is not proper strategy as by doing this, upper limit of sale priceis fixed but lower limit is not fixed.

Alternative 2: Buying Put Option for hedging of sale price

Manager purchased put option means he is holder of put Option. He has right to sell the shares. [For Understanding]

Share price of share on the exercise date Rs.560 Rs.540 Rs.525 Rs.490

Strike Price of Put Option Rs.530 Rs.530 Rs.530 Rs.530

Where should holder sell shares [higher of two] Market Market Writer Writer

Exercise of put option by holder No No Yes Yes

Sale price for manger Rs.560 Rs.540 Rs.530 Rs.530

Purchase price for manager Rs.510 Rs.510 Rs.510 Rs.510

Gian/(Loss) to manager Rs.50 Rs.30 Rs.20 Rs.20

Premium Paid by manager Rs.10 Rs.10 Rs.10 Rs.10

Net Gain or (Loss) to Manager Rs.40 Rs.20 Rs.10 Rs.10

Conclusion: buying a put option for hedging of sale price is proper strategy as by doing this, lower limit of sale price isfixed but upper limit is not fixed.

(b) Buying a share and writing a call does not protect investor from risk as by writing a call investor has fixed upper limitof sale price but lower limit is not fixed. Hence he has fixed his profit and did not fix loss.

(c) Put option can be purchased for hedging selling price of underlying assets in future.

Solution-7 UK exporter is to receive $10000 in 3 months. [$ - Sell; £ - Buy]We will check that LHC is to be sold or purchased.If LHC is to be sold then we should buy Put Option for hedgingIf LHC is to be purchased then we should buy Call Option for hedgingCase-1 Strike Rate £ 1 = $ 1.5LHC is £ i.e. to be purchased, hence UK Exporter will buy call Option at Strike Rate £ 1 = $ 1.5 for hedging of purchaseprice of £On maturity date

SR of £ on maturity date $ 1.7 $ 1.3

Strike Rate of Call Option $ 1.5 $ 1.5

Where should holder buy £ [Lower of two] Writer Market

Exercise of Call option by holder Yes No

Purchase price of £ $ 1.5 $ 1.3

£ receivable by selling $ 10000 = $ 10000/1.5 = £ 6667 $ 10000/1.3 = £ 7692

Case-2 Strike Rate $ 1 = £ 0.667LHC is $ i.e. to be sold, hence UK Exporter will buy put Option at Strike Rate $ 1 = £ 0.667 for hedging of sale price of $On maturity date

SR of $ on maturity date £ 0.6 £ 0.8

Strike Rate of Put Option £ 0.6667 £ 0.667

Where should holder sell $ [Higher of two] Writer Market

Exercise of Put option by holder Yes No

Sale price of $ £ 0.6667 £ 0.8

£ receivable by selling $ 10000 = $ 10000*0.6667 = £ 6667 $ 10000*0.8 = £ 8000

Solution-8XYZ is to pay JY 500000 in 3 months [JY – Buy; Rs.-Sell]SR Rs. 1 = JY 1.9516 – 1.97113 months FR Rs. 1 = JY 1.9726 – 1.9923(a) Hedging through Forward CoverRs. required to buy JY 500000 at 3months FR = JY 500000/1.9726 = Rs.253472.60

(b) Hedging through OptionStrike Rate Rs. 1 = JY 2.125 [LHC-Rs.-Sell- buy put Option]For hedging, XYZ will buy put option at Strike Rate Rs. 1 = JY 2.125 for hedging of sale price of Rs.No of Put Option to be purchased = JY500000/2.125 = 235295Premium payable = 235295*0.098 = JY 23059Rs. required to pay Premium = JY 23059/1.9516 = Rs.11815On maturity dateAssuming Put option is exercisable, henceRs. required to buy JY 500000 at Strike Rate = JY 500000/2.125 = Rs.235295Total payment under Put Option = 235295+11815 = Rs.247110

Conclusion: Hedging through Put option is better

Solution-9$100 m is receivable and it is to be sold by Company [$ - Sell; Rs. – Buy]Option 1 No HedgingIf Put option is not purchasedExpected exchange rate after 3 months = 35*0.20 + 35.50*0.30 + 36*0.30 + 36.50*0.20 = 35.75Expected exchange rate after 3 month $ 1 = Rs.35.75Amt receivable in $ = $100 mAmt receivable in Rs. = $100*35.75 = Rs.3575 m

Option 2 Hedging through put OptionStrike Rate = $1 = Rs.37 [LHC-$-Sell-Buy Put Option]

Put option is purchased for sell of $ 100 m at strike Rate $ 1 = Rs.37Premium paid = $ 1 = Rs.1On Expiry Date

Exchange rateafter 3 months

Strike Rate $ shouldbe sold

Sale price of $ PremiumPaid

Net Sale price Prob Net Sale Rate

$1 = Rs.35.00 $1 = Rs.37.00 To Writer $1 = Rs.37.00 $1 = Rs.1 $1 = Rs.36.00 0.20 7.20

$1 =Rs.36.00

Amt receivable in $ = $100 mAmt receivable in Rs. = $100*36 = Rs.3600 mConclusion: We should purchase put option.

Solution-10(c) Hedging through call optionXYZ is to pay £ 300000 in 180 days [$ - Sell and £ - Buy][£ is LHC and it is to be purchased, hence for hedging of purchase price, we should buy Call option]

Strike rate of Call Option = £ 1 = $ 1.97; Premium on Call Option £ 1 = $ 0.04

Expected Spot ratein 180 days

StrikeRate

Exercise ofCall Option

Purchase Rate(Delivery)

Prempaid

Total Purchaseper unit

Prob. ExpectedPurchase Rate

1.91 1.97 No 1.91 0.04 1.95 0.25 0.4875

1.95 1.97 No 1.95 0.04 1.99 0.60 1.194

2.05 1.97 Yes 1.97 0.04 2.01 0.15 0.3015

£ 1 = 1.983

$ required to buy £3,00,000 at Expected purchase rate = £3,00,000*1.983 = $594900

Solution-11Strike Rate GBP 1 = USD 1.70 [USD-RHC–Buy; GBP-LHC-Sell]LHC is GBP i.e. to be sold, hence A Ltd will buy put Option at Strike Rate GBP 1 = USD 1.70 for hedging of sale price ofGBPSize of 1 Put Option Contract = GBP 12500No of GBP to be sold = USD 364897/1.70 = GBP 214645.30No of Put Option to be purchased = GBP 214645.30/12500 = 17.17 Contract i.e. 17 ContractsNo of GBP to be sold by 17 Contract = 12500*17 = GBP 212500Hence USD that can be purchased by selling GBP 212500 by put Option = GBP 212500*1.70 = USD 361250Balance USD would be purchased at FR of 6 month = 364897 – 361250 = USD 3647 @ 1.5455Premium payable = 212500*0.096 = USD 20400GBP required to pay Premium at SR = USD 20400/1.5617 = GBP 13062.70On maturity dateAssuming Put option is exercisable, henceGBP required to buy USD 3647 at FR = USD 3647/1.5455 = GBP 2359.75

Total Payment under Put Option = 212500+2359.75+13062.70 = GBP 227922.50

Option Payment

Forward cover GBP 236102.89

Money market GBP 236510.10

Currency option GBP 227923.00

The company should take currency option for hedging the risk.

Solution-12London firm has supplied machine to New York for $120 mLondon firm will receive $120 m in 4 months. [$ - Sell, £ - Buy]Strike rate of 1 £ = $ 1.60[£ is LHC and it is to be purchased, hence for hedging of purchase price, we should buy Call option]But in question, it is stated that for hedging London based firm has purchased put option for selling $ hence we willcalculate strike rate by making $ as LHCStrike Rate 1 $ = £ 1/1.60 = £0.625

After 4 months

Exchange rate $ 1 = £0.625 £0.65 £0.615

Strike Rate of put option £0.625 £0.625 £0.625

Where should holder sell $ [Higher of Two] Market Market Writer

Exercise of Put option by holder No No Yes

Sale price of $ for London Firm £0.625 £0.65 £0.625

Amt receivable in £ £0.625*120 = £75 m £0.65*120 = £78 m £0.625*120 = £75 m

(ii)Put Option Premium £ 1 = $0.0002No of $ to be sold through Put Option = $120No of £ to be purchased through put option at strike rate = $120/1.60 = £ 75mPremium paid on purchase of Put Option = £ 75*0.0002 = $ 0.015 mToday Spot rate 1 £ = $ 1.58 or$ 1 = £1/1.58 = £ 0.6329Premium paid on purchase of Put Option in £ = $0.015*SR = $0.015/1.58 = £ 0.009494 m

Solution-13An American firm is to pay Can$ 1010000 and Can$ 705000 on 31st July and 30th Sep respectively [Buy Can $ and Sell US$]

Option 1 - Forward Cover1 Month Forward Rate Can$ 1 = US$0.93013 Months Forward Rate Can$ 1 = US$0.9356

For hedging, an American firm will purchase1 month forward contract for Can$ 1010000 @ Can$ 1 = US$0.93013 month forward contract for Can$ 705000 @ Can$ 1 = US$0.9356

US $ required to buy Can$ 1010000 at the end of 1 month = Can$ 1010000*0.9301 = US $ 939401US $ required to buy Can$ 705000 at the end of 3 months = Can$ 705000*0.9356 = US $ 659598

Option 2 – Option CoverStrike Rate of 1 month call option Can$ 1 = US$0.94 [Premium payable 1.02 cents payable]Strike Rate of 3 month call option Can$ 1 = US$0.95 [Premium payable 1.64 cents payable]No of Can $ in 1 call option = 50000

Hedging of 1 month obligationAmerican Firm will purchase 1 month call option = 1010000/50000 = 20.2 contracts means 20 ContractIn 20 contracts, firm can hedge only Can $ = 50000*20 = Can $ 1000000Balance Can $ 10000 will be purchased at spot rate of 1 monthPremium payable for 20 contracts = Can$1000000*1.02 cents = US $ 10200

For hedging of 3 months obligationAmerican Firm will purchase 3 month call option = 705000/50000 = 14.1 contracts means 14 ContractIn 14 contracts, firm can hedge only Can $ = 50000*14 = Can $ 700000Balance Can $ 5000 will be purchased at spot rate of 3 monthPremium payable for 14 contracts = Can$700000*1.64 cents = US $ 11480

Total payment under optionJuly Sep

Particulars Can $ Rate US $ Can $ Rate US $

No of Can $ Covered by Option 1000000 0.94 940000 700000 0.95 665000

Balance Can $ not covered by option 10000 0.9301 9301 5000 0.9356 4678

Total Cost under option 959501 681158

Comments: Payment under forward cover is less than option cover, hence forward cover is recommended in bothobligation.

Solution-14Current price of share = Rs.100Strike price of Call Option = Rs.100Premium Paid = Rs.5Break even price for call option = Strike Price + Premium paid = 100+5 = Rs.105Spot price on expiry date = Rs.105If Market price of share on maturity is Rs.105, then there will be not profit or loss.

Solution-15(a) Expected Price of Share at expiry date = 30*0.1 + 36*0.25 + 40*0.3 + 44*0.25 + 50*0.1 = Rs.40(b) Value of Call Option at expiration

Market price ofShare at Expiration

Strike Price ofCall Option

Exercise of Calloption by Holder

[Lower]

Value of CallOption at

expiration

Probability Expected Value of CallOption at Expiration

30 38 No 0 0.10 0

36 38 No 0 0.25 0

40 38 Yes 2 0.30 0.60

44 38 Yes 6 0.25 1.50

50 38 Yes 12 0.10 1.20

Expected value of Call Option at expiration date = Rs.3.30

(c) Interest rate 12% p.a. NCCPeriod of Option = 6 monthsInterest rate for 6 months = 6%Value of Option today = Value of Option at expiration/(1+PIR) = 3.30/1.06 = Rs.3.11

(d) Interest rate = 12% p.a. CCPeriod of Option = 6 months = 0.5 YrsValue of Option today = Value of Option at expiration*e-rt = 3.30*e-0,12*0.5 = 3.30*e-0.06 = Rs.3.30*0.94176 = Rs.3.107

Solution-16(a)Strike Price of 1 year Call Option = Rs.90Today Spot Price of Share = Rs.100Maturity Period = 1 yearInterest rate = 10% p.a. NCCValue of Call Option today = Today Spot Price of Share – (Strike Price/1+PIR) = 100 – 90/1.1 = Rs.18.19

(b) CMP of 1 year Call Option = Rs.15

CMP of Call Option < TFV of Call Option, hence arbitrage profit is possible.Arbitrage process for Call OptionFollowing three transaction are done today(a) Buy Call Option by paying premium of Rs.15(b) It is assumed the person holds the share which he sells at the CMP at Rs.100(c) Balance = (100-15) = Rs.85 is invested @10% for 1 yearAt the end of 1 yearSettlement of above three transactions under 3 different prices of Share on maturity date

Assume Share price on the exercise date Rs.93 Rs.90 Rs.85

Strike Price of Call Option Rs.90 Rs.90 Rs.90

Exercise of call option (Lower) Yes No No

(d) Gain to Holder on settlement of Call Option +Rs.3 Rs.0 Rs.0

(e) Purchase of share from market -Rs.93 -Rs.90 -Rs.85

(f) Amt receivable from investment (Rs.85*1.1) Rs.93.50 Rs.93.50 Rs.93.50

Net Cash Flow [Arbitrage profit] Rs.3.50 Rs.3.50 Rs.8.50

Solution-16A(a)Strike Price of 1 year Call Option = Rs.180CMP of Share = Rs.200Maturity Period = 1 yearInterest rate = 10% p.a. CCTFV of Call Option today = CMP of share - Strike Price*e-rt = 200 - 180*e-0,10*1 = 200 - 180*e-0.1

= 200 - 180*0.904837 = Rs.37.129

(b) CMP of Call option = Rs.30

CMP of Call Option < TFV of Call Option, hence arbitrage profit is possible.Arbitrage process for Call OptionFollowing three transaction are done today(a) Buy Call Option by paying premium of Rs.30(b) It is assumed the person holds the share which he sells at the CMP at Rs.200(c) Balance = (200-30) = Rs.170 is invested @10% for 1 year CCAt the end of 1 yearSettlement of above three transactions under 3 different prices of Share on maturity date

Strike Price of Call Option Rs.180 Rs.180 Rs.180

Exercise of call option (Lower) Yes No No

(d) Gain to Holder on settlement of Call Option +Rs.10 Rs.0 Rs.0

(e) Purchase of share from market -Rs.190 -Rs.180 -Rs.170

(f) Amt receivable from investment (Rs.170*e-0.1) Rs.187.87 Rs.187.87 Rs.187.87

Solution-17(a)Strike Price of 6 months Put Option = Rs.200CMP of Share = Rs.185Maturity Period = 6 monthsInterest rate = 5% p.a. NCCTFV of Put Option today = Strike Price*PVF(6months, 2.5%) - CMP of Share = 200*0.97561 - 185 = Rs.10.122

(b) CMP of Put Option = Rs.5CMP of Put Option < TFV of Put Option, hence arbitrage profit is possible

Arbitrage process for Put OptionFollowing three transaction are done today(a) Buy Put Option by paying premium of Rs.5(b) Buy share at the CMP at Rs.185(c) Borrow = (5+185) = Rs.190 @2.5% for 6 monthsAt the end of 6 monthsSettlement of above three transactions under 3 different prices of Share on maturity date

Strike Price of Put Option Rs.200 Rs.200 Rs.200

Exercise of call option (Higher) Yes No No

(d) Gain to Holder on settlement of Put Option Rs.10 0 0

(e) Sale of share in market Rs.190 Rs.200 Rs.210

(f) Repayment of borrowing (Rs.190*1.025) - Rs.194.75 - Rs.194.75 - Rs.194.75

Solution-17A(a)Strike Price of 6 months Put Option = Rs.400CMP of Shares = Rs.370Maturity Period = 6 monthsInterest rate = 5% p.a. CCValue of put option today = Strike Price*e-rt - CMP of Share = 400*e-0.05*1/2 – Rs.370= 400*e-0.025 – Rs.370 = 400*0.975323 - 370 = Rs.20.129

(b) CMP of Put Option = Rs.10CMP of Put Option < TFV of Put Option, hence arbitrage profit is possible

Arbitrage process for Put OptionFollowing three transaction are done today(a) Buy Put Option by paying premium of Rs.10(b) Buy share at the CMP at Rs.370(c) Borrow = (10+370) = Rs.380 @2.5% for 6 months CCAt the end of 6 monthsSettlement of above three transactions under 3 different prices of Share on maturity date

Strike Price of Put Option Rs.400 Rs.400 Rs.400

Exercise of call option (Higher) Yes No No

(d) Gain to Holder on settlement of Put Option Rs.10 0 0

(e) Sale of share in market +Rs.390 +Rs.400 +Rs.410

(f) Repayment of borrowing Rs.380*e.025 = Rs.380*1.025302 - Rs.389.61 - Rs.389.61 - Rs.389.61

Solution-18(a)S1 = Rs.60; S2 = Rs.40; Strike Price (K) = Rs.50; CMP of Share (S) = Rs.50C1 = Value of Option at expiration at S1 = Max[(Spot Price at expiration – Strike Price),0] = Max[(60-50),0] = Rs.10C2 = Value of Option at expiration at S2 = Max[(Spot Price at expiration – Strike Price),0] = Max[(40-50),0] = Rs.0Hedge Ratio Δ = C1-C2/S1-S2 = 10-0/60-40 = 0.50Borrowing = Δ*(S2-C2)/1+r = 0.50*(40-0)/1.12 = Rs.17.85 orBorrowing = Δ*S1-nC1/1+r = (0.50*60-1*10)/1.12 = Rs.17.85 orValue of Call Option under BM = Δ*CMP of Share – Borrowing = 0.50*50 - 17.85 = Rs.7.15Maturity Period = 1 year

(b)Now, the investor can have two possible strategies:

Option Cash Flow at t0

1 Buy one Call Option by paying a premium - 7.50

2 Buy Replicating Portfolio

(a) Buy 0.50 shares at CMP of Rs.50 -25.00

(b) Borrowing @12% p.a. for 1 year +17.50

- 7.50

Holding position of cash under both option at expiration

Market Price of Share S1 = Rs.60 S2 = Rs.40

1 Strike Price of Call Option Rs.50 Rs.50

Exercise of Call Option by Holder (Lower) Yes No

Gain on Settlement of Call Option (Lower) +10 0

2 Settlement of Replicating Portfolio

(a) Sale of 0.5 Share at CMP +30 +20

(b) Repayment of borrowing = Rs.17.50*1.12 -20 -20

(c) (i)CMP of Call Option = Rs.8TFV of Call Option = Rs.7.15CMP of Call Option > TFV of Call Option, hence we should sell call option and buy a replicating portfolio.

Process for Arbitrage ProfitToday

Particulars Cash Flow at t0

(a) Sell Call Option at CMP (Writer) + 8

(b) Buy Replicating Portfolio

(i) Buy 0.5 Shares at CMP -25

(ii) Borrow (25-8) = Rs.17 for 1 year @12% p.a. +17

Cash Position at the end of one year

Particulars Share price = Rs.60 Share price = Rs.40

(a) Loss to Writer on settlement of Call Option -10 0

(b) Settlement of Replicating Portfolio

(i) Sale of 0.50 Shares at Market Price +30 +20

(ii) Repayment of borrowing = 17*1.12 -19.04 -19.04

Arbitrage profit +0.96 +0.96

(ii)CMP of Call Option = Rs.5TFV of Call Option = Rs.7.15CMP of Call Option > TFV of Call Option, hence we should buy call option and sell a replicating portfolio.Process for Arbitrage ProfitToday

Particulars Cash Flow at t0

(a) Buy Call Option at CMP (Holder) - 5

(b) Sell Replicating Portfolio

(i) Sell 0.5 Shares at CMP +25

(ii) Deposit (25-5) = Rs.20 for 1 year @12% p.a. -20

Cash Position at the end of one year

Particulars Share price = Rs.60 Share price = Rs.40

(a) Gain to Holder on settlement of Call Option +10.00 0.00

(b) Settlement of Replicating Portfolio

(i) Purchase of 0.50 Shares at Market Price -30.00 -20.00

(ii) Amt receivable from Deposit = 20*1.12 +22.40 +22.40

Arbitrage profit +2.40 +2.40

Solution-18AS1 = Rs.250; S2 = Rs.140; Strike Price = Rs.180; CMP of Share (S) = Rs.190C1 = Value of Option at expiration at S1 = Max[(Spot Price at expiration – Strike Price),0] = Max[(250-180),0] = Rs.70C2 = Value of Option at expiration at S2 = Max[(Spot Price at expiration – Strike Price),0] = Max[(140-180),0] = Rs.0(i) Hedge Ratio Δ = C1-C2/S1-S2 = 70-0/250-140 = 0.64(ii) Borrowing = Δ*(S2-C2)/1+r = 0.6363*(140-0)/1.09 = Rs.82.20 orBorrowing = Δ*S1-nC1/1+r = (0.64*250-1*70)/1.09 = Rs.82.20 or

(iii) TFV of Call option under BM = Δ*Today Spot Price –Borrowing = 0.64*190 – 82.20 = Rs.39.40Assuming CMP of Call Option = Rs.39.40(iv)Now, the investor can have two possible strategies:

Option Cash Flow at t0

1 Buy one Call Option by paying a premium - 39.40

2 Buy Replicating Portfolio

(a) Buy 0.64 shares at CMP of Rs.190 -121.60

(b) Borrowing (121.60-39.40) = Rs.82.20 @ 9% p.a. for 1 year +82.20

- 39.40

Holding position of cash under both option at expiration

Market Price of Share S1 = Rs.250 S2 = Rs.140

1 Strike Price of Call Option Rs.180 Rs.180

Exercise of Call Option by Holder (Lower) Yes No

Gain on Settlement of Call Option (Lower) +70 0

2 Settlement of Replicating Portfolio

(a) Sale of 0.64 Share at Market Price 250*0.64 = Rs.160 140*0.64 = Rs.90

(b) Repayment of borrowing = Rs.82.20*1.09 -90 -90

Solution-19Exercise Price = Rs.450, S1 = Rs.500, S2 = Rs.400; CMP of Share (S) = Rs.420Maturity Period = 3 monthsC1 = Value of Option at expiration at S1 = Max[(Spot Price at expiration – Strike Price),0] = Max[(500-450),0] = Rs.50C2 = Value of Option at expiration at S2 = Max[(Spot Price at expiration – Strike Price),0] = Max[(400-450),0] = Rs.0P1 = Prob of S1 = [Current Price*ert - S2]/(S1 - S2) = (420*1.0202 – 400)/(500-400) = 0.28484P2 = Prob of S2 = 1 – 0.28484 = 0.71516Value of Call Option at expiration = C1P1 + C2P2 = 50*0.28484 + 0*0.71516 = Rs.14.242Value of Call Option today = 14.242*e-rt = 14.242*0.9802 = 13.96

Not part of SolutionValue of Call Option under BMHedge Ratio Δ = C1-C2/S1-S2 = (50-0)/(500-400) = 0.5Borrowing = Δ*(S2-C2)/1+r = 0.5*(400-0) *e-rt = Rs.200*0.9802 = 196.04Value of Call Option under BM = Δ*Today Spot Price – Borrowing = 0.5*420 – 196.04 = Rs.13.96

Solution-19AS1 = Rs.592; S2 = Rs.411; CMP of Share = Rs.421; IR = 3.6% for one month CC [Assume]P1 = Prob of S1 = [CMP of Share*ert - S2]/(S1 - S2) = (421*1.037 – 411)/(592 - 411) = 0.14Prob of S1 = 0.14

Solution-19BCMP of Share = Rs.200Exercise Price of Call Option = Rs.220u = 1.4; d = 0.90; r = 0.15S1 = CMP of Share*u = Rs.200*1.4 = Rs.280S2 = CMP of Share*d = Rs.200*0.9 = Rs.180C1 = Value of Option at expiration at S1 = Max[(Spot Price at expiration – Strike Price),0] = Max[(280-220),0] = Rs.60C2 = Value of Option at expiration at S2 = Max[(Spot Price at expiration – Strike Price),0] = Max[(180-220),0] = Rs.0

Risk Neutralisation MethodP1 = Prob of S1 = [Current Price*(1+PI) - S2]/S1 - S2 = [200*(1.15) – 180]/[280-180] = 0.5P2 = 1 – 0.5 = 0.5Value of Call Option at expiration = C1P1 + C2P2 = 60*0.5 + 0*0.5 = Rs.30Value of Call Option today = 30/1+PI = 30/1.15 = Rs.26.09

Solution-20CMP of Share = Rs.600Exercise Price of Call Option = Rs.630S1 = Rs.780S2 = Rs.480C1 = Value of Option at expiration at S1 = Max[(Spot Price at expiration – Strike Price),0] = Max[(780-630),0] = Rs.150C2 = Value of Option at expiration at S2 = Max[(Spot Price at expiration – Strike Price),0] = Max[(480-630),0] = Rs.0

(i) Hedge Ratio Δ = C1-C2/S1-S2 = 150-0/780-480 = 0.5For 1 call option, writer should buy 0.5 share for perfect hedge.(ii) Value of Option TodayRisk Neutralisation MethodP1 = 0.6P2 = 0.4Value of Call Option at expiration = C1P1 + C2P2 = 150*0.6 + 0*0.4 = Rs.90Value of Call Option today = 90/1+PI = 90/1.025 = Rs.87.80

Solution-21(i) If apartments are to be sold now

Particulars Option 1 Option 2

No of Apartments 10 15

Construction Cost (Lacs) 600 1025

CMP of each Unit (Lacs) 80 80

Market value of Apartment (Lacs) 800 1200

Profit (Lacs) 200 175

Option 1 is better

(ii) If apartments are to be sold after 1 year

Particulars Buoyant Market Sluggish Market

Option 1 Option 2 Option 1 Option 2

No of Apartments 10 15 10 15

Construction Cost at t0 (Lacs) 600 1025 600 1025

MP of each Unit at the end of Year (Lacs) 91 91 75 75

Market value of Apartment at the end of year (Lacs) 910 1365 750 1125

Profit (Lacs) 310 340 150 100

If market is buoyant, than Option 2 is better and if market is sluggish than Option 1 is better

(iii) Determination of Value of Vacant PlotWe will use Binomial Model (Risk Neutral Method) as followsIf flat is constructed at t0 and given on rent for 1 year thanIf market is buoyant, then S1 = 91+7 = 98 lacsIf market is sluggish, then S2 = 75+7 = 82 lacsP1 = Prob of S1 = [Current Price*(1+PI) - S2]/S1 - S2 = [80*(1.1) – 82]/[98-82] = 0.375P2 = 1 – 0.375 = 0.625Expected profit at the end of year = 340*0.375 + 150*0.625 = Rs.221.25 lacsPV of Expected Profit = 221.25/1.1 = Rs.201.12 lacsValue of vacant land = Rs.201.12 lacs

Solution-22CMP of Share = Rs.60; d = 0.7; Period = 1 year; RF = 12%; Exercise Price = Rs.55S1 = ?S2 = CMP of Share*d = 60*0.70 = Rs.42Suppose Hedge ratio = nCalculation of value of hedge position at expiration dateCMP of Call Option = Rs.15Assume CMP of Call Option = TFV of Call Option under BMValue of Call option under BM = Δ*CMP of Share – Borrowing15 = Δ*60 – Δ*S2/(1+PI)15 = Δ*60 – Δ*42/1.1215 = Δ*60 – Δ*37.50Δ*22.50 = 15Δ = 15/22.50 = 0.667Δ = C1-C2/S1-S20.667 = [(S1-55)-0]/(S1-42)0.667S1 – 0.667*42 = S1-550.333 S1 = (55-28.014)S1 = 26.986/0.333 = Rs.81u = S1/S = 81/60 = 1.35Alternative SolutionP1 = (60*1.12-42)/(S1-42)P1 = 25.20/(S1-42)P2 = 1 – P1C1 = S1-55C2 = 0Value of Call Option today = C1P1 + C2P2/(1+PIR)

15 = (S1-55)*25.20/(S1-42)*1.1215 = 25.2S1 – 1386/(1.12S1-47.04)15*(1.12S1 - 47.04) = 25.2S1 – 138616.8S1 – 705.60 = 25.2S1 – 13868.4S1 = 680.4S1 = 680.4/8.4 = Rs.81

Solution-23CMP of Share = Euro 500; S1 = Euro 550; S2 = Euro 450; Rf = 14%; Exercise Price of Put Option = Euro 510Period of Put Option = 6 monthsPI for 6 months = 7%C1 = Value of Put Option at expiration at S1 = Max[(Strike Price - Spot Price at expiration),0] = Max[(510-550),0] = Rs.0C2 = Value of Put Option at expiration at S2 = Max[(Strike Price - Spot Price at expiration),0] = Max[(510-450),0] =Rs.60

Prob of S1 = (Current Price*ert - S2)/(S1 - S2) = (500*1.072508 – 450)/(550-450) = 0.86254P2 = 1 – 0.86254 = 0.13746Value of Put Option at expiration = C1P1 + C2P2 = 0*0.86254 + 60*0.13746 = Rs.8.24Value of Put Option today = Value of Put Option at expiration/1+PI = 8.24/1.07 = Rs.7.70

Solution-24Today Spot Rate 1 $ = Rs.50Period of Call Option = 1 yearExercise Rate 1 $ = Rs.60Expiration date higher Rate S1 = 1 $ = Rs.70Expiration date Lower Rate S2 = 1 $ = Rs.40C1 = Value of Option at expiration at S1 = Max[(Spot Price at expiration – Strike Price),0] = Max[(70-60),0] = Rs.10C2 = Value of Option at expiration at S2 = Max[(Spot Price at expiration – Strike Price),0] = Max[(40-60),0] = Rs.0Interest rate in India (RHC) = 10% p.a.Interest rate in USA (LHC) = 15% p.a

P1 = (Today Spot Rate*(1+PIRHC) - S2*(1+PILHC))/(S1*(1+PIRHC) - S2*(1+PIRHC))= (50*1.1 – 40*1.15)/(70*1.15-40*1.15) = 0.2609

P2 = 1 – 0.2609 = 0.7391Value of Call Option at expiration = (10*0.2609 + 0*0.7391) = Rs.2.609Value of Call Option today = 2.609/1.1 = Rs.2.37

Note: Cross Checking1) Suppose the Indian investor has Rs.50If he invest the money in India then value at year end = 50*1.1 = Rs.552) Suppose Rs.50 is converted in 1 $ amt and invested in USAAt one year end 1 $ amt will be equal to = 1.15 $Year end value of invested amt (at higher price) = Rs.1.15 x 70 = Rs.80.50Year end value of invested amt (at lower price) = Rs.1.15 x 40 = Rs.46Prob of High Price of 1 $ = [50 x (1.1) – 46]/[80.50 - 46] = 0.2609Expected overall value invested amount = 80.5*0.2609 + 46*0.7391 = Rs.55

Solution-24AToday Spot Rate 1 £ = Rs.60Exercise Rate 1 £ = Rs.64Expiration date higher Rate 1 £ = Rs.76.25 = S1Expiration date Lower Rate 1 £ = Rs.45.00 = S2Interest rate in India (RHC) = 15% p.a.Interest rate in London (LHC) = 20% p.aC1 = Value of Option at expiration at S1 = Max[(Spot Price at expiration – Strike Price),0] = Max[(76.25-64),0] =Rs.12.25C2 = Value of Option at expiration at S2 = Max[(Spot Price at expiration – Strike Price),0] = Max[(45-64),0] = Rs.0

P1 = (Current Price*(1+PIRHC) - S2*(1+PILHC))/(S1*(1+PIRHC) - S2*(1+PIRHC))

= (60*1.15 – 45*1.20)/(76.25*1.20-45*1.20) = 0.4

P2 = 1 – 0.4 = 0.6Value of Call Option at expiration = (12.25*0.4 + 0*0.6) = Rs.4.90Value of Call Option today = 4.90/1.15 = Rs.4.26

Solution-25CMP of share = Rs.100Dividend payable after 2 months = Rs.5S1 = 140; S2 = Rs.80; Rf = 12%; Strike price = Rs.110Interest rate for 2 months = 2%PV of Dividend at T0= Rs.5/1.02 = Rs.4.9019Future value of Dividend at the end of 3 months = Rs.5*1.01 = Rs.5.05C1 = Value of Option at expiration at S1 = Max[(Spot Price at expiration – Strike Price),0] = Max[(140-110),0] = Rs.30C2 = Value of Option at expiration at S2 = Max[(Spot Price at expiration – Strike Price),0] = Max[(80-110),0] = Rs.0

BM ModelΔ = (C1-C2)/(S1-S2) = (30-0)/(140-80) = 0.50Borrowing = Δ*S2/1.03 = 0.50*80/1.03 = Rs.38.83Value of Option = Δ*(CMP of Share – PV of Dividend) – Borrowing = 0.50*(100 – 4.90) – 38.83 = Rs.8.72

RNMP1 = (CMP of Share*(1+PI) - S2 – FV of Dividend)/(S1 - S2) = (100*1.03 – 80 - 5.05)/(140-80) = 0.2992

P2 = 1 – 0.2992 = 0.7008Value of Call Option at expiration = C1P1 + C2P2 = (30*0.2992 + 0*0.7008) = Rs.8.976Value of Call Option today = 8.976/1.03 = Rs.8.71

Solution-26Stock prices in the two step Binominal treeCMP of Share = Rs.50; u = 1.2; d = 0.8; IR = 6%(a) S1 for first year = Rs.60; S2 for first year = Rs.40(c)P1 of Rs.60 = (1+R-d)/(u-d) = (1.06-0.80)/(1.20-0.08) = 0.26/0.04= 0.65P2 of Rs.40 = 1-0.65 = 0.35

(b) Four possibilities regarding possible prices for next year

Possibilities Possible Price

Up by 20% in first year and again up by 20% in next year = S3 = S*d1*d2 50*1.2*1.2 = 72

Up by 20% in first year and down by 20% in next year = S4 = S*d1*u2 50*1.2*0.8 = 48

Down by 20% in first year and up by 20% in next year = S5 = S*u1*d2 50*0.8*1.2 = 48

Down by 20% in first year and down by 20% in next year = S6 = S*u1*u2 50*0.8*0.8 = 32

(d) Calculation of Prob of all four prices

Prob of Rs.72 from Rs.60 in 2nd year = P3 = (S1*(1+PIR) – S4)/(S3 – S4) (60*1.06-48)/(72-48) = 0.65

Prob of Rs.48 from Rs.60 in 2nd year = P4 = P4 = 1 – P3 = 1-0.65 = 0.35

Prob of Rs.48 from Rs.40 in 2nd year = P5 = (S2*(1+PIR) – S6)/(S5 – S6) = (40*1.06-32)/(48-32) = 0.65

(e) Joint Probability of all four prices at the end of 2nd year

Joint Probability of Rs.72 from Rs.50 JP1 of S3 = P1*P3 0.65*0.65 = 0.4225

(f) Computation on value of ECO at expiration of 2nd Period

Price of Share on maturity Strike Price Value of Call Option JP Expected Value of Option

72 50 22 0.4225 9.295

48 50 0 0.455 0

32 50 0 0.1225 0

Expected value of Call option at the end of 2nd year = 9.295(g) TFV of ECO option today = 9.295*e-0.12 = Rs.9.295*0.88692 = Rs.8.2439American OptionComputation on value of American Call Option at end of First year at Point B

Price on maturity Strike Price Value of Call Option Prob. Expected Gain

72 50 22 0.65 14.30

48 50 0 0.35 0

Expected value of ACO at point B = 14.30/1.06 = 13.49

Computation on value of ACO at end of First year at Point C

Price on maturity Strike Price Value of Call Option Prob. Expected Gain

48 50 0 0.65 0

32 50 0 0.35 0

Expected value of option at point C = 0/1.06 = 0

Value of ACO at the end of first year = 13.49*0.65 + 0*0.35 = Rs.8.7685

Value of ACO today = 8.7685/1.06 = Rs.8.272

Solution-26AToday spot price of share = Rs.100; u = 1.1; d = 0.9; IR = 8%(a) S1 = 110; S2 = Rs.90; for first six monthsRf = 8%; Strike price = Rs.100(c)P1 of Rs.110 = (100xe0.08x.50 – 90)/(110-90) = 0.70405P2 of Rs.90 = 0.29595(b)Four possibilities regarding possible prices for next six months

Possibilities Possible Price

Up by 10% in first 6 months and again up by 10% in next 6 months = S*d1*d2 100x1.1x1.1 = 121

Up by 10% in first 6 months and down by 10% in next 6 months = S*d1*u2 1600x1.1x0.9 = 99

Down by 10% in first 6 months and down by 10% in next 6 months = S*u1*u2 100x0.9x0.9 = 81

Down by 10% in first 6 months and up by 10% in next 6 months = S*u1*d2 100x0.9x1.1 = 99

(d) Calculation of Prob of all four prices

Prob of Rs.121 from Rs.110 in 1 year = P3 = (S1*(1+PIR) – S4)/(S3 – S4) = (100* e0.04 - 90)/(110-90) = 0.70405

Prob of Rs.99 from Rs.110 in 1 year = P4 = P4 = 1 – P3 = 1-0.70405 = 0.29595

Prob of Rs.81 from Rs.90 in 1 year = P5 = (S2*(1+PIR) – S6)/(S5 – S6) = (90*e0.04 - 81)/(99-81) = 0.70405

(e) Joint Probability of all four prices at the end of 2nd year

(f) Computation on value of ECO at expiration of 2nd Period

Price of Share on maturity Strike Price Value of Call Option JP Expected Value of Option

121 100 21 0.4956 10.41

99 100 0 0.2084 0

81 100 0 0.0876 0

Expected value of Call Option at maturity = 10.41TFV of Call Option today = 10.41*e-0.08 = Rs.9.61

Solution-27 [P]CMP of share S = Rs.100Rf = 12%; Strike price K = Rs.101For first 3 monthsPricing going up by 10% over first 3 months time, hence S1 = 110;Pricing going down by 10% over first 3 months time, hence S2 = 90;Interest for 3 months = 3%P1 of Rs.110 = (100*1.03 -90)/(110 -90) = 0.65P2 of Rs.90 = 1-0.65 = 0.35

For the next 3 monthsPricing going up by 8% over next 3 months and Pricing going down by 6% over next 3 months time, hence expectedprice at the end of 6 months and their probability

Price at the endof 3 months

% of Changein Price

Expected Price at theend of 6 months

Probability of Price JointProbability

110 8% up Rs.118.80 (110*1.03-103.40)/(118.80-103.40) = 0.6429

0.65*0.6429 0.4179

110 6% Down Rs.103.40 1-0.6429 = 0.3571 0.65*0.3571 0.2321

90 8% up Rs.97.20 0.6429 0.35*0.6429 0.2250

90 6% Down Rs.84.60 0.3571 0.35*0.3571 0.1250

Computation of Expected value of EPO at expiration

Price on maturity Strike Price of Put Option Value of Put Option Prob. Expected Value of Put Option

118.80 101 0 0.4179 0

103.40 101 0 0.2321 0

97.20 101 3.80 0.2250 0.855

84.60 101 16.40 0.1250 2.05

Expected value of Put at Maturity = Rs. 2.905TFV of Put Option today = 2.905/1.06 = Rs.2.7406

Solution-28CMP of Share S = Rs.80Strike Price of Call Option K = Rs.75r = 12% p.a. CC; t = 6 months = 0.5SD = 0.4(d1) = [In (S/K) + (r + 0.5*SD2)*t]/SD√t(d1) = [In(80/75) + (0.12 + 0.5*0.40*0.40)*0.5]/0.40*√0.5 = In(1.0667) + 0.1]/0.4*√0.5= (0.0645 + 0.1)/0.2828 = 0.5817d2 = d1 - σ√t = 0.5817 – 0.2828 = 0.2989Nd1 = N (0.5817) = N(0.58) + [N(0.59) - N(0.58)]*0.17 = 0.7190 + (0.7224-0.7190)*0.17 = 0.7195Nd2 = N (0.2989) = N(0.29) + [N(0.30) - N(0.29)]*0.89 = 0.6141 + (0.6179-0.6141)*0.89 = 0.6174e-rt = e-0.12 x 0.50 = e-0.06 = 0.9417Value of Call Option = S*N(d1) – K*e-rt *N(d2) = 80*0.7195 – 75*e-0.06*0.6174 = 57.56 – 46.305*0.9418 = Rs.13.95

Solution-28ACMP of Share S = Rs.185Strike Price of Call Option K = Rs.170r = 7% p.a. CC; t = 3 years = 3SD = 0.18

(d1) = [In (S/K) + (r + 0.5*SD2)*t]/SD√t

(d1) = [In(185/170) + (0.07 + 0.5*0.18*0.18)*3]/0.18*√3= In(1.08823) + 0.2586]/0.18*1.7320= (0.08454 + 0.2586)/0.31176 = 1.1006d2 = d1 - σ√t = 1.1006 – 0.31176 = 0.78884Nd1 = N(1.1006) = 0.8643Nd2 = N(0.78884) = N(0.78) + [N(0.79) - N(0.78)]*0.884 = 0.7823 + (0.7852-0.7823)*0.884 = 0.7848e-rt = e-0.07*3 = e-0.21 = 0.810584

Value of Call Option = S*N(d1) – K*e-rt *N(d2) = 185*0.8643 – 170*0.810584*0.7848 = 159.8955 – 108.1448= Rs.51.75

Solution-29 [P]Dividend receivable = Rs.10 after 2 monthsPV of Dividend = Rs.10*e-rt = Rs.10*e-0.05*2/6 = Rs.10*e-0.01667 = 10*0.983479 = 9.83479e-0.01667 = e-0.01667 = e-0.01 + [e-0.02 - e-0.01]*0.667 = 0.99005 + (0.980199-0.99005)*0.667 = 0.983479(d1) = [In (Current Price of Share-PV of Dividend/Strike Price) + (r + 0.5*SD2)*t]/SD√t(d1) = [In(408-9.83479/400) + (0.05 + 0.5*0.22*0.22)*0.25]/0.22*√0.25 = In(0.995413) + 0.01855]/0.22*0.5= (-0.00543713 + 0.01855)/0.11 = 0.119d2 = d1 - σ√t = 0.119 – 0.11 = 0.009Nd1 = N(0.119) = N(0.11) + [N(0.12) - N(0.11)]*0.9 = 0.5438 + (0.5478-0.5438)*0.9 = 0.5474Nd2 = N(0.009) = N(0.00) + [N(0.01) - N(0.00)]*0.9 = 0.5 + (0.5040-0.5)*0.9 = 0.5036

Working NoteIn(0.995413) = In(9.95413/10) = In(9.95413) – In(10) = 2.29715287 – 2.30259 = - 0.00543713In(9.95413) = In(9.95) + [In(9.96) – In(9.95)]*0.413 = 2.29757 – (2.29858-2.29757)*0.413 = 2.29715287e-rt = e-0.05*0.25 = e-0.0125 = e-0.01 + [e-0.02 - e-0.01]*0.25 = 0.99005 + (0.980199-0.99005)*.25 = 0.987587

Value of Call Option = (S-PV of Dividend)*N(d1) – K*e-rt *N(d2)= (408-9.83479)*0.5474 – 400*0.987587*0.5036 = 217.9556 – 198.9395 = Rs.19.0161

Solution-30(d1) = [In (Current Price of Share/Strike Price) + (r + 0.5*SD2)*t]/SD√t(d1) = [In(120/112) + (0.05 + 0.5*0.3*0.3)*0.25]/0.3*√0.25 = In(1.0714) + 0.02375]/0.3*0.5= (0.068961 + 0.02375)/0.15 = 0.6180In(1.0714) = In(1.07) + [In(1.08) - In(1.07)]*0.14 = 0.067659 + (0.076961-0.067659)*0.14 = 0.068961d2 = d1 - σ√t = 0.618 – 0.15 = 0.468Nd1 = N(0.618) = N(0.61) + [N(0.62) - N(0.61)]*0.8 = 0.7291 + (0.7324-0.7291)*0.8 = 0.73174Nd2 = N(0.468) = N(0.46) + [N(0.47) - N(0.46)]*0.8 = 0.6772 + (0.6808-0.6772)*0.8 = 0.68008e-rt = e-0.07*0.25 = e-0.0175 = e-0.01 + [e-0.02 - e-0.01]*0.75 = 0.99005 + (0.980199-0.99005)*.75 = 0.982662Value of Put Option = K*e-rt *(1-N(d2)) - S*(1-N(d1)) = 112*0.982662(1-0.68008) – 120*(1-0.73174) =

= Rs.3.0186

Solution-31If Market Price of Share at expiry = Rs.55

Mr X Buy 1 1

Exercise of Option by Mr X No Yes

Value of Option 0 5 +5

Net Gain/ (Loss) -2 +2 0

If Market Price of share at Expiry = Rs.60

Mr X Buy 1 1

Value of Option 0 0 0

If Market Price of share at expiry = Rs.65

Mr X Buy 1 1

If Market Price of share at expiry = Rs.76

Mr X Buy 1 1

Exercise of Option by Mr X Yes No

Net Gain/ (Loss) 9 -3 6

Solution-32Cost =Premium of both the options =Rs.11Break-even will be there in following two mutual exclusive cases:Breakeven point on exercise of Put Option = Strike Price of Put Option – Premium Paid = Rs.185 – Rs.11 = Rs.174Breakeven point on exercise of Call Option = Strike Price of Call Option + Premium Paid = Rs.190 + Rs.11 = Rs.201

Comments: If Market Price of Share on Expiration is Rs.174 or Rs.201 then there will be no profit or loss.

Solution-33If market price of share at expiry = Rs.90

Investor Buy 1 1

Exercise of Option by Holder No Yes

Value of Option 0 +7 +7

Net Gain/ (Loss) -3 +5 +2

If market price of share at expiry = Rs.97

Investor Buy 1 1

Exercise of Option by Holder No No

If market price of share at expiry = Rs.105

Investor Buy 1 1

Exercise of Option by Holder Yes No

Value of Option +8 0 +8

Net Gain/ (Loss) +5 -2 +3

So, the investor will be benefited whether price is less than or more than the strike price on the expiry day.

Solution-33ATotal Premium paid = CHF = 2+3 = CHF 5Strike price of Call and Put = CHF 75

MP of Share at Maturity Gain on Put Option to X Gain on Call option to X X’s pay-off Y’s pay-off

60 15 0 -5 (prem.) + 15 =+10 -10

65 10 0 -5 (prem.) +10 =+5 -5

70 5 0 -5 (prem.) + 5 =+0 0

71 4 0 -5 (prem.) + 4 = -1 +1

72 3 0 -5 (prem.) + 3 = -2 +2

73 2 0 -5 (prem.) + 2 = -3 +3

74 1 0 -5 (prem.) + 1 = -4 +4

75 0 0 -5 (prem.) + 0 = -5 +5

76 0 1 -5 (prem.) + 1 = -4 +4

77 0 2 -5 (prem.) + 2 = -3 +3

78 0 3 -5 (prem.) + 3 = -2 +2

79 0 4 -5 (prem.) + 4 = -1 +1

80 0 5 -5 (prem.) + 5 = -0 0

85 0 6 -5 (prem.) + 10 = 5 -5

90 0 7 -5 (prem.) + 15 = 10 -10

Solution-34(i) Straddle is a portfolio of a CALL & a PUT option with identical Strike Price. A trader sells Straddle of at the MoneyStraddle will be selling a Call option & a put option with Strike Price of USD per EUR.

Investor sell (Writer) 1 1

Premium Received ($) 0.035 0.04 0.075

Strike Price Euro 1 = $ 1.20 $ 1.20

If market Price of Rate at expiry $ 1.29 $ 1.29

Gain to Holder 0.09 0 0.09

Loss to Writer 0.09 0 0.09

Premium Received 0.035 0.04 0.075

Net Loss 0.055 -0.04 0.015

Particulars Call Option Put Option

Premium Paid Rs.0.12 Rs.0.04

Strike Price Rs.44.80 Rs.44.80

Gain 0.20 0

Premium Paid 0.12 Rs.0.04

Net Gain/ (Loss) 0.08 -0.04

Hence we should buy call option to earn profitNet gain on purchase of call option for USD 1500000 = USD 1500000*0.08 = Rs.120000

Solution-35Strike price of Call and Put Option = Rs.60Premium on call and put option = Rs.1Maturity Period of both Option = 3 months

Spot Price of Shareat expiration

Strike Price ofCall and Put

Exercise ofCall

Gain onCall

Exercise ofPut

Gainon Put

Total Gain PremiumPaid

NetPayoff

55 Rs.60 No 0 Yes 5 0+5*2=10 -3 7

56 Rs.60 No 0 Yes 4 0+4*2=8 -3 5

57 Rs.60 No 0 Yes 3 0+3*2=6 -3 3

58 Rs.60 No 0 Yes 2 0+2*2=4 -3 1

59 Rs.60 No 0 Yes 1 0+1*2=2 -3 -1

60 Rs.60 No 0 No 0 0+0*2=0 -3 -3

61 Rs.60 Yes 1 No 0 1+0*2=1 -3 -2

62 Rs.60 Yes 2 No 0 2+0*2=2 -3 -1

63 Rs.60 Yes 3 No 0 3+0*2=3 -3 0

64 Rs.60 Yes 4 No 0 4+0*2=4 -3 1

65 Rs.60 Yes 5 No 0 5+0*2=5 -3 2

Solution-36Net Premium = -10-5+14 = -1Pay-off table

Spot price Call at 55 Two Calls at 60 Call at 65 Premium Pay-off

51 - - - -1 -1

52 - - - -1 -1

53 - - - -1 -1

54 - - - -1 -1

55 - - - -1 -1

56 1 - - -1 0

57 2 - - -1 +1

58 3 - - -1 +2

59 4 - - -1 +3

60 5 - - -1 +4

61 6 -2 - -1 +3

62 7 -4 - -1 +2

63 8 -6 - -1 +1

64 9 -8 - -1 0

65 10 -10 - -1 -1

66 11 -12 1 -1 -1

67 12 -14 2 -1 -1

68 13 -16 3 -1 -1

69 14 -18 4 -1 -1

70 15 -20 5 -1 -1

Solution-37

Condor SpreadBuy 1 Call (97)Sell 1 Call (100)Sell 1 Call (102)Buy 1 Call (103)Net Premium = -2+1.50+1-0.70 = -0.20

Market price of Share on maturity Call 97 Call 100 Call 102 Call 103 Net premium Net profit/loss

96 0 0 0 0 -0.20 -0.20

97 0 0 0 0 -0.20 -0.20

98 1 0 0 0 -0.20 +0.80

99 2 0 0 0 -0.20 +1.80

100 3 0 0 0 -0.20 +2.80

101 4 -1 0 0 -0.20 +2.80

102 5 -2 0 0 -0.20 +2.80

103 6 -3 -1 0 -0.20 +1.80

104 7 -4 -2 1 -0.20 +1.80

Solution-38Strategy: Buy Call with lower strike price, sell with higher strike price.Net Premium Paid = 5 – 3 = Rs.2.

Spot Price of Share atexpiration

Exercise of Call(100)

Gain on Call(100)

Loss on Call(115)

PremiumPaid

NetPayoff

95 No No 0 0 -2 -2

100 No No 0 0 -2 -2

105 Yes No 5 0 -2 3

110 Yes No 10 0 -2 8

115 Yes No 15 0 -2 13

125 Yes Yes 25 -10 -2 13

Maximum Loss Rs.2 and maximum Gain Rs.13

Solution-38A(a) The best strategy for Mr X would be long call spread.Strategy: Buy Call with lower strike price (Rs.125), sell with higher strike price (Rs.130)(b) Payoff Position can be computed as follows:Net Premium Paid = 3.30 – 1.80 = Rs.1.50

Exercise of Call(125) – Holder

Exercise of Call(130) – Writer

Gain on Call(125)

Loss on Call(130)

PremiumPaid

NetPayoff

124 No No 0 0 -1.50 -1.50

125 No No 0 0 -1.50 -1.50

126 Yes No 1 0 -1.50 -0.50

127 Yes No 2 0 -1.50 0.50

128 Yes No 3 0 -1.50 1.50

129 Yes No 4 0 -1.50 2.50

130 Yes No 5 0 -1.50 3.50

131 Yes Yes 6 -1 -1.50 3.50

Maximum Loss Rs.1.50 and maximum Gain Rs.3.50Break even price of Share = Strike Price + premium Paid = 125+1.50 = 126.50

Solution-39Bull Put SpreadBuy Put Option of 105 by paying Premium of Rs.1Sell Put Option of 115 by receiving Premium of Rs.10Net Premium received = Rs.9

Exercise of Put(105)

Gain on Put(105)

Loss on Put(115)

PremiumReceived

TotalGain

100 Yes Yes 5 -5 9 9

105 No Yes 0 -5 9 4

110 No Yes 0 -10 9 -1

115 No No 0 0 9 9

120 No No 0 0 9 9

125 No No 0 0 9 9

CommentLoss is limited to Re.1 per share while the profit is limited to Rs.9 per share.The bull spread limits the investor’s upside (profit) as well as downside risk (loss).

Solution-40Bear Call SpreadBuy Call Option of 105 by paying Premium of Rs.2Sell Call Option of 95 by receiving Premium of Rs.8Net Premium Received = Rs.6

Gain on Call(105)

Loss on Call(95)

PremiumReceived

TotalGain

90 No No 0 0 6 6

95 No No 0 0 6 6

100 No Yes 0 -5 6 1

105 No Yes 0 -10 6 -4

110 Yes Yes 5 -15 6 -4

115 Yes Yes 10 -20 6 -4

CommentLoss is limited to Re.4 per share while the profit is limited to Rs.6 per share.

Solution-41Bear Put SpreadBuy Put Option of 105 by paying Premium of Rs.3Sell Put Option of 95 by receiving Premium of Rs.2Net Premium Paid = Rs.1

Exercise of Put(95)

Gain on Put(105)

Loss on Put(115)

PremiumPaid

TotalGain

90 Yes Yes 15 -5 -1 9

95 Yes No 10 0 -1 9

100 Yes No 5 0 -1 4

105 No No 0 0 -1 -1

110 No No 0 0 -1 -1

115 No No 0 0 -1 -1

CommentLoss is limited to Re.1 per share while the profit is limited to Rs.9 per share.

CHAPTER-12A OPTION DERIVATIVE - SUMMARY 12A_D.1

12A.0 INDIAN CAPITAL MARKET

a) Broadly Indian Financial Market consists of Capital Market, Money Market and the Debt Market

b) The organized part of the Indian financial system can be classified from the point of view of regulatoryauthority as- RBI regulating Commercial Banks, Foreign Exchange Markets, Financial Institutions, NBFC etc.- SEBI regulating Primary Market, Secondary Market, Derivatives Market and market intermediaries likeMutual Funds, Brokers, Merchant Banks, depositories.

12A.0.1 INDIAN CAPITAL MARKET

(a) Role of Capital Market It is the indicator of the inherent strength of the economy. It is the largest source of funds with long and indefinite maturity for companies and thereby

enhances the capital formation in the country. It offers a number of investment avenues to investors. It helps in channeling the savings pool in the economy towards optimal allocation of capital in the

country.

12A.0.2 STOCK MARKET AND ITS OPERATIONS

1. Secondary markets are also referred to as Stock Exchange.

2. It is a place where the securities issued by the Government, public bodies and Joint Stock Companiesare traded.

3. There are 21 Stock Exchanges in the country.

List of recognized stock exchange

3. Leading Stock Exchanges in India: Bombay Stock Exchange (BSE) and National StockExchange (NSE).

12A.0.3 Functions of Stock Exchanges[T-1] [M11-6bi-4] Write short notes on Function of Stock Exchange

(a) Liquidity and Marketability of Securities:(b) Fair Price Determination:(c) Source for Long term Funds:(d) Helps in Capital Formation:

(e)Reflects the General State of Economy:

12A.1 Derivatives[T-2] [M04-06] [M03-06] [PM-J17-17, 21] [PM-J15-17, 21] What is a “derivatives’? Briefly explainthe recommendation of the L C Gupta Committee on derivatives.[N07-5c-8](a) What are derivatives?

Capital Market

Primary Market

A market where new securities are bought and sold for thefirst time is called the New Issues market or the IPO market

Secondary Market

It is a Market in which issued securities are sold andpurchased by investor. It is the stock exchanges and the over-

the-counter market.

(b) Who are the users and what are the purposes of use?(c) Enumerate the basic differences between cash and derivatives market.

[M11-7d-4] [RTP-M14-20d] [PM-J17-18] [PM-J15-18] What is the meaning of underlying in relationto a derivative instrument?

(a) Derivatives:It is a financial asset which derives its value from some specified underlying assets.Derivatives do not have any physical existence but emerges out of a contract between two parties.It does not have any value of its own but its value depends on the value of other physical assets.The underlying assets may be shares, debentures, tangible commodities etc.The parties to the contract of derivatives are the parties other than the issuer of the assets.The transactions in derivatives are settled by the offsetting in the same derivative. The difference invalue of the derivatives is settled in cash.There is no limit on number of units transacted in the derivative market because there is no physicalassets to be transacted.

(b) Users of Derivatives market: Hedgers ; Speculators; Arbitrages;

(c) Function of Derivatives MarketsThey help in transferring risk from risk averse people to risk oriented people.They help in discoveries of future prices.

12A.2 Option[T-3] [N02-03] [PM-J17-24] [PM-J15-24] Write short notes on the Option.[N97-05] Call and put option with reference to debentures.

(a) Options: Options are contracts which provide the holder the right to sell or buy a specified quantityof an underlying asset at a fixed price on or before the expiration of the option date.Options provide a right and not the obligation to buy or sell.The holder of the option can exercise the option at his discretion or may allow the option tolapse.

Type of Derivative

Commodity and Financial derivatives

Commodity DerivativesIt is a contract on differenttype of commodity such as

sugar, Jute, Gur etc.

Financial DerivativesIt is a contract on different

type of FinancialInstruments such as Shares,

Currencies etc.

Basic and Complex derivatives

Basic Derivatives:It is traded in Stock

ExchangeFutures and Options

Complex Derivative (OTC)It is not traded in stock

exchangeIt is a Contract between 2

partiesEx: Interest Swaps; Caps,Floor and Collar; Forward

Rate Agreement;Swaptions; Currency Swaps;

Forward Contracts;

Option

Call Option (Right to Buy UA)

It provides to the holder a Right to Buy UA at stike price on orbefore strike date.

Holder - Buyer of Call OptionHe pays premium on call option.

He has right to buy UAMaximum Loss = Premium Paid

Writer - Seller of Call Option.He receives premium on call option.

He has obligation to sell UA on exercise of call option by holderMaximum Loss = Unlimited

Maximum Gain - Premium Gain

Put Option (Right to Sell UA)

It provides to the holder a Right to Sell UA at stike price on orbefore strike date.

Holder - Buyer of Put Option.He pays premium on put option.

He has right to sell UAMaximum Loss = Premium Paid

Writer - Seller of Put Option.He receives premium on put option

He has obligation to buy UA on exercise of put option byholder

Maximum Loss = UnlimitedMaximum Gain - Premium Gain

Excercie of Call Option at expiry date (Lower of Spot Price of UA and Strike Price)

Status - Out of the Money

Exercise

Gain/(Loss) on settlement toHolder = Spot Price - Strike PriceWriter = Spot Price - Strike PriceValue of CO at Expiry = Gain on

Settlement

Status = In the Money

b) Strike or Exercise Price: The specified price at which the option can be exercised is known as theStrike Price.

c) Option Premium/Price:In options, the buyer pays option premium to seller.In case, the right is not exercised later, then the premium is not refunded by the option writer.

d) By buying Call option Holder fixes upper limit of its purchase price but does not fix lower limit ofpurchase price

f) Long and short position:Buyer of an option = long positionSeller of an option = short position

g) Today 01/09/2012There will be maximum 3 Options on same underlying assets of 3 different maturity dates

Excercie of Put Option at expiry date (Higher of Spot Price of UA and Strike Price)

Exercise

Gain/(Loss) on settlement toHolder = Strike Price - Spot PriceWriter = Strike Price - Spot PriceValue of PO at Expiry = Gain on

Settlement

Status - In the Money

Status = Out of the Money

In Case of Hedging

Call Option

Holder

Purchase Price of UA = MP ofUA - Gain on Settlement

Writer

Sale Price of UA = MP of UA -Loss on Settlement

Put Option

Holder

Sale Price of UA = MP of UA +Gain on Settlement

Writer

Purchase Price of UA = MP ofUA + Loss on Settlement

Type of Option (Both)

American and European Option

American Option:It can be Exercised at anytimeon or before expiration date

European Option:It can be exercised only on

expiration date

Naked and Covered Option

Naked Option:Option is not covered by UA

Covered OptionOption is covered by UA

Sep Call, Oct Call, Nov Call.Option is settled on last Thursday of month.

h) Option is distinguished by Underlying Assets, Maturity Date and Strike Price.Today Date = 10/09/2012CMP of Share of X Ltd = Rs.100Call Option on Share’s of X Ltd may be as follows for Sep monthSep Call 120, Sep Call 140, Sep Call 110 etc. All three Call options are different product.

12A.3 Calculation of Gain/(Loss) on Settlement of OptionExample-2*** [Understanding of Call Option]Example-3*** [Understanding of Put Option]Question-2 [M06-5b-7] [PM-J17-48] [PM-J15-44] [ICWA-J07]**Question-2A [M16-1d-5] [SP]Question-2B [N08-2c-6] [N09-O-5a-6] [N11-6b-8] [M10-1b-4] [PM-J17-51] [PM-J15-47] [SP]Question-2C [PM-J17-45] [PM-J15-42] [SP]Question-3 [ICWA-D08]**

12A.4 Calculation of Value of Option/Intrinsic Value of Option at expiration

Question-4 [N12-3a-8] [PM-J17-53] [PM-J15-49]***Question-4A [N10-1c-5] [PM-J17-52] [PM-J15-48] [SP]

12A.5 Factors affecting value of Option[T-4] [M14-7b-4] [PM-J17-31] [PM-J15-30] Factors affecting value of an option

Summary of effect of various factors on value of option

Factor Call Option Value Put Option Value

Increase in value of Underlying Asset Increases Decreases

Extent of Volatility in Value of Asset Increases Increase

Increase in Strike Price Decreases Increases

Longer Expiration Time Increases Increases

Increase in Rate of Interest Increases Decreases

Increase in Income from Asset Decreases Increases

Question-5**(a)

12A.6 Uses of Option

(a) Hedging:

Calculation of Value of Option at Expiration date

If only one Spot of Price of UA is given

TVCO = Max[(Spot Price – Strike Price),0] TVPO = Max[(Strike Price – Spot Price),0]

If more than one Spot of Price of UA isgiven with Probability

EVOExpiry = VO1P1 + VO2P2 + VO3P3 +VO4P4

Where VO is value of Option at eachprice of UA

(b) Speculative Transaction:

(c) Arbitrage Profit:

Question-6 [ICWA-J04]***

12A.6.1 Hedging of Foreign Exchange receivable/ Payable through Option

Question-7***Question-8 [N15-1d-5] [PM-J17-39-FOREX]***Question-9***Question-10 [M07-2a-8] [SP]**Question-11 [M10-O-4b-8]***Question-12Question-13 [N13-2b-8] [PM-J17-43-FOREX] [PM-J15-36-FOREX]

12A.7 Breakeven Point for Call or Put Option

(a) Breakeven Point for Call Option = Strike Price + Premium Paid

(b) Breakeven Point for Put Option = Strike Price - Premium Paid

12A.8 Calculation of Value of Option at beginning

(a) The value of option is the price at which it can be purchased or sold. Premium payable on option isalso known as value of option.

12A.9 Calculation of Value of Option at beginning by Expected Gain Approach

Question-15***(a)

Hedging of Forex risk through Option

If LHC-Sale-Buy Put Option If LHC-Buy-Buy Call Option

Calculation of Value of Option (TFVO) at Beginning

Expected Gain Approach Price Differencial Approach Binomial Model/RiskNeutralisation Method Black Scholes Model

Expected Gain Appraoch

Calculate Value of Option at expiration as given in Point 12A.4TVCO = Max[(Spot Price – Strike Price),0]TVPO = Max[(Strike Price – Spot Price),0]

If interest rate is Simple Coumpounding

TFVO today = Value of Option at expiration*PVF

If Interest Rate is Continuous Compounding

TFVO today = Value of Option at expiration*e-rt

12A.10 Calculation of Value of Option by Price Differential Approach

a) Under price differential approach, the value of option is taken as equal to difference between PV ofStrike Price and Spot Price on the valuation date.

Question-16***Question-16A [SP]Question-17**Question-17A [SP]

12A.11 Calculation of Value of Option by Binomial Model Tree or Risk NeutralisationMethod

a) Assumption of BM: CMP of the share is S and it can take two possible values at maturity, S1 or S2such that S1 > S > S2.

b) The investor can borrow or lend an amount (B) at risk free rate of interest 'r'

c) The strike price, K, is given

d) Hedge Ratio is known as delta. It refers to the number of units of stock one should hold for each optionsold to create a risk-free hedge.

e) The BM is based on the concept of Replicating Portfolio, which refers to a portfolio consisting of theunderlying asset and a riskless asset, which generates the same cash flow as a specified call/putoption.

Replicating Portfolio = Borrowing + Δ number of units of the underlying asset

Calculation of Value of Option under Price Differencetial Approach

TFVCO = Spot Price of UAtoday – PV of Strike Price TFVPO = PV of Strike Price - Spot Price of UAtoday

Whether Arbitrage Profit under PDA is possible or not

Call Option

If CMP of CO < TFVCO,then arbitrage profit is

possible

If CMP of CO > TFVCO,then arbitrage profit is not

possible

Put Option

If CMP of PO < TFVPO,then arbitrage profit is

possible

If CMP of PO > TFVPO,then arbitrage profit is not

possible

Steps for Arbitrage Profit

Call Option

Today1. Buy CO at CMP = a2. Assuming we have one Share, and sell it at CMP = b3. Investment (c) = (b – a) at interest rate given

At Maturity date4. Gain on Settlement of CO = (d)5. Purchase of Share from Market = (e)6. Realization of Investment (f) = (c)*(1+PIR) or (c)*ert

7. Arbitrage Profit = (d) + (f) – (e)

Put Option

Today1. Buy PO at CMP = a2. Buy one Share at CMP = b3. Borrow (c) = (a + b) at interest rate given

At Maturity Date4. Gain on Settlement of Put Option = (d)5. Sale of Share in Market = (e)6. Repayment of Borrowing (f) = (c)*(1+PIR) or (c)*ert

7. Arbitrage Profit = (d) + (e) – (f)

Question-18***Question-18A [CS-J04] [SP]

12A.11.1 Risk Neutralisation Method

(a) The current price of the share is S and it can take two possible values at maturity, S1 or S2 such thatS1 > S > S2.

Question-19 [M11-1b-5] [PM-J15-50] [PM-J15-46] [RTP-M13-16]***

Calculation of TFVCO under BM

Calculate Hedge Ratio =

Calculate Borrowing

TFVCO under BM =

C1 = Max((S1-K),0)

C2 = Max((S2-K),0)

Δ = (C1 - C2) /(S1- S2)

Borrowing = Δ*S2/(1+r) OR (Δ*S1-nC1)/(1+r)

Δ*CMP of Share – Borrowing

Whether Arbitrage Profit under Binomial Model is possible or not

Call Option

If CMP of CO > TFVCO, then arbitrage profit is possible

Today1. Sell Call Option at CMPBuy Replicating Portfolio2. Buy Δ no of shares at CMP3. Borrow at interest rate given

At Maturity date4. Loss on settlement of Call option (Writer)Settlement of Replicating Portfolio5. Sell Δ no of shares at Market Price6. Repayment of Borrowing

If CMP of CO < TFVCO, then arbitrage profit is possible

Today1. Buy Call Option at CMPSell Replicating Portfolio2. Sell Δ no of shares at CMP3. Deposit at interest rate given

At maturity Date4. Gain on settlement of Call option (Holder)Settlement of Replicating Portfolio5. Buy Δ no of shares at Market Price6. Realisation of Deposit

Calculation of TFVO under RNM

Calcualte Value of Option at expiration =

TFV of Option today =

(CMP of Share*(1+PIR) – S2)/(S1 – S2)

1 – P1

C1P1 + C2P2

Value of Option at expiration*PVF ORValue of Option at expiration* e-rt

b) Calculation of Probability in alternative way

P1 for S1 = [SP x (1+r)/SP – LP/SP]/[HP/SP – LP/SP] = [1+r – d/u – d]

Where r = PIR; u = S1/S; d = S2/S

Question-19A [M12-6a-8] [PM-J17-46] [PM-J15-43] [SP]Question–19B [SP]Question-20 [N15-1c-5] [PM-J17-47]**Question-21 [M13-1c-5] [PM-J15-42-CB]*

12A.11.2 Calculation of S1 or S2 if TFV of Option is givenQuestion-22 [SP]*

12A.11.3 Calculation of TFVPO under RNMQuestion-23**

12A.11.4 Value of Option for foreign currency under RNM

a) In case of Foreign exchange transaction, interest rate is given for LHC and RHC.

b) P1 = (CMP of Share*(1+PIRHC) - S2*(1+PILHC))/(S1*(1+PILHC) - S2*(1+PILHC))

Question-24***Question-24A [SP]

12A.11.5 Value of Option under BM or RNM if Dividend is paid

Question-25***

12A.11.6 Two Stage binomial method

In this case, we will apply movements of price for two periods.

(a) Calculation of 2 prices of UA at the end of 1st periodS1 = S*d1

S2 = S*u1

(b) Calculation of 4 prices of UA at the end of 2nd period as followsS3 = S*d1*d2 Or S1*d2

S4 = S*d1*u2 Or S1*u2

S5 = S*u1*d2 Or S2*d2

S6 = S* u1*u2 Or S2*u2

(c) Calculation of Probabilities for S1 and S2P1 = (S*(1+PIR) – S2)/(S1 – S2)P2 = 1 – P1

(d) Calculation of Probabilities for S3, S4 from S1 and Probabilities of S5, S6 from S2P3 = (S1*(1+PIR) – S4)/(S3 – S4)P4 = 1 – P3

P5 = (S2*(1+PIR) – S6)/(S5 – S6)

TFVO under BM/RNM if dividend is paid

TFVCO = Δ*(CMP of UA - PV of Dividend) – Borrowing

P1 = [CMP of UA*(1+PIR) - FV of Dividend] – S2)/(S1 – S2)

P6 = 1 – P3

(e) Calculation of Join Probabilities S3, S4, S5, S6 from SJP1 of S3 = P1*P3

JP2 of S4 = P1*P4

JP3 of S5 = P2*P5

JP4 of S6 = P2*P6

(f) Calculate Value of Option at Maturity at S3, S4, S5 and S6

Expected value of ECO at maturity = JP1*S3 + JP2*S4 + JP3*S5 + JP4*S6

(g) TFV of Option today = PV of ECO at maturity

(h) Calculation of ACO (American Call Option)

Question-26 [M09-1a-8] [PM-J15-49] [PM-J15-45]***Question-26A [SP]Question-27 [SP]

12A.12 Black Scholes Models[T-5] [M15-7c-04] [PM-J17-56] [PM-J15-52] State any four assumptions of Black Scholes Model

(a) The Black-Scholes model is used to calculate a theoretical price of an Option.

Basis and assumption for calculation of TFVO under BSM

It is based on 5 function

The model is based on thefollowing assumptions

1. CMP of Share (S)2. Strike Price (K)3. Time to expiry (t)4. Interest rate (r) = It is always Continues Compounding5. Volatility of the underlying assets (σ) = SD of continuously compounded return of the asset

1. The option is the European option;2. The underlying shares do not pay any dividend during the option period;3. There are no taxes and the transaction cost;4. Share prices move randomly in continuous time;5. The short term risk free interest rate is known and is constant during option period6. The short selling in share is permitted without penalty.

Steps for calculation of TFVO under BSM

Calculation d1

Calculate d2

Calculate N(d1) and N(d2) from Table

TFVCO =

TFVPO =

d1 = [In([S - PV of Dividend]/K) + (r + 0.5 σ2)t]/σ√tIn = Natural Log i.e. log to the base e.

d2 = d1 - σ√t

It represents the hedge ratio of shares to Options necessary to maintain a fully hedgeposition.

= (S - PV of Dividend)*N(d1) – K*e-rt xN(d2)

= K*e-rt *[1-N(d2)] – (S-PV of Dividend)*[1-N(d1)]

Note K*e-rt*N(d2) represents this borrowing which is equivalent to the present value of the exercise pricetimes an adjustment factor of N(d2)

b) The market price of the share will go down after the payment of the dividend. The value of call optionwill decrease and the value of the put option will increase as more and more dividends are paid.

Question-28 [N06-4a-8] [PM-J17-56] [PM-J15-52] [ICWA – J07]***Question-28A [N08-1a-12] [PM-53] [SP]

12A.12.1 The BSM and the dividend PaymentQuestion-29 [ICWA-D06]

12A.12.2 Value of Put Option under BSMQuestion-30 [ICWA-D08] [SP]

12A.13 Different Type of Strategy for earning profit through Option

By adopting following strategy, we may earn certain profit in option

Summary of above StrategiesSl Strategies Option Option Maturity Date Strike Price

1 Strangle Buy 1 Call Buy 1 Put Same K of the Put < K of Call

2 Straddle Buy 1 Call Buy 1 Put Same K of the Put = K of Call

3 Strips Buy 1 Call Buy 2 Put Same K of the Put = K of Call

4 Straps Buy 2 Call Buy 1 Put Same K of the Put = K of Call

5 Butter Flies Buy 1 Call at K1Buy 1 Call at K2

Sell 2 Call at K3 Same K1 > K2 andK3 = (K1+K2)/2

6 Condor Spread Buy 1 Call at K1Buy 1 Call at K3

Sell 1 Call at KSell 1 Call at K2

Same K1 < S; K = SK2 > S; K3 > K2

7 Bull Call Spread Buy 1 Call at K1 Sell 1 Call at K2 Same K1 < K2

8 Bear Call Spread Buy 1 Call at K1 Sell 1 Call at K2 Same K1 > K2

9 Bull Put Spread Buy 1 Put at K1 Sell 1 Put at K2 Same K1 < K2

10 Bear Put Spread Buy 1 Put at K1 Sell 1 Put at K2 Same K1 > K2

11 Bull Calendar Spread Buy 1 Call1 at K Sell 1 Call1 at K MP of Call1 > MP of Call2 Same

12 Bear Calendar Spread Buy 1 Put1 at K Sell 1 Put1 at K MP of Put1 > MP of Put2 Same

12A.14 TheoryQ No Exam PM-J15 PM-J16 PM-J17 RTP

T-6 N04-5c-4, M06-2b-4

[T-6] [N04-5c-4] Explain the term ‘intrinsic value of an option’ and the ‘time value of an option.

CHAPTER-12B OPTIONS - Shoundik Sinha & Co.

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