Derivatives•Derivatives are financial instruments whose value depends on something else (such as stock, stock index, foreign currency, bond or commodity price)

•Examples of derivatives include options, futures, forwards and swaps

Options

• Options Contracts are the agreements between two parties to buy or sell a particular security at a predetermined price on or before a particular date

• An option is a contract which gives its holder the right, but not the obligation, to buy (or sell) an asset at some predetermined price within a specified period of time.

• Main characteristic of options: It does not obligate its owner to take any action. It merely gives the owner the right to buy or sell an asset.

Options Terminology• Call option: An option to buy a specified number of shares of a

security within some future period.• Example : Assuming ACC company shares are trading at Rs 40

right now. You bought a call stock options contract that allows you to buy ACC shares at Rs40 anytime before it expires in 2 months. 1 month later, ACC company shares are trading at Rs50 but you still own the right to buy it at Rs 40 through the call stock options.

• Put option: An option to sell a specified number of shares of a security within some future period.

• Assuming you own ACC company shares trading at Rs 40 right now. You bought a put stock options contract that allows you to sell your ACC shares at Rs 40 anytime before it expires in 2 months. 1 month later ACC company shares are trading at Rs 30 but you still own the right to sell it at Rs 40 through the put stock options.

• Exercise (or strike) price: The price stated in the option contract at which the security can be bought or sold.

• `

• Option price: The market price of the option contract.

• Expiration date: The date the option matures.

• Exercise value: The value of a call option if it were exercised today = Current stock price - Strike price.Note: The exercise value is zero if the stock price is less than the

strike price.

• Covered option: A call option written against stock held in an investor’s portfolio.

• Naked (uncovered) option: An option sold without the stock to back it up.

Options Moneyness . It describes the relationship between options strike price and the price of

the underlying asset and determines if intrinsic value exists in an option.

• In-the-money : A call whose exercise price is less than the current price of the underlying stock.

It is the state of options moneyness where intrinsic value exists in an option.

Call Options are In The Money when its strike price (exercise price) is lower than the price of the underlying asset and

Put Options are In The Money when its strike price is higher than the price of the underlying asset.

•At The Money (ATM) At the money is the state of options moneyness where the strike price of an option is equal to the price of the underlying asset. •Out of The Money (OTM) Out of the money is the state of options moneyness where no intrinsic value exists and that the price of an option consists only of extrinsic value. A call option is Out of The Money when its strike price is higher than the price of the underlying asset and

A put option is Out of The Money when its strike price is lower than the price of the underlying asset.

• Out-of-the-money call: A call option whose exercise price exceeds the current stock price.

• LEAPs: Long-term Equity Anticipation securities that are similar to conventional options except that they are long-term options with maturities of up to 2 1/2 years. As long term in the money LEAPS call options behave almost exactly like its underlying asset, it is a great way to leverage the same amount of money to control more quantity of the underlying asset.

• Example : Assuming you have Rs1000 to invest on the shares of XYZ company trading at Rs40. Its Rs40 strike price call options is trading at Rs2.00. You could control 25 shares (Rs1000 / Rs40 = 25) of XYZ company through buying its stocks or you could control 500 shares of XYZ company through buying 2 contracts of its call options (Rs1000 / Rs2 = 500)

• Being able to control more shares with the same amount of money also means that profitability is far greater trading Stock Options on the same amount of money relative to trading stocks.

• Example : Assuming XYZ company rallies from Rs40 to Rs60.

Buying Shares: (Rs60 - Rs40) x 25 = Rs500 profit

Buying Call Options: (Rs60 - Rs40) x 500 = Rs10,000 profit

• FLEX : FLEX stands for Flexible Exchange Index options. It enables option traders to customise key contract terms like expiration date, exercise style and exercise price.

• Lot Size : The number of shares of the underlying stock that is represented with each stock options contract. In the market, each Stock Options contract usually represents 100 shares of the underlying stock.

• Exchange Traded Stock Options : These are Stock Options which anyone can trade with in the public stock options trading exchanges through a broker. They are also known as "Listed Options".

• Over-The-Counter (OTC) Stock Options : These are Stock Options which are highly customized and traded in Over-The-Counter (OTC) markets which are less liquid and less assessable to the public.

• Exotic Options : Exotic options are Stock Options that are highly customized and complex and usually traded only in OTC markets.

• Employee Stock Options : Stock Options given to employees by their companies. The company in this case acts as the seller of the stock options to employees and usually gives these Employee Stock Options as incentives.

Factors that influence the Options Price

If this variable increases

Call price Put price

Stock Price (S) Increases Decreases

Exercise Price (X)

Decreases Increases

Volatility (б) Increases Increases

Time to expiration (t)

Increases Increases

Interest rate (rf)

Increases Decreases

Dividend payouts (D)

Decreases Increases

Options Premium

Exercise price = Rs25.Stock Price Call Option PriceRs25 Rs 3.00 30 7.50 35 12.00 40 16.50 45 21.00 50 25.50

Price of Strike Exercise ValueStock (a) Price (b) of Option (a) - (b)Rs 25.00 Rs 25.00 Rs 0.00 30.00 25.00 5.00 35.00 25.00 10.00 40.00 25.00 15.00 45.00 25.00 20.00 50.00 25.00 25.00

Exercise Value Mkt. Price Premium of Option (c) of Option (d) (d) - (c) Rs 0.00 Rs 3.00 Rs 3.00

5.00 7.50 2.50 10.00 12.00 2.00 15.00 16.50 1.50 20.00 21.00 1.00 25.00 25.50 0.50

What happens to the premium of the option price over the exercisevalue as the stock price rises?The premium of the option price over the exercise value declines as the stock price increases.

This is due to the declining degree of leverage provided by options as the underlying stock price increases, and the greater loss potential of options at higher option prices.

Intrinsic ValueStock Option Pricing Two Main Components, Intrinsic Value & Extrinsic Value The price of an option contract, or sometimes known as the option premium, consists of 2 main

components : Intrinsic Value and Extrinsic Value, governed by the principle of Put Call Parity.

• The intrinsic value of a call option is obtained simply by deducting the prevailing market price of the underlying stock by the strike price of the call option.

Intrinsic Value For Call Option = Stock Price - Call Strike Price• Example : Assume ACC is trading at Rs350 and it's March Rs 300 Call Option is

asking for Rs 52.00. It's intrinsic value would be : Rs350 - Rs300 = Rs50.• The intrinsic value of a put option is obtained simply by deducting the strike price

of the put option by the prevailing market price of the underlying stock.

Intrinsic Value For Put Option = Put Strike Price - Stock Price • Example : Assume ACC is trading at Rs 350 and its March Rs 400 Put option is

asking for Rs51.80. It's intrinsic value would be : Rs 400 – Rs 350 = Rs50.

• A negative value indicates that there is no intrinsic value. An option which contains intrinsic value is known as an In The Money (ITM) Option.

Extrinsic Value

• Extrinsic Value, or sometimes known as the Premium Value or Time Value, of an option is the part of the price that is determined by factors other than the price of the underlying stock.

• This is what you are paying the seller of the option for the risk that the seller is undertaking for selling you the option contract.

• determined by 4 main factors : Time to expiration, Interest Rates, Volatility and Dividends payable.

• The extrinsic value of a call option is obtained simply by deducting the price of the call option by it's intrinsic value.

• Extrinsic Value Of Call Option = Call Option Price - Intrinsic Value

• Following up from the previous example : Assume ACC is trading at Rs 350 and it's March Rs 300 Call Option is asking for Rs 52.00. It's intrinsic value is Rs 50. It's Extrinsic Value would be Rs 52 – Rs 50 = Rs2.

• The Extrinsic Value of a put option is obtained simply by deducting the price of the put option by its intrinsic value.

• Extrinsic Value of Put Option = Put Option Price - Intrinsic Value

• Following up from the previous example: Assume ACC is trading at Rs 350 and its March Rs 400 Put option is asking for Rs 51.80. It's intrinsic value is Rs 50. It's Extrinsic Value would be Rs 51.80 – Rs 50 = Rs 1.80.

Put Call Parity

• Put Call Parity - Definition Put Call Parity is an option pricing concept that requires the extrinsic values of call and put options to be in equilibrium so as to prevent arbitrage. Put Call Parity is also known as the Law Of One Price.

• Put Call Parity - Introduction Put-call parity is an important principle in options pricing first identified by Hans Stoll in his paper, The Relation Between Put and Call Prices, in 1969.

• It states that the premium of a call option implies a certain fair price for the corresponding put option having the same strike price and expiration date, and vice versa. S

• upport for this pricing relationship is based upon the argument that arbitrage opportunities would materialize if there is a divergence between the value of calls and puts.

• The relation doesn't hold for American-style options.

• Arbitrageurs would come in to make profitable, riskless trades until the put-call parity is restored.

• To begin understanding how the put-call parity is established, let's first take a look at two portfolios,

• A and B. Portfolio A consists of a European call option and cash equal to the number of shares covered by the call option multiplied by the call's striking price.

• Portfolio B consist of a European put option and the underlying asset. Note that equity options are used in this example.

• Portfolio A = Call + Cash, where Cash = Call Strike Price

• Portfolio B = Put + Underlying Asset

• It can be observed from the diagrams above that the expiration values of the two portfolios are the same.

• Call + Cash = Put + Underlying Asset• Eg. JUL 25 Call + Rs2500 = JUL 25 Put + 100 ACC

Stock• If the two portfolios have the same expiration value,

then they must have the same present value. • Otherwise, an arbitrage trader can go long on the

undervalued portfolio and short the overvalued portfolio to make a riskfree profit on expiration day.

• Hence, taking into account the need to calculate the present value of the cash component using a suitable risk-free interest rate, we have the following price equality:

• Each of the securities in the Put Call Parity Theorem can thus be expressed as:

Stock Price = C - P + X / (1+RFR)t

Put Premium = C - S + X / (1+RFR)t

Call Premium = S + P - X / (1+RFR)t

Present Value Of Strike Price = S + P - C

The above relationships assumes that no dividends are being paid. The Put Call Parity Theorem for dividend paying stocks is:

P = C - S + x/(1+RFR)t + d/(1+RFR)t

C = P + S - x/(1+RFR)t - d/(1+RFR)t

Where d = Dividend To Be Paid• Put Call Parity - Limitations • Put Call Parity applies mainly to European style options as American Style options allows early

exercise which can result in profit opportunities that lies beyond the Put Call Parity Theorem. Put Call Parity - Assumptions The assumptions under the Put Call Parity Theorem are: 1. Constant Interest Rate 2. Future dividends are known for sure

Black-Scholes Model

• Black-Scholes Model – Definition• A mathematical formula designed to price an option as a

function of certain variables-generally stock price, striking price, volatility, time to expiration, dividends to be paid, and the current risk-free interest rate.

• Options traders compare the prevailing option price in the exchange against the theoretical value derived by the Black-Scholes Model in order to determine if a particular option contract is over or under valued, hence assisting them in their options trading decision.

• The difference in the pricing of European options and American options is that options pricing of European options do not take into consideration the possibility of early exercising.

• American options therefore command a higher price than European options due to the flexibility to exercise the option at anytime.

The exact 6 assumptions of the Black and Scholes Model are :

• 1. Stock pays no dividends • 2. Option can only be exercised upon

expiration • 3. Market direction cannot be predicted,

hence "Random Walk" • 4. No commissions are charged in the

transaction • 5. Interest rates remain constant • 6. Stock returns are normally distributed,

thus volatility is constant over time

Known Problems of the Black-Scholes Model• First, the Black-Scholes Model assumes that the risk-free rate

and the stock’s volatility are constant. This is obviously wrong as risk free rate and volatility fluctuates according to market conditions.

• Second, the Black-Scholes Model assumes that stock prices are continuous and that large changes (such as those seen after a merger announcement) don’t occur.

• Third, the Black-Scholes Model assumes a stock pays no dividends until after expiration.

• Fourth, analysts can only estimate a stock’s volatility instead of directly observing it, as they can for the other inputs.

• Fifth, the Black-Scholes Model tends to overvalue deep out-of-the-money calls and undervalue deep in-the-money calls.

• Sixth, the Black-Scholes Model tends to misprice options that involve high-dividend stocks.

• Black-Scholes Formula

• C0 = S0N(d1) - Xe-rTN(d2) Where:d1 = [ln(S0/X) + (r + σ2/2)T]/ σ √T And:d2 = d1 - σ √T

• And where:C0 = current option valueS0 = current stock priceN(d) = value of cumulative normal distribution evaluated at dX = exercise pricee = 2.71828, the base of the natural log functionr = risk-free interest rate (annualized continuously compounded rate on a safe asset with the same maturity as the expiration of the option; usually the money market rate for a maturity equal to the option’s maturity.)T = time to option’s maturity, in years (time remains before the expiration date expressed as fraction of a year)ln = natural logarithm functionσ = standard deviation of the annualized continuously compounded rate of return on the stock

Here's the Black-Scholes Model for Dividend Stocks formula :

• C = SN(d1) - Xe-rTN(d2)

Cit = S0 (N d1) - Ke-rT N(d2) Pit = Ke−rT N(−d2) − S0 N(−d1)

Where: d1 = [ln(S0/X) + (r - d + σ2/2)T]/ σ √T

And: d2 = d1 - σ √T

Implied Volatility

• Option traders can never fully understand the dynamics behind pricing of stock options and stock option price movements without understanding what is volatility and implied volatility.

• the implied volatility of an option contract is the volatility implied by the market price of the option based on an option pricing model.

• IV is inferred in the market from option prices using a suitable option pricing model. It is a measure of the amount and speed of price change in either direction. This indicates the expensiveness of option premium for the traders.

• In other words, it is the volatility that, when used in a particular pricing model, yields a theoretical value for the option equal to the current market price of that option.

• the implied volatility of an option is a more useful measure of the

option's relative value than its price. This is because the price of an option depends most directly on the price of its underlying security.

Charting Implied Volatility

• Implied volatility of options of the same underlying asset and expiration date are often plotted to arrive at it's Volatility Smile or Volatility Skew.

• Volatility Smile or Volatility Skew of implied volatility facilitates option traders to see a glance which options are more expensive and also indicative of whether the underlying stock is expected to make big moves in the short run.

• The Volatility smile is a variation of implied volatility with respect to options moneyness. The estimation of volatility smile, basically involves evaluating the relationship between the implied volatility and the level of moneyness for any given option.

• implied volatility function using linear and quadratic models given in (4) and (5) as suggested by previous literature [see: Shimko (1993), Dumas et al (1998) and Beber (2001)]:

• Linear: Y = 0 + 1X + • Quadractic:Y = 0 + 1X + 2X

2 + • (Where, Y represents the implied volatility and X

represents moneyness of the options. The simplicity in the case of two models is maintained in an endeavour to avoid overparameterization and obtain better estimates.

option trading strategies

• There are only 2 opinions on implied volatility from which you can hope to profit from trading volatility of stocks. Bullish or Bearish. Period. Listed here are some option trading strategies you can use to profit from both views.

Bullish On Implied Volatility • These option strategies allows you to profit from an increase in implied volatility without any

increase in the stock. Long Straddle Long Strangle Short Condor Short Butterfly

• The perfect strategy to profit from a bullish view on volatility has to be through the use of Delta and Gamma Neutral Hedging.

Bearish On Implied Volatility • These option strategies allows you to profit from a decrease in implied volatility without any

decrease in the stock. Short Straddle Short Strangle Long Butterfly Spread Long Condor Ratio Spreads

• Contango is when the futures price is above the expected future spot price. Because the futures price must converge on the expected future spot price, contango implies that futures prices are falling over time as new information brings them into line with the expected future spot price.

• Normal backwardation is when the futures price is below the expected future spot price. This is desirable for speculators who are "net long" in their positions: they want the futures price to increase. So, normal backwardation is when the futures prices are increasing.