OPTIONS -BASICS

• Terminology of Options• Call Option• Put Option• Moneyness of Options• Types of Options• Trading and Settlement• Differences with Forward

Options

• Forwards and futures are the contracts that create mutual and equal obligations on both the parties, that is binding.

• Options create obligation on one party while a right on another.

Call and Put Option• CALL OPTION: A right to BUY the underlying asset at

predetermined price within specified interval of time is called a CALL option.

• A right to buy a share of Reliance at say Rs 1,000 in 3 months is a call option.

• PUT OPTION:A right to SELL the underlying asset at predetermined price within specified interval of time is called PUT option.

• A right to sell a share of Reliance at say Rs 1,000 in 3 months is a put option.

Buyer and Seller

• BUYER or HOLDER: The person who obtains the right to buy or sell but has no obligation to perform is called the owner/ holder of the option.

• WRITER or SELLER:One who confers the right and undertakes the obligation to the holder is called seller/writer of an option.

Option Premium• While conferring a right to the holder, who is under no

obligation to perform, the writer is entitled to charge a fee upfront.

• This upfront amount is called the premium. • This is paid by holder to the writer to induce him to

grant the right.• The amount belongs to writer irrespective of whether

the option is exercised or not. • It is not adjustable against the future payment that

arise upon exercise of option.

Maturity and Strike Price• STRIKE PRICE:The predetermined price at the time of

buying/writing of an option at which it can be exercised is called the strike price.

• It is the price at which holder of an option buys/sells the asset.

• STRIKE DATE/MATURITY DATE: The right to exercise the option is valid for limited time.

• The latest time when the option can be exercised is called the time to maturity. It is also referred as expiry/maturity date.

Call Option

• A call option is a right but no obligation to buy an asset at predetermined price within the specified time

• Holder of call option exercises the option when price of underlying asset is more than the strike price.

• If spot price is less than the strike price the holder lets the option expire as it is worthless.

Call Option –PayoffValue of the call option = Max (0, S -X) –c

Put Option

• A put option is a right but no obligation to sell an asset at predetermined price within the specified time

• Holder of put option exercises the option when price of underlying asset is less than the strike price.

• If spot price is more than the strike price the holder lets the option expire as it is worthless.

•

Put Option -Payoff

Features of Options

• Options have unsymmetrical non-linear pay off, unlike forwards and futures because they do not create an obligation.

• Options are zero-sum game; the gain of holder is the loss of writer and vice-versa.

Moneyness of Options

Types of Options

• Options can be categorized in number of ways, such as:• Based on nature of exercise of options,• Based on how are they generated, traded and settled,• Based on the underlying asset on which options are created.

• American and European American options can be exercised at any point of time before the expiry date

of the option while European options are exercisable only upon maturity.

• OTC and Exchange Traded Options can be either tailor made to the requirement or may be exchange

traded in the standardised form.

Trading And Settlement• Prior to expiry options can be settledby exercising if American or by selling them prior to maturity, On maturity, they expire automatically.

• For exchange traded option the buyer and seller enter the contract, with buyer and seller unknown to each other.

• Assignment: When buyer of option exercises it the exchange assigns a seller who settles the claim.

Naked option• A trading position where the seller of an option contract does not

own any, or enough, of the underlying security to act as protection against adverse price movements.

• Naked trading is considered very risky since losses can be significant.• An options trader could sell, for example, call options with a strike

price of $10. If the stock's price rises to $20 or $30 on good news, and the option is naked (the seller does not own the underlying stock).

• He or she would be required to buy the specified number of shares at the current price, and sell them to the option buyer for the $10, resulting in a significant loss.

Covered Options

• When an option position is opened by selling an option, while simultaneously owning an equivalent position in the underlying security, it is called a "covered" position.

• Calls are covered by owning the underlying security and puts are covered with a short position in the underlying security.

• Covered Call (buy-write)When an investor owns a security and sells calls on that security, they are "covered

calls" as long as the investor owns 100 shares of the security for each call that is sold.

The sold calls are covered because the options can be exercised by selling the security to the option holder at the strike price of the call options.

Covered Put• When an investor has a short position in a security and sells puts on that short

security, they are "covered puts" • as long as the investor is short 100 shares of the security for each put that is

sold. The sold puts are covered because the options can be exercised by buying the security to close out the short position at the strike price of the put options.

Option Pricing • Determination of option premium has been major area of

research. But there also exist simple arbitrage based rule which explain a lot about the option price behaviour.

• Options are uneven contracts that gives right to one i.e. the holder or buyer while binds the other party i.e. writer or seller to a contract.

• Buyer can not enjoy the right free of cost else it becomes a lop-sided contract.

• Buyer of the right has to induce the writer to confer such right on him and undertake an obligation. The amount that is paid by the buyer of the option to the writer is called premium.

Intrinsic Value & Time Value

• The option premium consists of two components; the intrinsic value, and the time value

Two important factors that determine the price are: • the extent to which the option is in-the-money, and • the chances that before expiry the option will

become deeper in-the-money or will turn into in-the-money if it is presently out-of-the-money

Intrinsic Value • The value attached to the option if it is exercised now is called the

intrinsic value of the option. • The difference between spot price and exercise price will determine

this value. • The intrinsic value is• For call option :max {(S -X), 0}, and • For put option:max {(X -S), 0}

• Intrinsic value cannot be negative.• The least intrinsic value is for out-of-the-money option, which is

equal to zero.• An option cannot sell below its intrinsic value.

Time Value • The time value is the excess of actual value over intrinsic

value.• The value attached to the chances that strike price will be

moved in times to come before expiry is called the time value of an option.

• Time value of an option = Actual Price –Intrinsic Value• Time value cannot be negative. At best/worst it can have

zero value.• Time value of the option is greatest for ATM options. The

entire premium paid for ATM options is attributable to the time value as the intrinsic value of the option is zero.

Example–Intrinsic and Time Value• A 2-month call option on the Infosys with strike of Rs 2,100 is selling

for Rs140 when the share is trading at Rs 2,200. Find out the following:What is the intrinsic worth of the call option?

Why should one buy the call for a price in excess of intrinsic worth?

• a) The intrinsic worth of the option is (S –X) = 2,200 –2,100 = Rs. 100• b) The price of the option is Rs. 140 i.e. Rs. 40 more than the

intrinsic worth. This is the time value of the option and is paid because there are chances that in next two months the price of Infosys may rise further and holder stands to gain more than Rs. 100.

Option Value and Strike Price

• Call with higher strike price would cost less than the call with lower strike, and

• Put with lower strike price would cost less than the put with higher strike.

• No arbitrage

Put Call Parity

• Put call parity establishes the relationship of call and put prices for European options.

• The options must be on the same asset, with same strike price and with same time to maturity.

• For the same underlying asset, same exercise price and same time to expiry the call price would exceed the put price by the amount of differential of spot price and the present value of the exercise price.

Outcome of the Portfolio With no uncertainty in the value of the portfolio at expiration we can

state the following:

• An investor can borrow an amount equivalent to the present value of exercise price to create the portfolio,

• And since the value of the portfolio is certain at expiration date the lenders would lend the money at risk free rate,

• The portfolio can be funded by borrowing an amount equal to the present value of the maturity amount of X, and

• This portfolio can be said to be equivalent to a bond which matures to the value equal to X and with maturity coinciding.

Put Call Parity -Equation • Initial cost of the portfolio of long stock, short call and long put = Amount that can be borrowed at risk free rate = Present value of the bond maturing to the exercise price

• If S is the current price of the share, c the call premium and p the put premium, then

• S -c + p = PV of X = X/(1+r)• = X e-rt (for continuous compounding)• Or c –p = S –X e-rt

• If the put call parity does not hold it presents an arbitrage opportunity by forming portfolios of call, put, bond and stock.

Implications –Put Call Parity

• Put call parity also links the equity, bonds and derivative markets for any inconsistent returns in any of them restoring the balance among the three.

• Put call parity also helps synthesise the stock, call, put and bond with the help of other three.

c + X e-rt = p + S

American Vs European Call • American call option is priced equal to European call.• Though it seems that flexibility of American option should be

more valuable than the necessity of exercising on maturity.• By exercising early one realizes only the intrinsic value and

foregoes time value.• An option would always have some time value as long as there

is time left for its expiration. • Selling a call is would fetch more value than exercising it, and

hence one would always sell rather than exercise, till maturity.• Therefore American call would be priced same as European

call.

American Vs European Put • The minimum value of European put is given by X e-rt –S.• The intrinsic value of put is X –S. • With positive rates of interest the minimum value of put would

be less than its intrinsic worth. • For extreme case of stock price of zero, exercise of the put would

have payoff of X. One cannot get higher payoff than this. If one waits further he only stands to lose. There are circumstances when put option is more beneficial to exercise before maturity.

• Therefore, American put could be more valuable than European put.

Put Call Parity -American Options

• With American call valued same as European call, and American put more valuable than the European put the put call parity would not be an equality.

• For American option put call parity would following inequality:

• pa≥ p = c + X . e-rt -S • Since ca= c the put call parity for American options

as below:• pa≥ ca+ X . e-rt -S

Put Call Parity –With Dividend • Put call parity for European option with the underlying

paying dividend before expiry of options is modified by the amount of dividend.

• Put call parity for dividend paying stock with dividend of D at time t’ would be:

• c + X e-rt= p + S –D e-rt

• Put call parity for dividend paying stock with continuous dividend of q would be:

• c + X e-rt = p + S e-qt

Put Call Parity –Currency Options• Put call relationship rests on the equivalency of portfolio a)

call option and bond that matures to X, with b) put option and c) the underlying asset.

• For options on currencies the underlying asset is foreign currency.

• The underlying asset, the foreign currency is like a dividend paying asset that yields risk free interest in foreign currency, rf.

• Therefore today’s equivalent would be S e-rft

• Therefore put call parity for currency options would be c + X e-rt = p + S e-rft