Mechanics of Options Markets Chapter 8 Mechanics of Options Markets

Assets Underlying Exchange-Traded Options Page 183-184 Stocks Stock Indices Futures Foreign Currency Bond options VIX

Options Options are generally different from forwards & futures contracts. An options gives the holder of the option the right to do something Call options Put options Buyer or holder Seller or writer Premium Strike price Maturity date

Contract Specifications Market type : N Instrument Type : OPTSTK Underlying : Symbol of underlying security Expiry date : Date of contract expiry Option Type : CE / PE Strike Price: Strike price for the contract Trading cycle: Options contracts have a maximum of 3-month trading cycle - the near month (one), the next month (two) and the far month (three).  Options, Futures, and Other Derivatives, 7th Edition, Copyright © John C. Hull 2008

Call Option A call option is a right, but not an obligation to buy an asset at a predetermined price within a specified time. Long call- expect price rise. Holder of the call has an option to exercise call or not. For this right he pays premium. Short Call-The call writer does not believe the price of the underlying security is likely to rise. The writer sells the call to collect the premium and does not receive any gain if the stock rises above the strike price.

When S<X buyer lets the call expire When S=X buyer is indifferent Payoffs (Call option) When S<X buyer lets the call expire When S=X buyer is indifferent When S>X buyer exercise the call option Loss=premium c Gain=S-X-c Options, Futures, and Other Derivatives, 7th Edition, Copyright © John C. Hull 2008

A Long position in a Call option Profit from buying one European call option: option price = $5, strike price = $100, option life = 2 months Max(S-X, 0) 30 20 10 -5 70 80 90 100 110 120 130 Payoff ($) Terminal stock price ($)

A Short position in a Call (Figure 8.3, page 182) Profit from writing one European call option: option price = $5, strike price = $100. Min(X-S, 0) -30 -20 -10 5 70 80 90 100 110 120 130 Payoff ($) Terminal stock price ($)

Put option A put option is a right, but not an obligation to sell an asset at a predetermined price within a specified time. Long put- expect price fall. Holder of the put has an option to exercise putor not. For this right he pays premium. Short put- doesn’t receive any gain if SP< Strike Price The option writer receives a premium and incurs an obligation to purchase (if a put is sold) the underlying asset at a stipulated price until a predetermined date.

Payoffs (Put option) When S>X buyer wont exercise the put When S=X buyer is indifferent When S<X buyer exercise the put option Loss=premium p Gain=X-S-p Options, Futures, and Other Derivatives, 7th Edition, Copyright © John C. Hull 2008

A Long position in a Put (Figure 8.2, page 181) Profit from buying a European put option: option price = $7, strike price = $70 Max(X-S, 0) 30 20 10 -7 70 60 50 40 80 90 100 Payoff ($) Terminal stock price ($)

A Short position in a Put (Figure 8.4, page 182) Profit from writing a European put option: option price = $7, strike price = $70 Min(S-X, 0) -30 -20 -10 7 70 60 50 40 80 90 100 Payoff ($) Terminal stock price ($)

Zero- sum game Payoff of call option X=190 Price of the assets Payoff-call buyer Payoff-call writer Buy from writer Sell in the market Profit/loss Sell to holder Buy from market 125 Holders doesn’t exercise the call option, losses premium paid Obligation of writer doesn’t arise, gains premium received 150 175 200 190 10 -10 225 35 -35

Zero- sum game Payoff of put option X=160 Price of the assets Payoff-put buyer Payoff-put writer Sell to writer Buy from the market Profit/loss Pay to holder Sell in the market 125 160 35 -35 150 10 -10 175 Holders doesn’t exercise the put option, losses premium paid Obligation of writer doesn’t arise, gains premium received 200 225

Payoffs from Options What is the Option Position in Each Case? K = Strike price, ST = Price of asset at maturity Payoff Payoff K K ST ST Payoff Payoff K K ST ST

Terminology Moneyness : At-the-money option would have no cash flows In-the-money option would have positive CFs to the buyer Out-of-the-money option would result in cash outflow if exercised Intrinsic value Time value Based on the nature of exercise Based on how they are traded & settled Based on the underlying asset on which option is created

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 Options, Futures, and Other Derivatives, 7th Edition, Copyright © John C. Hull 2008

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. Options, Futures, and Other Derivatives, 7th Edition, Copyright © John C. Hull 2008

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 pierced 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. Options, Futures, and Other Derivatives, 7th Edition, Copyright © John C. Hull 2008

Dividends & Stock Splits Suppose you own N options with a strike price of K : No adjustments are made to the option terms for cash dividends When there is an n-for-m stock split, the strike price is reduced to K/(1+ bonus ratio) the no. of options is increased to N*(1+bonus ratio) Stock dividends are handled in a manner similar to stock splits

Dividends & Stock Splits (continued) Consider a call option to buy 100 shares for $20/share How should terms be adjusted: for a 2-for-1 stock split? for a 25% stock dividend?