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topic05_note - EC372 Bond and Derivatives Markets Topic#5...

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EC372 Bond and Derivatives Markets Topic #5: Options Markets I: fundamentals R. E. Bailey Department of Economics University of Essex Outline Contents 1 Call options and put options 1 2 Payoffs on options 3 3 Option-like assets 6 4 Upper and lower bounds for option prices 6 4.1 Lower bounds for European option premiums . . . . . . . . . . . . . . . . . . . . . 6 5 The put-call parity relationship 8 Reading: Economics of Financial Markets , chapter 18 1 Call options and put options Call options and put options Options provide a right but not an obligation to take an action Call option: the right but not the obligation to buy , on or before the expiry date, an underlying asset for the exercise price Put option: the right but not the obligation to sell , on or before the expiry date, an underlying asset for the exercise price Holders (buyers) and Writers (issuers) Holder ’ owns the option: has ‘long’ position (an asset) Writer ’ has issued the option: has a ‘short’ position (a liability) Two styles: American style: exercise at any time prior to expiry date European style: exercise at expiry date only Options can die, unexercised – options are exercised only if it is profitable to do so 1
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Call Option Holder : May buy asset for Exercise price from Writer. Writer : Must sell asset for Exercise price, at Holder’s discretion. Put Option Holder : May sell asset for Exercise price to Writer. Writer : Must buy asset for Exercise price, at Holder’s discretion. Option contracts and markets The option contract specifies: Underlying asset Expiry date, T Exercise (or, strike) price, X Whether the option is call or put Whether the option is American or European Exotic options: more complicated specification The market determines: Underlying asset price, S Option premium option price : c = European call; C = American call; p = European put; P = American put. Interest factor: R ( t, T ) ($1 invested at t becomes R ( t, T ) at T ) Time to expiry: τ = T - t , where t = ‘today’ Trading in options Exchange traded options: standardized, anonymous, guaranteed by exchange authorities. Over The Counter (OTC) options: private agreements between named counter-parties. Margin deposits Option buyer pays the premium, no further obligation Option writer makes margin deposit – collateral for contingent liability Termination of an option contract: 1. Option dies , unexercised at T 2. Holder exercises the option 3. Offsetting trade (holder sells or writer buys) 2
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2 Payoffs on options Payoffs on options Assumption: frictionless markets European call option payoff at T : c T = max[ S T - X, 0] c T = S T - X , if S T X c T = 0 , if S T < X (option dies) European put option payoff at T : p T = max[ X - S T , 0] p T = X - S T , if S T X p T = 0 , if S T > X (option dies) American options: can be exercised at any time, hence premiums cannot be less than payoff from immediate exercise: American call C ( t ) max[ S ( t ) - X, 0] at every t T American put P ( t ) max[ X - S ( t ) , 0] at every t T 3
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