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Unformatted text preview: Intro to options • Definition : contractual agreement giving owner the right (not obligation) to buy or sell an asset at a predetermined price on or before a specified date • Features: • To buy ( call option; c); to sell ( put option; p) • (predetermined) exercise price , E (i.e., strike) • Specified ( expiration ) date, T • If can be exercise before T; American option • If can be exercised only at T; European option When to exercise…. • Call options: owner will exercise if the asset price, S, is greater than E • Put options: owner will exercise if asset price S is less than E • Call: inthemoney if S>E at T; else outof money • Put option: inthemoney if S<E at T; else outofmoney Why options? • First traded on the CBOE in 1973 • seminal academic paper by Black & Scholes 1973 (rejected at topjournal) • Scholes gets N.P; Black ineligible – widely used in managerial “compensation” packages – buy a call if belief asset price will rise – buy a put if own asset and belief price may fall – Buy a combination as speculative strategy Value of call option at expiration S T E Value of a put option at expiration E S T Example • Suppose you purchased a 3 month call option on INTEL at $8; the exercise price is $26; current price of INTL is $28 • Graph the value of the call at T=3 • Graph the profit function • Find the breakeven price • Graph the seller’s payoff Example: the buyer’s position S T 26 34 pr of it S if S if S T T T =  ≤ 26 8 26 8 26 26 Seller’s (short) position….. 26 34 S T prof it if S S if S T T T = <   ≥ 8 26 26 8 26 ( ) American vs. European options….. • At expiration, the two types have the same value • But American can be exercised before expiration – If any time t, S<E, do not exercise – But if S>E at any t<T, not always optimal to exercise; value embedded from waiting could be higher – So valuation of American is complicated Lower bound for call price • Assumption: – asset pays no dividend – assume a risk free rate of return of r% • Let c=call price, S t =current price of asset; E=exercise price; and T=expiration date • Then; • Proof: A standard proof …create and compare values of two portfolios c S Ee t rT ≥  Strategies:… • Portfolio A: one European call option plus cash of $(EerT ) invested in riskfree asset – Value of portfolio A: $(c+ EerT ) • Portfolio B: a unit of the stock – Value S t • At time T, either (i) S T >E, or (ii) S T <E – Case (i) “A” is worth $S T ; “B” is worth $S T – Case (ii) “A” is worth $E; “B” is worth $S T • So “A” must be worth at least “B” now. Example… • Find the lower bound for the price of a European call option on a nondividend paying stock if the stock price is $51, E=$50 and has 6 months to expire. Let r=12% • Ans: • Exx: Show that lower bound for a European put on a nondividend paying stock is: c S Ee e t rT ≥  =  =  51 50 91 0 12 2 ( . )/ $3 ....
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This note was uploaded on 03/26/2008 for the course EC 150 taught by Professor Kutsoati during the Spring '08 term at Tufts.
 Spring '08
 KUTSOATI
 Economics

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