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Unformatted text preview: Slide 91 American vs. European Options Chapter 3, Section 3.2 Slide 92 Review • Putcall parity for European options: C ( S , Q , T – t ) – P ( S , Q , T – t ) = F P t,T ( S ) – F P t,T ( Q ) = PV(F t,T (S)) – PV(F t,T (Q)) • PC parity as a “cookbook”: – Synthetic forwards (long call+short put), synthetic Tbills – Call = levered position in stock + insurance (put) – Put = short position in stock + insurance (call) • Bounds on option prices: – Bounds implied by putcall parity – Options with different strike prices: the price of an option is given by a Slide 92 Review • Putcall parity for European options: C ( S , Q , T – t ) – P ( S , Q , T – t ) = F P t,T ( S ) – F P t,T ( Q ) = PV(F t,T (S)) – PV(F t,T (Q)) • PC parity as a “cookbook”: – Synthetic forwards (long call+short put), synthetic Tbills – Call = levered position in stock + insurance (put) – Put = short position in stock + insurance (call) • Bounds on option prices: – Bounds implied by putcall parity – Options with different strike prices: the price of an option is given by a monotone and convex functions of the strike price Slide 93 Today • American vs. European options – Early exercise – How option prices depend on the time to expiration • Supplementary material: exdividend arbitrage • Foundations for option pricing Slide 94 American vs. European options Since an American option can be exercised at anytime, whereas a European option can only be exercised at expiration, an American option must always be at least as valuable as an otherwise identical European option: C Amer ( S , K , T ) > C Eur ( S , K , T ) P Amer ( S , K , T ) > P Eur ( S , K , T ) Slide 95 Option price boundaries • The call price cannot – be negative – exceed stock price – be less than price implied by putcall parity using zero for put price: S > C Amer ( S , K , T ) > C Eur ( S , K , T ) > max [0, PV 0,T ( F 0,T ) – PV 0,T ( K )] • The put price cannot – be negative – be more than the strike price – be less than price implied by putcall parity using zero for call price: K > P Amer ( S , K , T ) > P Eur ( S , K , T ) > max [0, PV 0,T ( K ) – PV 0,T ( F 0,T )] Slide 96 Early Exercise of American Options • An American call option on a nondividendpaying underlying asset should never be exercised early: – Throw away the “put protection” – Accelerate payment of strike C Amer > C Eur ( S , K , Tt...
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This note was uploaded on 10/25/2009 for the course 15 15.402 taught by Professor Bergman during the Fall '09 term at MIT.
 Fall '09
 Bergman

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