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X2Options_A_vs_E

X2Options_A_vs_E - American vs European Options Chapter 3...

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Slide 9-1 American vs. European Options Chapter 3, Section 3.2
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Slide 9-2 Review Put-call 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 T-bills Call = levered position in stock + insurance (put) Put = short position in stock + insurance (call) Bounds on option prices: Bounds implied by put-call parity Options with different strike prices: the price of an option is given by a monotone and convex functions of the strike price
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Slide 9-3 Today American vs. European options Early exercise How option prices depend on the time to expiration Supplementary material: ex-dividend arbitrage Foundations for option pricing
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Slide 9-4 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 )
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Slide 9-5 Option price boundaries The call price cannot be negative exceed stock price be less than price implied by put-call 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 put-call 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 )]
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Slide 9-6 Early Exercise of American Options An American call option on a non-dividend-paying underlying asset should never be exercised early: Throw away the “put protection” Accelerate payment of strike C Amer > C Eur ( S , K , T-t ) = S t –K + P Eur ( S , K , T-t ) + K (1- e -r ( T-t ) ) > max(0, S t K) If there are dividends, early exercise may be optimal. Stock price is sufficiently high (option is in the money) Dividends are sufficiently high C Amer > C Eur ( S , K , T-t ) = S t –K +P Eur ( S , K , T-t )+ K (1- e -r ( T-t ) ) - PV(Div) >max(0, S t –K) -PV(Div)
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Slide 9-7 Early Exercise of American Options An American put on a non-dividend paying underlying asset may be exercised early if the option is sufficiently in the money (stock price is sufficiently low).
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