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Unformatted text preview: Hint: One way is to use Lemma 2.3.4. c) Let : (0 , ) [0 , ) be a function such that R d = 1. Show that P [ A ] := Z A ( ) d e P is also a risk-neutral measure. d) Show that E [ ( S T K ) + ] = Z v ( T,S ,s ) ( s ) ( ds ) , where v ( T,S ,s ) is the price of the plain vanilla European call option ( S T K ) + in a Black-Scholes model with zero interest rate, spot S , and volatility s > 0. e) Conclude that inf P P E [ ( S T K ) + ] = ( S K ) + and sup P P E [ ( S T K ) + ] = S , where P denotes the set of all risk-neutral measures, and give a verbal interpretation of this fact. Hint: We already know from class and from Exercise 2 in homework set 4 that v ( T,S ,s ) & ( S K ) + for s 0 and v ( T,S ,s ) % S as s . 1...
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- Spring '08