Exercise 5.2 (Exchange Option) Consider the price of an exchange option (E) = EQ[max{X, Y }], where

Exercise 5.2 (Exchange Option) Consider the price of an exchange option

π(E) = EQ[max{X, Y }], where the option holder can receive a better asset at the maturity. Supposing Y > 0 a.s., define η = Y/EQ[Y ], and consider a new probability measure Q^Y by Q^Y (A) = E^Q[η1A]. Show that

Note that the second quantity is the call option price of the underlying asset X/Y with strike price 1 evaluated under the new probability measure QY .

Transcribed Image Text:

(E) = E[Y] + E[Y]E Y - +