Exercise 5.1 Suppose that the price of a call option is given by (C) = E Q

Exercise 5.1 Suppose that the price of a call option is given by π(C) =

E^Q[{S − K}₊], where S denotes the future price of the underlying asset.

Supposing S > 0 a.s., define η = S/E^Q[S], and consider a new probability measure eQ by eQ

(A) = E^Q[η1A]. Show that

Here, eQ {S > K} is the probability that the call option will be in-the-money, that is, S > K, under the new probability measure eQ ; cf. (5.15).

Transcribed Image Text:

T(C) = E[S]Q{S > K} - KQ{S > K}.