1. Question (a) Let W be a standard Brownian motion and Ft the associated filtration. Using Ito's lemma, show that e 1 2 2 t+Wt is a Ft-martingale, where is a non-negative constant.

(b) In the Black-Scholes market, a European call option is currently $0.25 more expensive than the corresponding European put option on the stock. It both the call and the put options expire in one year with the same strike $65, then calculate the continuously compounded risk-free interest rate. The current price of the stock is $63 and a dividend is $0.50 is paid in six months.