1. Consider a Cox-Ross-Rubinstein model with two periods (N = 2) and with interest rate r = 0.03. Assume the risky asset S has initial value So = 100 and at every step, it can move up by a factor 1 +u with u = 0.05 or move down by a factor 1 + d with d = - 0.05.
(a) Compute the unique risk neutral probability measure?
(b) Compute the price of a European put with strike price K = 100. (c) Compute the price of a European call with strike price K = 100. (d) Compute the price and the hedging strategy of an American put with strike price K = 100
2. Under the Black-Scholes model compute the price and the hedging strategy of a European derivative with payoff G = (K — ST) ² .