An up-and-out barrier call option with barrier B, strike price K and exercise time T has payoff H(T) = (S(T) − K) + if max {S(t)| 0 ≤ t ≤ T} < B, 0 otherwise, that is, the payoff is that of a call option if the underlying stock price does not reach or exceed the barrier B at any time up to and including time T, and 0 otherwise. For an up-and-out barrier call option with barrier B = 140, strike price K = 90 and exercise time T = 3 in the binomial model with parameters U = 0.2, D = −0.1, R = 0.1 and S(0) = 100 compute the following. (a) The option price at time 0;

An up-and-out barrier call option with barrier B, strike price K and exercise time T has payoff H(T) = (S(T) − K) + if max {S(t)| 0 ≤ t ≤ T} < B, 0 otherwise, that is, the payoff is that of a call option if the underlying stock price does not reach or exceed the barrier B at any time up to and including time T, and 0 otherwise. For an up-and-out barrier call option with barrier B = 140, strike price K = 90 and exercise time T = 3 in the binomial model with parameters U = 0.2, D = −0.1, R = 0.1 and S(0) = 100 compute the following. (a) The option price at time 0;