A stock has an initial price of So=40. Sn denotes the price at time n, where we assume the binomial lattice model with parameters u=1.25, d=0.80, p=0.60. The interest rate is 0.05. Compute:
-The price Co of a European call option (the payoff is Ct=(St-K) ) with strike price K=45 when the espiration time is T=1, and for T=2.
-Suppose now T=3. Compute P(S3 > 45), the real probability that C3>0, the probability that you will be in the money.
-Compute the price of a digital option having payoff at time T=3 of (this i capital) I { S3 > 45}