Consider a 3-step Binomial Asset Pricing Model with probability p of going up by a factor u, and probability q = 1 p of going down by a factor d. We denote by Sn the stock price at step n.

Compute E1(S3) the conditional expectation of S3 given the information available up to time 1.

Compute E2(S3) and use it to compute E1[E2(S3)]. How does it compare with E1(S3)?

Use E1(S3) to compute E0(S3).

Now assume that u = 2, d = 1/2, r = 1/4 and S0 = 4. Generalize the result obtained from (3) to compute directly (in a single step using a Martingale property) the Risk Neutral value of a European Call option with maturity T = 3 and Strike price K = 9.