For the binomial lattice model, Sn = S0 Y1 × · · ·×Yn , suppose p = 0.75,d = 0.90, u = 1.5:
(a) If S0 = 2, compute E(S2 ) and V ar(S2 ).
(b) If S0 = 2, compute P (S3 ≤ 2).
(c) When r = 0.05: Show that the stochastic process Mn = Sn /(1 + r)n , n ≥ 0, forms a SUBmartingale