2. Consider a three period (T = 3) binomial model with initial stock price S0 = $8, u = 3, d = 1/2, r = 1/10, p = 2/5.

(a) Draw the binary tree illustrating the possible paths followed by the stock price process.

(b) In your diagram, record the probabilities (when the up probability is p and the down probability is 1 p) associated with the individual elements of the sample space .

(c) List the events making up the -field F1 determined by S1. (Be sure to include the empty set and the whole sample space.)

(d) Indicate on your binary tree the values (one for each path) of a European contingent claim whose payoff at T = 3 is X = max(S0, S1, S2, S3).