1. [10 marks] CRR model: European contingent claim. Consider the CRR model M = (B, S) with the horizon date T = 2, the interest rate r = 0.2, and the stock price SD = 80, Si' = 104, Sf = 88. Let X be the European contingent claim maturing at T = 2 with the payoff given by the following expression with K = 116 _ _ _ |82K|, on the event {|32K| >10}, X _ '82 KIIHSQ'KINO} _ { 0, on the event {|82 Kl g 10}. (a) Find the parameters u and d, compute the stock price at time t = 2, and nd the risk-neutral probability IP. (b) Compute the arbitrage price of X using the risk-neutral valuation formula WAX) = BtIEXBEI m), at: 0,1,2. (c) Find the replicating strategy (p1 = (90(1),ch at time t = 1 for the claim X and check that Vrp) = 1(X). ((1) Find the replicating strategy (p0 = (908, (p3,) at time t = 0 for the claim X and check that VOW) = om. (e) Show that the following equality is always satised in the CRR model (do not use numbers to derive this equality) E(S231J=T(1+T)So. (1) Compute the price of Y = |82 81| at time 0 using equation (1)