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[10 marks] CRR model: American call option. Assume the CRR model with T=2, the stock price S0=45,S1u=49.5,S1d=40.5 and the interest rate r=0.05. Consider the American call option with the reward process g(St,t)=(StKt)+ for t=0,1,2 where the random strike price satisfies K0=40,K1()=35.5 for {1,2},K1()=38.5 for {3,4} and K2=36.45. (a) Find the parameters u and d, compute the stock price at time t=2 and find the unique martingale measure P. (b) Compute the price process Ca for this option using the recursive relationship Cta=max{(StKt)+,(1+r)1Ep~(Ct+1aFt)} with the terminal condition C2a=(S2K2)+. (c) Find the rational exercise time 0 for the holder of this option. (d) Find the issuer's replicating strategy for the option up to the rational exercise time 0 and show that the wealth of the replicating strategy matches the price computed in part (b). (e) Compute the profit of the issuer at time T if the holder decides to exercise the [10 marks] CRR model: American call option. Assume the CRR model with T=2, the stock price S0=45,S1u=49.5,S1d=40.5 and the interest rate r=0.05. Consider the American call option with the reward process g(St,t)=(StKt)+ for t=0,1,2 where the random strike price satisfies K0=40,K1()=35.5 for {1,2},K1()=38.5 for {3,4} and K2=36.45. (a) Find the parameters u and d, compute the stock price at time t=2 and find the unique martingale measure P. (b) Compute the price process Ca for this option using the recursive relationship Cta=max{(StKt)+,(1+r)1Ep~(Ct+1aFt)} with the terminal condition C2a=(S2K2)+. (c) Find the rational exercise time 0 for the holder of this option. (d) Find the issuer's replicating strategy for the option up to the rational exercise time 0 and show that the wealth of the replicating strategy matches the price computed in part (b). (e) Compute the profit of the issuer at time T if the holder decides to exercise the