2. Control-Variate Monte Carlo: Assume we are in an economy where we can define - C(K) as the Black-Scholes price for a 1-year K-strike European call option on a nondividend-paying stock, and - Cs(K),Ps(K) denote the Monte Carlo prices for a 1-year K-strike European call and put option on the stock, respectively, calculated by using 5 random 1-year stock prices simulated under the risk-neutral probability measure. Furthermore, assume you are given: - P(50)=0.25 - Five simulated stock prices at T=0.25 are 49,50,51,52,53. Finally, denote the price estimate of a 1-year 52-strike European call option on the stock using the control variate method as C(52) : C(52)=Cs(52)+[P(50)Ps(50)]. Compute the optimal (25 pts) and corresponding (optimized) C(52), assuming r=0. (25 pts) 2. Control-Variate Monte Carlo: Assume we are in an economy where we can define - C(K) as the Black-Scholes price for a 1-year K-strike European call option on a nondividend-paying stock, and - Cs(K),Ps(K) denote the Monte Carlo prices for a 1-year K-strike European call and put option on the stock, respectively, calculated by using 5 random 1-year stock prices simulated under the risk-neutral probability measure. Furthermore, assume you are given: - P(50)=0.25 - Five simulated stock prices at T=0.25 are 49,50,51,52,53. Finally, denote the price estimate of a 1-year 52-strike European call option on the stock using the control variate method as C(52) : C(52)=Cs(52)+[P(50)Ps(50)]. Compute the optimal (25 pts) and corresponding (optimized) C(52), assuming r=0. (25 pts)