Assume S0 = $100, r = 0.05, = 0.25, = 0, and T = 1. Use Monte Carlo valuation to compute the price of a claim that pays $1 if ST > $100, and 0 otherwise. (This is called a cash-or-nothing call. The actual price of this claim is $0.5040.) 614 Monte Carlo Valuation a. Running 1000 simulations, what is the estimated price of the contract? How close is it to $0.5040? b. What is the standard deviation of your Monte Carlo estimate? What is the 95% confidence interval for your estimate? c. Use a 1-year at-the-money call as a control variate and compute a price using equation (9), setting = 1. d. Again use a 1-year at-the-money call as a control variate, only this time use equation (9) and set optimally. What is the standard deviation of your estimate? For the following three problems, assume that S0 = $100, r = 0.08, = 0.20, = 0.30, and = 0. Perform 2000 simulations. Note that most spreadsheets have built-in functions to compute skewness and kurtosis. (In Excel, the functions are Skew and Kurt.) For the norm