A stock price St follows the process dS1 = Si (u(t, St)dt + o(t, S)dW1) with initial condition So = 210 where ult, St) = 0.0525 and ot, St) = 0.15 x (1 + 0.5 x sin(0.0048 x St) x (1 + 0.5 x sin(2.5 xt)). In this question you must price an option with payoff (max{ST 198,0})? The option has maturity 0.4. All the assumptions of the Black-Scholes model hold except for the different price process. The risk free interest rate r is 0.005. Simulate 100000 realizations of the the stock price up to the maturity of the option using the Euler scheme with 100 steps. Use your answer to approximate the price of the option V and to compute a 95% confidence interval for this value. Repeat the calculation using the control variate method using the final stock price ST as the control variate. Again give the a 95% confidence interval. Your MATLAB code must contain a function called answerProblem which must take no parameters and return the following values in exactly this order: (i) price: The approximate price of the option at time 0 (ii) priceError: The width of the confidence interval for the price. (iii) priceCV: The price at time 0 computed using the control variate method. (iv) priceErrorcy: The width of the confidence interval for the control variate method. A stock price St follows the process dS1 = Si (u(t, St)dt + o(t, S)dW1) with initial condition So = 210 where ult, St) = 0.0525 and ot, St) = 0.15 x (1 + 0.5 x sin(0.0048 x St) x (1 + 0.5 x sin(2.5 xt)). In this question you must price an option with payoff (max{ST 198,0})? The option has maturity 0.4. All the assumptions of the Black-Scholes model hold except for the different price process. The risk free interest rate r is 0.005. Simulate 100000 realizations of the the stock price up to the maturity of the option using the Euler scheme with 100 steps. Use your answer to approximate the price of the option V and to compute a 95% confidence interval for this value. Repeat the calculation using the control variate method using the final stock price ST as the control variate. Again give the a 95% confidence interval. Your MATLAB code must contain a function called answerProblem which must take no parameters and return the following values in exactly this order: (i) price: The approximate price of the option at time 0 (ii) priceError: The width of the confidence interval for the price. (iii) priceCV: The price at time 0 computed using the control variate method. (iv) priceErrorcy: The width of the confidence interval for the control variate method
