Problem 4 (Stratified Sampling): Assume that the stock price follows GBM(r - q, ). We would like to calculate the price of deep-out-of-money (European) put for the following parameter set: spot price of So = $200, strike price of K = 120, risk-free rate r = 0.05, continuous divided rate of q = 0.025, volatility of o = 0.35, and maturity of T = 1 year. (a) Use standard simulation to estimate the option price and find approximate 99% confidence interval and compare it with the exact solution. (b) Use stratified sampling using sub-optimal choice for n; to estimate the option price and find approximate 99% confidence interval. (c) Use stratified sampling using optimal choice for n; to estimate the option price and find approximate 99% confidence interval. Use 20,000 simulation paths in your estimations. Compare your results with the exact solution (You should include your codes and print out the results)