3. (12 points) A stock is governed by a geometric Brownian motion with initial price of $60, an interest rate of 1%, a volatility of 40%. You monitor the stock price each week for twenty-six weeks ( one half of a year). Compute the price of a down-and-in put option with a strike price of $60 and a barrier of $55 with an absolute error of $0.01 using a) IID sampling, b) IID sampling with a control variate: the European call option, c) IID sampling with a control variate: the European put option, and d) Integration lattice sampling. Compare the performance of these three methods and attempt to explain intuitively why certain methods perform better than others