19. This problem builds on the previous problem using the same parameters, only valuing a call option instead of a bond. Using Monte Carlo, simulate the Vasicek process for 3 years. For each simulation trial, at the end of 3 years, use the Vasicek formula to compute the price of a 1-year zero-coupon bond, P3(3, 4). (Note that this price will depend upon the short-term interest rate in your simulation trial after 3 years.) For each trial compute max(0, P3(3, 4) − 0.95), and discount this at e

−

N i=1 r(i)h, where h is the time step. Take the mean of these calculations and compare your answer to that obtained using the formula in footnote 10. If you have several thousand iterations, it should be close.