Reference no: EM131524850

Consider a stock with a risk adjusted distribution that has a drift of r=.05 and a =.35. The distribution of a random variable z is normal with mean zero and variance 1. The value of a stock is S_{t}= S_{0} e^{(r-\frac{\sigma ^{2}}{2})T +z\sigma \sqrt{T}} . Now assume that T=.20 and S_{0}=62. the value of K = 60. Now draw a random value of z and find and the payoff to the option. To find random values of z in excel use Nomsinv(RAND()). In Python you would need to use numpy. For each random stock price find the payoff to the option. Repeat this 400 times and find the average value of the stock. Then find the average payoff to the option. Discount this value to find a present value using r= .05 . So you should have the average value of the stock at maturity and the average payoff at maturity. Then find the Black Scholes value and compare. Then do it again for another group of 400 replications.