Problem 1. The goal of this problem is to practice Monte Carlo simulations and calculations approach as an alternative method to analytic calculations. The example comes from option pricing. We assume here that the underlying model to describe the movement of a stock is of the form XT=X0e+WT, where WTN(0,T) (process X is called the geometric Brownian motion). We assume that the given parameters are =.15,=2,T=0.5,X0=100,K=105. a) Calculate first analytically P(XT>K), the probability for the stock to finish in the money you can use a table or calculator at the end); b) Use Monte Carlo simulations to calculate the above probability numerically. Use N=10,000 as the sample size of your simulations. The goal of this problem is to practice Monte Carlo simulations and calculations approach as an alternative method to analytic calculations. The example comes from option pricing. We assume here that the underlying model to describe the movement of a stock is of the form XT=X0e+WT, where WTN(0,T) (process X is called the geometric Brownian motion). We assume that the given parameters are =.15,=2,T=0.5,X0=100,K=105. a) Calculate first analytically P(XT>K), the probability for the stock to finish in the money you can use a table or calculator at the end); b) Use Monte Carlo simulations to calculate the above probability numerically. Use N=10,000 as the sample size of your simulations