Monte-Carlo Simulation

Implement Monte-Carlo simulation to value European Call and Put options. Provide any relevant mathematical expressions and describe how one use's Monte-Carlo simulation to value options. Use Word's Equation Editor for all formulaic expressions. You will then value European Call and Put options for the following inputs:

S_0=75,100,125

X=100

r=.05

=.20

T=1,0.5,.0001

nsteps=260

nsimulations=50,100,500,1000,10000,25000,50000

Using the above inputs, plot the value of the European Call and Put options (two separate graphs) for stock prices of 75, 100, and 125 and the number of simulations to illustrate convergence of the simulated option value to the Black-Scholes closed for solution. That is, you will have 6 graphs (stock prices of 75, 100, and 125, European Call, European Put) where you can see how the value obtained from the simulation converges to that of the Black-Scholes model for the same set of inputs. Briefly discuss what you see and how the values comport with the Black-Scholes model and your knowledge of option values.