Consider the linear SDE that represents the dynamics of a security price:

dSt = .01 Stdt + 0.5 StdWt

With S0 = 1 given.

Suppose a European call option with expiration T = 1 and strike K 1.5 is written on this security. Assume that the risk-free interest rate is 3%.

(a) Using your computer, generate 1hv normally distributed random variables with mean zero and variance √2.

(b) Obtain one simulated trajectory for the St. Choose ∆t = .2.

(c) Determine the value of the call at expiration.

(d) Now repeat the same experiment with five uniformly distributed random numbers with appropriate mean and variances.

(e) If we conducted the same experiment 1000 times would the calculated price differ significantly in two cases? Why?

(f) Can we combine the two Monte Carlo samples and calculate the option price using 2000 paths?