Consider the linear SDE that represents the dynamics of a security price: dSt = 0.01Stdt + 0.05StdWt with S0 = 1 given. Suppose a European

Consider the linear SDE that represents the dynamics of a security price:
dSt = 0.01Stdt + 0.05σStdWt
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 five normally distributed random variables with mean zero and variance √2.
(b) Obtain one simulated trajectory for the St. Choose Δt = 0.2.
(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 twoMonte-Carlo samples and calculate the option price using 2000 paths?