In Financial Derivatives:

a). Explain what we mean by a geometric Brownian motion (GBM) and if it is a reasonable representation of the real world behaviour of stock prices. Explain what information is required to simulate daily real world stock prices (over several periods) using a GBM.

b) Based on part (a), explain the steps required to price a one year, plain vanilla put option (on a stock) using Monte Carlo Simulation (MCS) and state any assumptions used. Explain the sources of the error in the MCS estimate of the put premium and explain how any errors might be reduced.

(15 marks)