Quant B - Question 9 
Question:
Assume we run a Monte Carlo simulation (Willmott reading) to simulate the price path of a single stock. Our algorithm assumes the stock’s returns are normally distributed (we will use Geometric Brownian Motion, GBM) and we will run a single simulation of 100 trials. The simulation will produce a distribution of final outcomes: simulated stock price levels at a future date. Must this simulated distribution (of future price levels) match any distrbution, and if so, which?
Answer:
First, the answer is no. A particular advantage of Monte Carlo simulation (over, say, a parametric VaR) is that we are not required to specify a distributional assumption. The point of the MCS is to “discover” how the outcomes are distributed and they need not conform to any distribution. This is their realistic strength.
Second, as the number of trails increase, we do expect a lognormal pattern to emerge. If returns are normally distributed, levels are lognormally distributed, and the distribution will tend toward the lognormal.
