Financial Analysis and Modeling Using Excel and VBA

Chapter 18. Simulating Stock Prices

In most of finance, especially in analysis of derivatives, we assume that asset prices are unpredictable and follow a geometric Brownian motion. Most people find it difficult to grasp exactly what this means, but having a good understanding of it is essentia! to do any work with derivatives. In this chapter we will build a few models that will help you understand exactly what a geometric Brownian motion is, what it implies for future prices of stocks, and how we can use it to simulate stock prices. Such simulations form the basis for Monte Carlo simulations, which is one of the three approaches used widely to price derivatives.

Review of Theory and Concepts

We will explore geometric Brownian motion starting with some preliminaries and a simple model of stock prices. After we discuss geometric Brownian motion and its implications, we will discuss how to estimate the necessary parameters from historical data to simulate stock prices.

Simulation

Simulating the price of a stock means generating price paths that a stock may follow in the future. (The price path of a stock is the graph of its price against time.) If the price of a stock were predictable, then there would be only one possible future price path for it, and there would be no need to simulate it. However, if a stock's price is not constrained by any rule, then it might follow any price path we can imagine or draw. In this case, it is meaningless to talk about simulating the stock's price. We ...