Monte Carlo Simulation for Advanced Option Pricing: A Simplifying Tool

Abstract

Finance students at the undergraduate and MBA levels are increasingly in possession of significant mathematical skills, corresponding with the rise in cross-listings of courses between mathematics and finance departments. This increase in mathematical skill has opened the door for the Black Scholes model to be presented to advanced undergraduate and MBA students. However, although these students can grasp the weaknesses of the Black Scholes model, they are often not mathematically advanced enough to handle more realistic option pricing models. We demonstrate how Monte Carlo simulation may be employed to open the field of advanced option pricing to students without requiring any more mathematical knowledge than basic calculus and intermediate statistics. As an example, we demonstrate how to simulate option values when the underlying process follows Heston's stochastic volatility process, and motivate the example by demonstrating the significant improvement of a properly specified stochastic volatility model over the Black Scholes model.

Keywords: Simulation, teaching

JEL Classification: A20