Option Pricing Using Monte Carlo Simulation

Monte Carlo Simulation can be used to price various financial instruments such as derivatives.

In this article, we will learn how to calculate the price of an option using the Monte Carlo Simulation.

Even though the option value can be easily calculated using the Black-Scholes Option pricing formula, we can make use of the Monte Carlo Simulation technique to achieve the same results.

Let us calculate the price of a call option. Assume that the underlying stock price (S) is 195, the exercise price(X) is 200, risk free rate (rf) is 5%, volatility (s) is 30%, and the time to expiry (t) is 0.25.

Step 1

The role of Monte Carlo simulation is to generate several future value of the stock based on which we can calculate the future value of the call option. The changes in the stock prices can be calculated using the following formula:

$\Delta S=Sr_{f}\Delta t +S\sigma \varepsilon \sqrt{t}$