Monte Carlo Simulation for Black-Scholes Option Pricing

In this article we will look at applying Monte Carlo simulation to price both a European Call and Put Option, following the Black-Scholes Market Model using Risk-Neutral Pricing.

1. The Black-Scholes Market Model
2. Risk-Neutral Measure
3. Call Option Pricing and Monte Carlo Simulation
4. Put Option Pricing and Monte Carlo Simulation
5. Put-Call Parity

1. The Black-Scholes Market Model

The Black-Scholes Market Model provides a stochastic differential equation that models the changes in a given stock’s price over time.

Assumptions of the Model

These assumptions are unrealistic however necessary for the model.

• There is a constant, continuously compounded, risk-free rate of 𝑟
• There is no default risk, no transaction costs, no spreads, no tax, and no dividends
• Markets are perfectly liquid with unlimited short selling permitted
• No arbitrage is possible

We have our filtered probability space:

Under the Black-Scholes model, the stock price’s dynamics are given by: