Pricing Options using Monte Carlo Simulation

Thu, 28 May 2026 16:01:00 +0800

Pricing European and Binary Options using Monte Carlo Simulation

1. Introduction

This report investigates the pricing of European and Binary call options using Monte Carlo simulation under the risk-neutral framework. According to the Fundamental Theorem of Asset Pricing, the value of an option $V(S,t)$ is the expected value of its discounted payoff under the risk-neutral measure $\mathbb{Q}$:

$$V(S, t) = e^{-r(T-t)} \mathbb{E}^\mathbb{Q} [\text{Payoff}(S_T)]$$

We assume the underlying asset follows Geometric Brownian Motion (GBM) governed by the Stochastic Differential Equation (SDE): $$dS_t = r S_t dt + \sigma S_t dW_t$$ where $r$ is the risk-free rate, $\sigma$ is the volatility, and $dW_t$ is a Wiener process.

Monte-Carlo on H&W

Pricing Options using Monte Carlo Simulation

Pricing European and Binary Options using Monte Carlo Simulation

1. Introduction