Pricing Options using Monte Carlo Simulation
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. ...