Pricing Digital Options with Monte Carlo Simulation
Summary
This article explains how to estimate European cash-or-nothing digital call and put prices with Monte Carlo simulation. At expiry, each option pays one unit if its strike condition is met and zero otherwise. The method simulates terminal underlying prices under a geometric Brownian motion model, applies a step payoff, averages the simulated payoffs, and discounts the average at the risk-free rate.
A C++ example illustrates the procedure, including Gaussian sampling with Box–Muller and separate payoff conditions for calls and puts. It reports sample prices for one stated set of inputs, but gives no comparison with a closed-form price, error estimate, or convergence analysis. The approach assumes the specified constant volatility and risk-free rate model, and the estimate is subject to Monte Carlo sampling error. The article focuses on basic implementation rather than calibration, variance reduction, or market frictions.
Key ideas
- A digital option pays a fixed amount when its expiry condition is met and zero otherwise.
- Monte Carlo pricing estimates value by averaging simulated expiry payoffs and discounting them.
- The call and put use opposite strike conditions in their step-function payoffs.
- Finite simulation counts create sampling error, and the example does not quantify it.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.