Pricing Double Digital Options with Monte Carlo Simulation
Summary
The document explains how to estimate the price of a double digital option using Monte Carlo simulation. The option pays one unit when the underlying asset’s value at expiry lies between a lower and an upper strike, inclusive, and pays nothing otherwise. The payoff is therefore an indicator of whether the terminal price falls inside the specified interval.
The example simulates terminal prices under a lognormal asset-price model using normally distributed random draws, averages the resulting payoffs, and discounts that average at the risk-free rate. It reports an illustrative price for a stated set of inputs and a large simulation count. The article focuses on a basic C++ implementation and does not provide an analytical comparison, convergence analysis, confidence interval, or discussion of alternative variance-reduction methods. It also notes that the repeated code structure is not suitable as a production design.
Key ideas
- A double digital pays a fixed amount when the terminal underlying price is within two specified strikes.
- Monte Carlo pricing estimates the expected payoff by simulating terminal asset prices.
- Discounting the average simulated payoff gives the option price under the example’s assumptions.
- The article presents an illustrative implementation without analyzing simulation error or comparing against a closed-form price.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.