GPU Monte Carlo Pricing for Down-and-Out Barrier Calls
Summary
This tutorial explains how to estimate the value of a down-and-out call using Monte Carlo simulation on a GPU. A simulated price path is invalidated if it crosses the lower barrier before expiry; absent a rebate, the payoff depends on the terminal price relative to the strike. The underlying evolves through discrete Euler steps with normally distributed random increments, and the discounted payoffs across paths are averaged to estimate option value.
The article maps paths to parallel GPU threads and uses CUDA’s random number library to generate normal variates. It describes timing the GPU and CPU calculations and comparing their estimated prices. The method illustrates how path dependence requires tracking intermediate prices, increasing the number of random draws and computations. The discretisation is presented as a simple approximation rather than the most accurate scheme, and the discussion notes that simulation precision depends on path count and random number quality. The code excerpt is incomplete, so it does not provide a fully assessable performance result.
Key ideas
- A down-and-out option expires worthless after its underlying touches the lower barrier, with the example excluding rebates.
- Monte Carlo estimates option value by averaging discounted payoffs across simulated price paths.
- Euler discretisation models price changes using normally distributed increments over time steps.
- GPU threads can simulate separate paths in parallel, while barrier monitoring requires multiple steps per path.
- Results depend on discretisation, path count, and random number quality.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.