Monte Carlo Pricing of Arithmetic and Geometric Asian Options
Summary
The article explains how discrete Asian options use sampled prices along an asset path to determine their payoff. It distinguishes arithmetic averaging from geometric averaging and models price paths with geometric Brownian motion. Monte Carlo pricing averages the simulated payoffs and discounts that average at the risk-free rate. The example uses a modular C++ design: payoff objects handle call or put payouts, while separate Asian option classes determine how path prices are averaged.
The article walks through an illustrative implementation and reports a sample arithmetic Asian option price from its stated inputs. It emphasizes that the object-oriented design makes it easier to add payoff types or averaging methods, while noting that path generation and sampling choices could be encapsulated more cleanly. The article does not present a convergence study, uncertainty interval, or comparison against a benchmark price, so its numerical example demonstrates the workflow rather than establishing pricing accuracy.
Key ideas
- Asian option payoffs depend on sampled prices throughout the contract, rather than solely on the final price.
- Arithmetic and geometric Asian options differ in how they calculate the average underlying price.
- Monte Carlo pricing simulates geometric Brownian motion paths, evaluates each path's payoff, averages the results, and discounts the average.
- Separate payoff and option classes allow call or put payouts and averaging methods to be extended independently.
- The example leaves sampling configuration and random path generation as areas for further design improvement.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.