Almost-Exact Simulation Scheme for Heston-type Models: Bermudan and American Option Pricing

TL;DR

This paper extends an Almost-Exact Simulation scheme for Heston models to efficiently price Bermudan and American options, demonstrating improved accuracy and computational speed over traditional Euler methods.

Contribution

It introduces a novel AES scheme for double Heston models and compares its performance with Euler schemes for American-style options.

Findings

AES provides higher accuracy than Euler methods.

AES reduces computational time significantly.

AES is robust for both Heston and double Heston models.

Abstract

Recently, an Almost-Exact Simulation (AES) scheme was introduced for the Heston stochastic volatility model and tested for European option pricing. This paper extends this scheme for pricing Bermudan and American options under both Heston and double Heston models. The AES improves Monte Carlo simulation efficiency by using the non-central chi-square distribution for the variance process. We derive the AES scheme for the double Heston model and compare the performance of the AES schemes under both models with the Euler scheme. Our numerical experiments validate the effectiveness of the AES scheme in providing accurate option prices with reduced computational time, highlighting its robustness for both models. In particular, the AES achieves higher accuracy and computational efficiency when the number of simulation steps matches the exercise dates for Bermudan options.