Simulation schemes for the Heston model with Poisson conditioning

TL;DR

This paper introduces a new exact simulation scheme for the Heston model that avoids computationally expensive Bessel function evaluations by leveraging Poisson conditioning, improving efficiency and accuracy for derivative pricing.

Contribution

A novel exact simulation method for the Heston model that simplifies calculations using Poisson conditioning, enhancing performance over existing schemes.

Findings

The new scheme reduces computational complexity.

It maintains high accuracy in derivative pricing.

It outperforms existing methods in efficiency and reliability.

Abstract

Exact simulation schemes under the Heston stochastic volatility model (e.g., Broadie-Kaya and Glasserman-Kim) suffer from computationally expensive modified Bessel function evaluations. We propose a new exact simulation scheme without the modified Bessel function, based on the observation that the conditional integrated variance can be simplified when conditioned by the Poisson variate used for simulating the terminal variance. Our approach also enhances the low-bias and time discretization schemes, which are suitable for pricing derivatives with frequent monitoring. Extensive numerical tests reveal the good performance of the new simulation schemes in terms of accuracy, efficiency, and reliability when compared with existing methods.