Adaptive Simulation of the Heston Model

TL;DR

This paper introduces an adaptive simulation method for the Heston model that effectively reduces bias with minimal additional computational effort, improving accuracy in pricing equity options.

Contribution

The paper presents a novel adaptive simulation strategy for the Heston model that systematically decreases bias efficiently, addressing a key challenge in stochastic volatility modeling.

Findings

The new method significantly reduces simulation bias.

It achieves near-minimal computational effort.

Numerical examples demonstrate improved accuracy.

Abstract

Recent years have seen an increased level of interest in pricing equity options under a stochastic volatility model such as the Heston model. Often, simulating a Heston model is difficult, as a standard finite difference scheme may lead to significant bias in the simulation result. Reducing the bias to an acceptable level is not only challenging but computationally demanding. In this paper we address this issue by providing an alternative simulation strategy -- one that systematically decreases the bias in the simulation. Additionally, our methodology is adaptive and achieves the reduction in bias with "near" minimum computational effort. We illustrate this feature with a numerical example.