A hybrid approach for the implementation of the Heston model

TL;DR

This paper introduces a hybrid tree-finite difference method for approximating the Heston model, demonstrating convergence and providing accurate option pricing through numerical experiments.

Contribution

It presents a novel hybrid numerical scheme combining tree and finite difference methods for the Heston model, with proven convergence and practical efficiency.

Findings

Accurate European and American option prices computed

The method converges reliably within the Heston model framework

Numerical experiments confirm the algorithm's efficiency

Abstract

We propose a hybrid tree-finite difference method in order to approximate the Heston model. We prove the convergence by embedding the procedure in a bivariate Markov chain and we study the convergence of European and American option prices. We finally provide numerical experiments that give accurate option prices in the Heston model, showing the reliability and the efficiency of the algorithm.