Parameter Estimation of the Heston Volatility Model with Jumps in the Asset Prices

TL;DR

This paper presents a Bayesian particle filtering approach for estimating the parameters of the Heston stochastic volatility model, including jumps, with a novel method to mitigate jump effects and improve estimation accuracy.

Contribution

It introduces a new estimation procedure for the Heston model with jumps, combining Bayesian regression and particle filtering, and proposes a method to handle jumps effectively.

Findings

Effective parameter estimation demonstrated through numerical simulations.

Proposed jump handling improves estimation robustness.

Provides a practical recipe for real data application.

Abstract

Parametric estimation of stochastic differential equations (SDEs) has been a subject of intense studies already for several decades. The Heston model for instance is driven by two coupled SDEs and is often used in financial mathematics for the dynamics of the asset prices and their volatility. Calibrating it to real data would be very useful in many practical scenarios. It is very challenging however, since the volatility is not directly observable. In this paper, a complete estimation procedure of the Heston model without and with jumps in the asset prices is presented. Bayesian regression combined with the particle filtering method is used as the estimation framework. Within the framework, we propose a novel approach to handle jumps in order to neutralise their negative impact on the estimates of the key parameters of the model. An improvement of the sampling in the particle filtering method is discussed as well. Our analysis is supported by numerical simulations of the Heston model to investigate the performance of the estimators. And a practical follow-along recipe is given to allow for finding adequate estimates from any given data.