A Simulation and Empirical Study of the Maximum Likelihood Estimator for Stochastic Volatility Jump-Diffusion Models

Bégin Jean-François () and Boudreault Mathieu ()
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Bégin Jean-François: Department of Statistics and Actuarial Science, Simon Fraser University, 8888 University Drive, V5A 1S6, Burnaby, British Columbia, Canada
Boudreault Mathieu: Department of Mathematics, 14845 Université du Québec à Montréal , C.P. 8888, Succursale Centre-ville, H3C 3P8, Montréal, Québec, Canada

Studies in Nonlinear Dynamics & Econometrics, 2025, vol. 29, issue 2, 147-175

Abstract: We investigate the behaviour of the maximum likelihood estimator (MLE) for stochastic volatility jump-diffusion models commonly used in financial risk management. A simulation study shows the practical conditions under which the MLE behaves according to theory. In an extensive empirical study based on nine indices and more than 6000 individual stocks, we nonetheless find that the MLE is unable to replicate key higher moments. We then introduce a moment-targeted MLE – robust to model misspecification – and revisit both simulation and empirical studies. We find it performs better than the MLE, improving the management of financial risk.

Keywords: maximum likelihood; jump-diffusion models; stochastic volatility; discrete nonlinear filtering; moment targeting (search for similar items in EconPapers)
JEL-codes: C13 C51 C58 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1515/snde-2023-0028

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