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

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  • Jarosław Gruszka

    (Hugo Steinhaus Center, Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, Wyspiańskiego 27, 50-370 Wrocław, Poland)

  • Janusz Szwabiński

    (Hugo Steinhaus Center, Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, Wyspiańskiego 27, 50-370 Wrocław, Poland)

Abstract

The parametric estimation of stochastic differential equations (SDEs) has been the subject of intense studies already for several decades. The Heston model, for instance, is based on two coupled SDEs and is often used in financial mathematics for the dynamics of 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 in 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. In addition, a practical follow-along recipe is given to allow finding adequate estimates from any given data.

Suggested Citation

  • Jarosław Gruszka & Janusz Szwabiński, 2023. "Parameter Estimation of the Heston Volatility Model with Jumps in the Asset Prices," Econometrics, MDPI, vol. 11(2), pages 1-26, June.
    • Handle: RePEc:gam:jecnmx:v:11:y:2023:i:2:p:15-:d:1162565
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    References listed on IDEAS

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    1. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    2. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    3. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, June.
    4. Jacquier, Eric & Polson, Nicholas G. & Rossi, P.E.Peter E., 2004. "Bayesian analysis of stochastic volatility models with fat-tails and correlated errors," Journal of Econometrics, Elsevier, vol. 122(1), pages 185-212, September.
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