IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2211.14814.html
   My bibliography  Save this paper

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

Author

Listed:
  • Jaros{l}aw Gruszka
  • Janusz Szwabi'nski

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.

Suggested Citation

  • Jaros{l}aw Gruszka & Janusz Szwabi'nski, 2022. "Parameter Estimation of the Heston Volatility Model with Jumps in the Asset Prices," Papers 2211.14814, arXiv.org.
  • Handle: RePEc:arx:papers:2211.14814
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2211.14814
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Michael S. Johannes & Nicholas G. Polson & Jonathan R. Stroud, 2009. "Optimal Filtering of Jump Diffusions: Extracting Latent States from Asset Prices," The Review of Financial Studies, Society for Financial Studies, vol. 22(7), pages 2559-2599, July.
    2. 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.
    3. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    5. 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.
    6. 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.
    7. Gunter Meissner & Noriko Kawano, 2001. "Capturing the volatility smile of options on high-tech stocks—A combined GARCH-neural network approach," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 25(3), pages 276-292, September.
    8. 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.
    9. Peter Christoffersen & Kris Jacobs & Karim Mimouni, 2007. "Models for S&P500 Dynamics: Evidence from Realized Volatility, Daily Returns, and Option Prices," CREATES Research Papers 2007-37, Department of Economics and Business Economics, Aarhus University.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jaros{l}aw Gruszka & Janusz Szwabi'nski, 2023. "Portfolio Optimisation via the Heston Model Calibrated to Real Asset Data," Papers 2302.01816, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jaros{l}aw Gruszka & Janusz Szwabi'nski, 2023. "Portfolio Optimisation via the Heston Model Calibrated to Real Asset Data," Papers 2302.01816, arXiv.org.
    2. Peter Christoffersen & Steven Heston & Kris Jacobs, 2009. "The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well," Management Science, INFORMS, vol. 55(12), pages 1914-1932, December.
    3. F. Cacace & A. Germani & M. Papi, 2019. "On parameter estimation of Heston’s stochastic volatility model: a polynomial filtering method," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 503-525, December.
    4. Diego Amaya & Jean-François Bégin & Geneviève Gauthier, 2022. "The Informational Content of High-Frequency Option Prices," Management Science, INFORMS, vol. 68(3), pages 2166-2201, March.
    5. Maciej Kostrzewski & Jadwiga Kostrzewska, 2021. "The Impact of Forecasting Jumps on Forecasting Electricity Prices," Energies, MDPI, vol. 14(2), pages 1-17, January.
    6. Hamed Ghanbari & Michael Oancea & Stylianos Perrakis, 2021. "Shedding light on a dark matter: Jump diffusion and option‐implied investor preferences," European Financial Management, European Financial Management Association, vol. 27(2), pages 244-286, March.
    7. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
    8. Gonçalo Faria & João Correia-da-Silva, 2014. "A closed-form solution for options with ambiguity about stochastic volatility," Review of Derivatives Research, Springer, vol. 17(2), pages 125-159, July.
    9. Kaeck, Andreas & Rodrigues, Paulo & Seeger, Norman J., 2017. "Equity index variance: Evidence from flexible parametric jump–diffusion models," Journal of Banking & Finance, Elsevier, vol. 83(C), pages 85-103.
    10. Moreno, Manuel & Serrano, Pedro & Stute, Winfried, 2011. "Statistical properties and economic implications of jump-diffusion processes with shot-noise effects," European Journal of Operational Research, Elsevier, vol. 214(3), pages 656-664, November.
    11. Bjørn Eraker & Aoxiang Yang, 2022. "The Price of Higher Order Catastrophe Insurance: The Case of VIX Options," Journal of Finance, American Finance Association, vol. 77(6), pages 3289-3337, December.
    12. Jingzhi Huang & Liuren Wu, 2004. "Specification Analysis of Option Pricing Models Based on Time- Changed Levy Processes," Finance 0401002, University Library of Munich, Germany.
    13. Peter Carr & Liuren Wu, 2004. "Variance Risk Premia," Finance 0409015, University Library of Munich, Germany.
    14. Griffin, J.E. & Steel, M.F.J., 2006. "Inference with non-Gaussian Ornstein-Uhlenbeck processes for stochastic volatility," Journal of Econometrics, Elsevier, vol. 134(2), pages 605-644, October.
    15. Alexander Subbotin & Thierry Chauveau & Kateryna Shapovalova, 2009. "Volatility Models: from GARCH to Multi-Horizon Cascades," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00390636, HAL.
    16. Cheng, Ai-ru (Meg) & Gallant, A. Ronald & Ji, Chuanshu & Lee, Beom S., 2008. "A Gaussian approximation scheme for computation of option prices in stochastic volatility models," Journal of Econometrics, Elsevier, vol. 146(1), pages 44-58, September.
    17. Bégin, Jean-François, 2020. "Levelling the playing field: A VIX-linked structure for funded pension schemes," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 58-78.
    18. Pawel J. Szerszen, 2009. "Bayesian analysis of stochastic volatility models with Lévy jumps: application to risk analysis," Finance and Economics Discussion Series 2009-40, Board of Governors of the Federal Reserve System (U.S.).
    19. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    20. Gudkov, Nikolay & Ignatieva, Katja, 2021. "Electricity price modelling with stochastic volatility and jumps: An empirical investigation," Energy Economics, Elsevier, vol. 98(C).

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2211.14814. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.