IDEAS home Printed from https://ideas.repec.org/a/taf/quantf/v12y2012i1p89-105.html

Extension of stochastic volatility equity models with the Hull--White interest rate process

Author

Listed:
  • Lech A. Grzelak
  • Cornelis W. Oosterlee
  • Sacha Van Weeren

Abstract

We present an extension of stochastic volatility equity models by a stochastic Hull--White interest rate component while assuming non-zero correlations between the underlying processes. We place these systems of stochastic differential equations in the class of affine jump-diffusion--linear quadratic jump-diffusion processes so that the pricing of European products can be efficiently performed within the Fourier cosine expansion pricing framework. We compare the new stochastic volatility Schöbel--Zhu--Hull--White hybrid model with a Heston--Hull--White model, and also apply the models to price hybrid structured derivatives that combine the equity and interest rate asset classes.

Suggested Citation

  • Lech A. Grzelak & Cornelis W. Oosterlee & Sacha Van Weeren, 2012. "Extension of stochastic volatility equity models with the Hull--White interest rate process," Quantitative Finance, Taylor & Francis Journals, vol. 12(1), pages 89-105, July.
    • Handle: RePEc:taf:quantf:v:12:y:2012:i:1:p:89-105
    DOI: 10.1080/14697680903170809
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/14697680903170809
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/14697680903170809?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Roger Lord & Remmert Koekkoek & Dick Van Dijk, 2010. "A comparison of biased simulation schemes for stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 177-194.
    2. Fang, Fang & Oosterlee, Kees, 2008. "Pricing Early-Exercise and Discrete Barrier Options by Fourier-Cosine Series Expansions," MPRA Paper 9248, University Library of Munich, Germany.
    3. Alan L. Lewis, 2001. "A Simple Option Formula for General Jump-Diffusion and other Exponential Levy Processes," Related articles explevy, Finance Press.
    4. Roger Lord & Christian Kahl, 2006. "Why the Rotation Count Algorithm works," Tinbergen Institute Discussion Papers 06-065/2, Tinbergen Institute.
    5. Gaspar, Raquel M., 2004. "General Quadratic Term Structures of Bond, Futures and Forward Prices," SSE/EFI Working Paper Series in Economics and Finance 559, Stockholm School of Economics.
    Full references (including those not matched with items on IDEAS)

    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. Kilin, Fiodar, 2006. "Accelerating the calibration of stochastic volatility models," MPRA Paper 2975, University Library of Munich, Germany, revised 22 Apr 2007.
    2. Roger Lord & Christian Kahl, 2006. "Optimal Fourier Inversion in Semi-analytical Option Pricing," Tinbergen Institute Discussion Papers 06-066/2, Tinbergen Institute, revised 05 Jun 2007.
    3. Carolyn E. Phelan & Daniele Marazzina & Gianluca Fusai & Guido Germano, 2019. "Hilbert transform, spectral filters and option pricing," Annals of Operations Research, Springer, vol. 282(1), pages 273-298, November.
    4. Roger Lord & Christian Kahl, 2006. "Why the Rotation Count Algorithm works," Tinbergen Institute Discussion Papers 06-065/2, Tinbergen Institute.
    5. Eduardo Abi Jaber, 2022. "The characteristic function of Gaussian stochastic volatility models: an analytic expression," Post-Print hal-02946146, HAL.
    6. Marjon Ruijter & Kees Oosterlee, 2012. "Two-dimensional Fourier cosine series expansion method for pricing financial options," CPB Discussion Paper 225, CPB Netherlands Bureau for Economic Policy Analysis.
    7. Giacomo Bormetti & Valentina Cazzola & Guido Montagna & Oreste Nicrosini, 2008. "Probability distribution of returns in the exponential Ornstein-Uhlenbeck model," Papers 0805.0540, arXiv.org, revised Oct 2008.
    8. Marcos Escobar-Anel & Weili Fan, 2023. "The SEV-SV Model—Applications in Portfolio Optimization," Risks, MDPI, vol. 11(2), pages 1-34, January.
    9. Eduardo Abi Jaber, 2022. "The characteristic function of Gaussian stochastic volatility models: an analytic expression," Working Papers hal-02946146, HAL.
    10. Eduardo Abi Jaber, 2022. "The characteristic function of Gaussian stochastic volatility models: an analytic expression," Finance and Stochastics, Springer, vol. 26(4), pages 733-769, October.
    11. Song-Ping Zhu & Xin-Jiang He, 2018. "A hybrid computational approach for option pricing," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 1-16, September.
    12. Marcelo G. Figueroa, 2006. "Pricing Multiple Interruptible-Swing Contracts," Birkbeck Working Papers in Economics and Finance 0606, Birkbeck, Department of Economics, Mathematics & Statistics.
    13. Bohua Wang & Xingchun Wang & Mengjie Zhao, 2025. "Valuing Vulnerable Basket Options with Stochastic Liquidity Risk in Reduced-form Models," Computational Economics, Springer;Society for Computational Economics, vol. 66(3), pages 2439-2455, September.
    14. Fang, Fang & Oosterlee, Kees, 2008. "A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions," MPRA Paper 9319, University Library of Munich, Germany.
    15. Martijn Pistorius & Johannes Stolte, 2012. "Fast computation of vanilla prices in time-changed models and implied volatilities using rational approximations," Papers 1203.6899, arXiv.org.
    16. Dong-Mei Zhu & Jiejun Lu & Wai-Ki Ching & Tak-Kuen Siu, 2019. "Option Pricing Under a Stochastic Interest Rate and Volatility Model with Hidden Markovian Regime-Switching," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 555-586, February.
    17. Sigurd Emil Rømer & Rolf Poulsen, 2020. "How Does the Volatility of Volatility Depend on Volatility?," Risks, MDPI, vol. 8(2), pages 1-18, June.
    18. Helin Zhu & Fan Ye & Enlu Zhou, 2013. "Fast Estimation of True Bounds on Bermudan Option Prices under Jump-diffusion Processes," Papers 1305.4321, arXiv.org.
    19. Rihito Sakurai & Haruto Takahashi & Koichi Miyamoto, 2025. "Learning Parameter Dependence for Fourier-Based Option Pricing with Tensor Trains," Mathematics, MDPI, vol. 13(11), pages 1-16, May.
    20. Ewald, Christian-Oliver & Menkens, Olaf & Hung Marten Ting, Sai, 2013. "Asian and Australian options: A common perspective," Journal of Economic Dynamics and Control, Elsevier, vol. 37(5), pages 1001-1018.

    More about this item

    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:taf:quantf:v:12:y:2012:i:1:p:89-105. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RQUF20 .

    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.