IDEAS home Printed from https://ideas.repec.org/a/taf/apmtfi/v14y2007i4p339-345.html
   My bibliography  Save this article

A Note on the Discontinuity Problem in Heston's Stochastic Volatility Model

Author

Listed:
  • Jia-Hau Guo
  • Mao-Wei Hung

Abstract

Although quasi-analytic formulas can be derived for European-style financial claims in Heston's stochastic volatility model, the inverse Fourier integration involved makes the calculation somewhat complicated. This challenge has puzzled practitioners for many years because most implementations of Heston's formula are not robust, even for customarily-used Heston parameters, as time to maturity is increased. In this article, a simplified approach is proposed to solve the numerical instability problem inherent to the fundamental solution of the Heston model. Specifically, the solution does not require any additional function or a particular mechanism for most software packages or programming library routines to correctly evaluate Heston's analytics.

Suggested Citation

  • Jia-Hau Guo & Mao-Wei Hung, 2007. "A Note on the Discontinuity Problem in Heston's Stochastic Volatility Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(4), pages 339-345.
    • Handle: RePEc:taf:apmtfi:v:14:y:2007:i:4:p:339-345
    DOI: 10.1080/13504860601170534
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/13504860601170534
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/13504860601170534?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 search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Susanne Kruse & Ulrich Nögel, 2005. "On the pricing of forward starting options in Heston’s model on stochastic volatility," Finance and Stochastics, Springer, vol. 9(2), pages 233-250, April.
    3. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, December.
    4. Unknown, 2005. "Forward," 2005 Conference: Slovenia in the EU - Challenges for Agriculture, Food Science and Rural Affairs, November 10-11, 2005, Moravske Toplice, Slovenia 183804, Slovenian Association of Agricultural Economists (DAES).
    5. Rainer Schöbel & Jianwei Zhu, 1999. "Stochastic Volatility With an Ornstein–Uhlenbeck Process: An Extension," Review of Finance, European Finance Association, vol. 3(1), pages 23-46.
    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. Feng, Shih-Ping & Hung, Mao-Wei & Wang, Yaw-Huei, 2014. "Option pricing with stochastic liquidity risk: Theory and evidence," Journal of Financial Markets, Elsevier, vol. 18(C), pages 77-95.
    2. Junkee Jeon & Jeonggyu Huh & Kyunghyun Park, 2020. "An Analytic Approximation for Valuation of the American Option Under the Heston Model in Two Regimes," Computational Economics, Springer;Society for Computational Economics, vol. 56(2), pages 499-528, August.
    3. Roger Lord, 2010. "Comment on: A Note on the Discontinuity Problem in Heston's Stochastic Volatility Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(4), pages 373-376.

    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. João Pedro Vidal Nunes & Tiago Ramalho Viegas Alcaria, 2016. "Valuation of forward start options under affine jump-diffusion models," Quantitative Finance, Taylor & Francis Journals, vol. 16(5), pages 727-747, May.
    2. Nicolas Langrené & Geoffrey Lee & Zili Zhu, 2016. "Switching To Nonaffine Stochastic Volatility: A Closed-Form Expansion For The Inverse Gamma Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(05), pages 1-37, August.
    3. Björn Lutz, 2010. "Pricing of Derivatives on Mean-Reverting Assets," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-02909-7, December.
    4. Giulia Di Nunno & Kk{e}stutis Kubilius & Yuliya Mishura & Anton Yurchenko-Tytarenko, 2023. "From constant to rough: A survey of continuous volatility modeling," Papers 2309.01033, arXiv.org, revised Sep 2023.
    5. Damien Ackerer & Damir Filipović & Sergio Pulido, 2018. "The Jacobi stochastic volatility model," Finance and Stochastics, Springer, vol. 22(3), pages 667-700, July.
    6. Cui, Zhenyu & Kirkby, J. Lars & Nguyen, Duy, 2017. "Equity-linked annuity pricing with cliquet-style guarantees in regime-switching and stochastic volatility models with jumps," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 46-62.
    7. Alexander Lipton, 2023. "Kelvin Waves, Klein-Kramers and Kolmogorov Equations, Path-Dependent Financial Instruments: Survey and New Results," Papers 2309.04547, arXiv.org.
    8. Elisa Alos & Antoine Jacquier & Jorge Leon, 2017. "The implied volatility of Forward-Start options: ATM short-time level, skew and curvature," Papers 1710.11232, arXiv.org.
    9. Fathi Abid & Bilel Kaffel, 2018. "The extent of virgin olive-oil prices’ distribution revealing the behavior of market speculators," Review of Quantitative Finance and Accounting, Springer, vol. 50(2), pages 561-590, February.
    10. Wendong Zheng & Pingping Zeng, 2016. "Pricing timer options and variance derivatives with closed-form partial transform under the 3/2 model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 23(5), pages 344-373, September.
    11. Michael Kurz, 2018. "Closed-form approximations in derivatives pricing: The Kristensen-Mele approach," Papers 1804.08904, arXiv.org.
    12. Susanne Griebsch & Uwe Wystup, 2011. "On the valuation of fader and discrete barrier options in Heston's stochastic volatility model," Quantitative Finance, Taylor & Francis Journals, vol. 11(5), pages 693-709.
    13. Mark Broadie & Özgür Kaya, 2006. "Exact Simulation of Stochastic Volatility and Other Affine Jump Diffusion Processes," Operations Research, INFORMS, vol. 54(2), pages 217-231, April.
    14. Damien Ackerer & Damir Filipovic & Sergio Pulido, 2017. "The Jacobi Stochastic Volatility Model," Working Papers hal-01338330, HAL.
    15. F. Antonelli & A. Ramponi & S. Scarlatti, 2016. "Random Time Forward-Starting Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(08), pages 1-25, December.
    16. Damien Ackerer & Damir Filipovi'c & Sergio Pulido, 2016. "The Jacobi Stochastic Volatility Model," Papers 1605.07099, arXiv.org, revised Mar 2018.
    17. Coqueret, Guillaume & Tavin, Bertrand, 2016. "An investigation of model risk in a market with jumps and stochastic volatility," European Journal of Operational Research, Elsevier, vol. 253(3), pages 648-658.
    18. Pingping Zeng & Ziqing Xu & Pingping Jiang & Yue Kuen Kwok, 2023. "Analytical solvability and exact simulation in models with affine stochastic volatility and Lévy jumps," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 842-890, July.
    19. Damir Filipovic & Damien Ackerer & Sergio Pulido, 2018. "The Jacobi Stochastic Volatility Model," Post-Print hal-01338330, HAL.
    20. Juho Kanniainen & Ye Yue, 2019. "The Arrival of News and Return Jumps in Stock Markets: A Nonparametric Approach," Papers 1901.02691, arXiv.org.

    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:apmtfi:v:14:y:2007:i:4:p:339-345. 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/RAMF20 .

    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.