IDEAS home Printed from https://ideas.repec.org/a/eee/finlet/v72y2025ics1544612324015502.html
   My bibliography  Save this article

Valuing options with hybrid default risk under the stochastic volatility model

Author

Listed:
  • Yun, Ana
  • Kim, Geonwoo

Abstract

In this paper, we study the valuation of options with hybrid default risk when the underlying assets are driven by a two-factor stochastic volatility model. The hybrid default model is developed by integrating the reduced-form and structural models, and the correlation between the underlying asset and default risk is considered. In the proposed framework, we adopt the probabilistic approach based on the measure-change technique to obtain an explicit pricing formula for the option. Finally, we present several numerical examples including discussions.

Suggested Citation

  • Yun, Ana & Kim, Geonwoo, 2025. "Valuing options with hybrid default risk under the stochastic volatility model," Finance Research Letters, Elsevier, vol. 72(C).
  • Handle: RePEc:eee:finlet:v:72:y:2025:i:c:s1544612324015502
    DOI: 10.1016/j.frl.2024.106521
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S1544612324015502
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.frl.2024.106521?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. Koo, Eunho & Kim, Geonwoo, 2017. "Explicit formula for the valuation of catastrophe put option with exponential jump and default risk," Chaos, Solitons & Fractals, Elsevier, vol. 101(C), pages 1-7.
    2. Xu, Guangli & Shao, Xinjian & Wang, Xingchun, 2019. "Analytical valuation of power exchange options with default risk," Finance Research Letters, Elsevier, vol. 28(C), pages 265-274.
    3. Johnson, Herb & Stulz, Rene, 1987. "The Pricing of Options with Default Risk," Journal of Finance, American Finance Association, vol. 42(2), pages 267-280, June.
    4. Kim, Donghyun & Kim, Geonwoo & Yoon, Ji-Hun, 2022. "Pricing of vulnerable exchange options with early counterparty credit risk," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    5. Fard, Farzad Alavi, 2015. "Analytical pricing of vulnerable options under a generalized jump–diffusion model," Insurance: Mathematics and Economics, Elsevier, vol. 60(C), pages 19-28.
    6. Chao Wang & Jianmin He & Shouwei Li, 2016. "The European Vulnerable Option Pricing with Jumps Based on a Mixed Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-9, December.
    7. 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.
    8. Xingchun Wang, 2020. "Analytical valuation of Asian options with counterparty risk under stochastic volatility models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(3), pages 410-429, March.
    9. Geonwoo Kim, 2020. "Valuation of Exchange Option with Credit Risk in a Hybrid Model," Mathematics, MDPI, vol. 8(11), pages 1-11, November.
    10. Liang-Chih Liu & Chun-Yuan Chiu & Chuan-Ju Wang & Tian-Shyr Dai & Hao-Han Chang, 2022. "Analytical pricing formulae for vulnerable vanilla and barrier options," Review of Quantitative Finance and Accounting, Springer, vol. 58(1), pages 137-170, January.
    11. Shengjie Yue & Chaoqun Ma & Xinwei Zhao & Chao Deng, 2023. "Pricing power exchange options with default risk, stochastic volatility and stochastic interest rate," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(5), pages 1431-1456, March.
    12. Wang, Xingchun, 2016. "Pricing power exchange options with correlated jump risk," Finance Research Letters, Elsevier, vol. 19(C), pages 90-97.
    13. Zhang, Jiayi & Zhou, Ke, 2024. "Analytical valuation of vulnerable chained options," The North American Journal of Economics and Finance, Elsevier, vol. 70(C).
    14. Guanying Wang & Xingchun Wang & Xinjian Shao, 2020. "The valuation of vulnerable European options with risky collateral," The European Journal of Finance, Taylor & Francis Journals, vol. 26(13), pages 1315-1331, July.
    15. Klein, Peter & Inglis, Michael, 2001. "Pricing vulnerable European options when the option's payoff can increase the risk of financial distress," Journal of Banking & Finance, Elsevier, vol. 25(5), pages 993-1012, May.
    16. Wang, Heqian & Zhang, Jiayi & Zhou, Ke, 2022. "On pricing of vulnerable barrier options and vulnerable double barrier options," Finance Research Letters, Elsevier, vol. 44(C).
    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. Geonwoo Kim, 2020. "Valuation of Exchange Option with Credit Risk in a Hybrid Model," Mathematics, MDPI, vol. 8(11), pages 1-11, November.
    2. Zhang, Jiayi & Zhou, Ke, 2024. "Analytical valuation of vulnerable chained options," The North American Journal of Economics and Finance, Elsevier, vol. 70(C).
    3. Jeon, Jaegi & Kim, Geonwoo & Huh, Jeonggyu, 2021. "An asymptotic expansion approach to the valuation of vulnerable options under a multiscale stochastic volatility model," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    4. Wang, Xingchun, 2020. "Valuation of Asian options with default risk under GARCH models," International Review of Economics & Finance, Elsevier, vol. 70(C), pages 27-40.
    5. Xingchun Wang, 2020. "Analytical valuation of Asian options with counterparty risk under stochastic volatility models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(3), pages 410-429, March.
    6. Zhang, Jiayi & Zhou, Ke, 2025. "Pricing options on the maximum or the minimum of several assets with default risk," The North American Journal of Economics and Finance, Elsevier, vol. 75(PA).
    7. Gechun Liang & Xingchun Wang, 2021. "Pricing vulnerable options in a hybrid credit risk model driven by Heston–Nandi GARCH processes," Review of Derivatives Research, Springer, vol. 24(1), pages 1-30, April.
    8. F. Antonelli & A. Ramponi & S. Scarlatti, 2021. "CVA and vulnerable options pricing by correlation expansions," Annals of Operations Research, Springer, vol. 299(1), pages 401-427, April.
    9. Wang, Xingchun, 2022. "Pricing vulnerable options with stochastic liquidity risk," The North American Journal of Economics and Finance, Elsevier, vol. 60(C).
    10. Junkee Jeon & Geonwoo Kim, 2024. "Analytical Valuation of Vulnerable Exchange Options with Stochastic Volatility in a Reduced-Form Model," Mathematics, MDPI, vol. 12(24), pages 1-11, December.
    11. Xie, Yurong & Deng, Guohe, 2022. "Vulnerable European option pricing in a Markov regime-switching Heston model with stochastic interest rate," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    12. Wang, Xingchun, 2016. "Pricing vulnerable options with stochastic default barriers," Finance Research Letters, Elsevier, vol. 19(C), pages 305-313.
    13. Junkee Jeon & Geonwoo Kim, 2023. "Valuation of Commodity-Linked Bond with Stochastic Convenience Yield, Stochastic Volatility, and Credit Risk in an Intensity-Based Model," Mathematics, MDPI, vol. 11(24), pages 1-11, December.
    14. Xingchun Wang, 2021. "Pricing vulnerable options with jump risk and liquidity risk," Review of Derivatives Research, Springer, vol. 24(3), pages 243-260, October.
    15. Wang, Xingchun, 2019. "Valuation of new-designed contracts for catastrophe risk management," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    16. Li, Zelei & Wang, Xingchun, 2020. "Valuing spread options with counterparty risk and jump risk," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    17. Wang, Xingchun, 2021. "Valuation of options on the maximum of two prices with default risk under GARCH models," The North American Journal of Economics and Finance, Elsevier, vol. 57(C).
    18. Antonelli, Fabio & Ramponi, Alessandro & Scarlatti, Sergio, 2022. "Approximate value adjustments for European claims," European Journal of Operational Research, Elsevier, vol. 300(3), pages 1149-1161.
    19. Wang, Heqian & Zhang, Jiayi & Zhou, Ke, 2022. "On pricing of vulnerable barrier options and vulnerable double barrier options," Finance Research Letters, Elsevier, vol. 44(C).
    20. Koo, Eunho & Kim, Geonwoo, 2017. "Explicit formula for the valuation of catastrophe put option with exponential jump and default risk," Chaos, Solitons & Fractals, Elsevier, vol. 101(C), pages 1-7.

    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:eee:finlet:v:72:y:2025:i:c:s1544612324015502. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/frl .

    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.