IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1907.12922.html
   My bibliography  Save this paper

CVA and vulnerable options in stochastic volatility models

Author

Listed:
  • Elisa Alos
  • Fabio Antonelli
  • Alessandro Ramponi
  • Sergio Scarlatti

Abstract

In this work we want to provide a general principle to evaluate the CVA (Credit Value Adjustment) for a vulnerable option, that is an option subject to some default event, concerning the solvability of the issuer. CVA is needed to evaluate correctly the contract and it is particularly important in presence of WWR (Wrong Way Risk), when a credit deterioration determines an increase of the claim's price. In particular, we are interested in evaluating the CVA in stochastic volatility models for the underlying's price (which often fit quite well the market's prices) when admitting correlation with the default event. By cunningly using Ito's calculus, we provide a general representation formula applicable to some popular models such as SABR, Hull \& White and Heston, which explicitly shows the correction in CVA due to the processes correlation. Later, we specialize this formula and construct its approximation for the three selected models. Lastly, we run a numerical study to test the formula's accuracy, comparing our results with Monte Carlo simulations.

Suggested Citation

  • Elisa Alos & Fabio Antonelli & Alessandro Ramponi & Sergio Scarlatti, 2019. "CVA and vulnerable options in stochastic volatility models," Papers 1907.12922, arXiv.org.
    • Handle: RePEc:arx:papers:1907.12922
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1907.12922
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. BRIGO, Damiano & VRINS, Frédéric, 2018. "Disentangling wrong-way risk: pricing credit valuation adjustment via change of measures," European Journal of Operational Research, Elsevier, vol. 269(3), pages 1154-1164.
    2. Carl Chiarella & Boda Kang & Gunter H Meyer, 2014. "The Numerical Solution of the American Option Pricing Problem:Finite Difference and Transform Approaches," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8736, August.
    3. 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.
    4. 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.
    5. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
    6. Klein, Peter, 1996. "Pricing Black-Scholes options with correlated credit risk," Journal of Banking & Finance, Elsevier, vol. 20(7), pages 1211-1229, August.
    7. Wang, Guanying & Wang, Xingchun & Zhou, Ke, 2017. "Pricing vulnerable options with stochastic volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 485(C), pages 91-103.
    8. 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.
    9. 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.
    10. Damiano Brigo & Thomas Hvolby & Frédéric Vrins, 2018. "Wrong-Way Risk Adjusted Exposure: Analytical Approximations for Options in Default Intensity Models," World Scientific Book Chapters, in: Kathrin Glau & Daniël Linders & Aleksey Min & Matthias Scherer & Lorenz Schneider & Rudi Zagst (ed.), Innovations in Insurance, Risk- and Asset Management, chapter 2, pages 27-45, World Scientific Publishing Co. Pte. Ltd..
    11. Fabio Antonelli & Sergio Scarlatti, 2009. "Pricing options under stochastic volatility: a power series approach," Finance and Stochastics, Springer, vol. 13(2), pages 269-303, April.
    12. Lee, Min-Ku & Yang, Sung-Jin & Kim, Jeong-Hoon, 2016. "A closed form solution for vulnerable options with Heston’s stochastic volatility," Chaos, Solitons & Fractals, Elsevier, vol. 86(C), pages 23-27.
    13. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    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. Xingchun Wang, 2022. "Valuing fade-in options with default risk in Heston–Nandi GARCH models," Review of Derivatives Research, Springer, vol. 25(1), pages 1-22, April.
    2. Wang, Xingchun & Zhang, Han, 2022. "Pricing basket spread options with default risk under Heston–Nandi GARCH models," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    3. Alòs, Elisa & Antonelli, Fabio & Ramponi, Alessandro & Scarlatti, Sergio, 2023. "CVA in fractional and rough volatility models," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    4. Alessandro Ramponi, 2022. "Spread Option Pricing in Regime-Switching Jump Diffusion Models," Mathematics, MDPI, vol. 10(9), pages 1-15, May.
    5. Elisa Al`os & Fabio Antonelli & Alessandro Ramponi & Sergio Scarlatti, 2022. "CVA in fractional and rough volatility models," Papers 2204.11554, 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. 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.
    2. Alòs, Elisa & Antonelli, Fabio & Ramponi, Alessandro & Scarlatti, Sergio, 2023. "CVA in fractional and rough volatility models," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    3. Elisa Al`os & Fabio Antonelli & Alessandro Ramponi & Sergio Scarlatti, 2022. "CVA in fractional and rough volatility models," Papers 2204.11554, arXiv.org.
    4. 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.
    5. 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.
    6. 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).
    7. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    8. Geonwoo Kim, 2020. "Valuation of Exchange Option with Credit Risk in a Hybrid Model," Mathematics, MDPI, vol. 8(11), pages 1-11, November.
    9. 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).
    10. 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).
    11. Wang, Guanying & Wang, Xingchun & Zhou, Ke, 2017. "Pricing vulnerable options with stochastic volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 485(C), pages 91-103.
    12. Huang, Shoude & Guo, Xunxiang, 2022. "Valuation of European-style vulnerable options under the non-affine stochastic volatility and double exponential jump," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    13. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2011, January-A.
    14. Carl Chiarella & Samuel Chege Maina & Christina Nikitopoulos-Sklibosios, 2010. "Markovian Defaultable HJM Term Structure Models with Unspanned Stochastic Volatility," Research Paper Series 283, Quantitative Finance Research Centre, University of Technology, Sydney.
    15. 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.
    16. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    17. Cheikh Mbaye & Frédéric Vrins, 2022. "Affine term structure models: A time‐change approach with perfect fit to market curves," Mathematical Finance, Wiley Blackwell, vol. 32(2), pages 678-724, April.
    18. Kaustav Das & Nicolas Langren'e, 2020. "Explicit approximations of option prices via Malliavin calculus in a general stochastic volatility framework," Papers 2006.01542, arXiv.org, revised Jan 2024.
    19. Alexander Lipton & Andrey Gal & Andris Lasis, 2014. "Pricing of vanilla and first-generation exotic options in the local stochastic volatility framework: survey and new results," Quantitative Finance, Taylor & Francis Journals, vol. 14(11), pages 1899-1922, November.
    20. Elisa Alòs & Yan Yang, 2014. "A closed-form option pricing approximation formula for a fractional Heston model," Economics Working Papers 1446, Department of Economics and Business, Universitat Pompeu Fabra.

    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:1907.12922. 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.