IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v144y2018icp235-246.html
   My bibliography  Save this article

Pricing of defaultable options with multiscale generalized Heston’s stochastic volatility

Author

Listed:
  • Lee, Min-Ku
  • Kim, Jeong-Hoon

Abstract

The possibility of default risk of an option writer becomes a more important issue in over-the-counter option market when systemic risk increases. It is desirable for the option price to reflect the default risk. On the other hand, it is known that a single scale, single factor stochastic volatility model such as the well-known Heston model would not price correctly in- and out-of-the money options. So, this paper studies the pricing of defaultable options under a multiscale generalized Heston’s stochastic volatility model introduced by Fouque and Lorig (2011) to resolve these issues. We derive an explicit solution formula for the defaultable option price and investigate the characteristics of the resultant price in comparison to the price under the original Heston model.

Suggested Citation

  • Lee, Min-Ku & Kim, Jeong-Hoon, 2018. "Pricing of defaultable options with multiscale generalized Heston’s stochastic volatility," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 144(C), pages 235-246.
    • Handle: RePEc:eee:matcom:v:144:y:2018:i:c:p:235-246
    DOI: 10.1016/j.matcom.2017.08.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475417303166
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2017.08.005?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. Klein, Peter, 1996. "Pricing Black-Scholes options with correlated credit risk," Journal of Banking & Finance, Elsevier, vol. 20(7), pages 1211-1229, August.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    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. 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).
    2. Zaevski, Tsvetelin S. & Kounchev, Ognyan & Savov, Mladen, 2019. "Two frameworks for pricing defaultable derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 309-319.
    3. 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).
    4. Panhong Cheng & Zhihong Xu & Zexing Dai, 2023. "Valuation of vulnerable options with stochastic corporate liabilities in a mixed fractional Brownian motion environment," Mathematics and Financial Economics, Springer, volume 17, number 3, December.

    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. 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).
    2. 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).
    3. 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.
    4. Geonwoo Kim, 2020. "Valuation of Exchange Option with Credit Risk in a Hybrid Model," Mathematics, MDPI, vol. 8(11), pages 1-11, November.
    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. 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.
    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. Marcelo Fabián Perillo, 2023. "Valuación de Títulos de Deuda Indexados al Comportamiento de un Índice Accionario: Un Modelo con Riesgo de Crédito," Revista de Análisis Económico y Financiero, Universidad de San Martín de Porres, vol. 6(02), pages 01-06.
    9. Jeon, Junkee & Kim, Geonwoo, 2019. "Pricing of vulnerable options with early counterparty credit risk," The North American Journal of Economics and Finance, Elsevier, vol. 47(C), pages 645-656.
    10. 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).
    11. Jinghai Shao & Sovan Mitra & Andreas Karathanasopoulos, 2022. "Optimal feedback control of stock prices under credit risk dynamics," Annals of Operations Research, Springer, vol. 313(2), pages 1285-1318, June.
    12. Zonggang Ma & Chaoqun Ma & Zhijian Wu, 2022. "Pricing commodity-linked bonds with stochastic convenience yield, interest rate and counterparty credit risk: application of Mellin transform methods," Review of Derivatives Research, Springer, vol. 25(1), pages 47-91, April.
    13. Marcelo F. Perillo, 2021. "Valuación de Títulos de Deuda Indexados al Comportamiento de un Índice Accionario: Un Modelo con Riesgo de Crédito, Parte 2," CEMA Working Papers: Serie Documentos de Trabajo. 790, Universidad del CEMA.
    14. Kim, Geonwoo & Koo, Eunho, 2016. "Closed-form pricing formula for exchange option with credit risk," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 221-227.
    15. Xingchun Wang, 2021. "Pricing vulnerable options with jump risk and liquidity risk," Review of Derivatives Research, Springer, vol. 24(3), pages 243-260, October.
    16. 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.
    17. 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.
    18. Sun-Yong Choi & Sotheara Veng & Jeong-Hoon Kim & Ji-Hun Yoon, 2022. "A Mellin Transform Approach to the Pricing of Options with Default Risk," Computational Economics, Springer;Society for Computational Economics, vol. 59(3), pages 1113-1134, March.
    19. Chueh-Yung Tsao & Chao-Ching Liu, 2012. "Asian Options with Credit Risks: Pricing and Sensitivity Analysis," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 48(S3), pages 96-115, September.
    20. 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.

    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:matcom:v:144:y:2018:i:c:p:235-246. 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.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.