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Pricing vulnerable options with stochastic volatility

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  • Wang, Guanying
  • Wang, Xingchun
  • Zhou, Ke

Abstract

In this paper, we investigate the pricing issue of vulnerable options with stochastic volatility by decomposing stochastic volatility into the long-term and short-term volatility. We describe the short-term fluctuation of stochastic volatility using a mean-reverting process, and assume the long-term volatility to be a constant. Based on the proposed model, we derive a pricing formula of vulnerable options in a special case. Numerical results are presented to illustrate the impacts of two stochastic volatility components on vulnerable option prices.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:485:y:2017:i:c:p:91-103
    DOI: 10.1016/j.physa.2017.04.146
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    1. JosE Da Fonseca & Martino Grasselli & Claudio Tebaldi, 2008. "A multifactor volatility Heston model," Quantitative Finance, Taylor & Francis Journals, vol. 8(6), pages 591-604.
    2. Gong, Xiaoli & Zhuang, Xintian, 2016. "Option pricing for stochastic volatility model with infinite activity Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 455(C), pages 1-10.
    3. Leland, Hayne E & Toft, Klaus Bjerre, 1996. "Optimal Capital Structure, Endogenous Bankruptcy, and the Term Structure of Credit Spreads," Journal of Finance, American Finance Association, vol. 51(3), pages 987-1019, July.
    4. Leland, Hayne E, 1994. "Corporate Debt Value, Bond Covenants, and Optimal Capital Structure," Journal of Finance, American Finance Association, vol. 49(4), pages 1213-1252, September.
    5. Damiano Brigo & Agostino Capponi & Andrea Pallavicini, 2014. "Arbitrage-Free Bilateral Counterparty Risk Valuation Under Collateralization And Application To Credit Default Swaps," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 125-146, January.
    6. Mao‐Wei Hung & Yu‐Hong Liu, 2005. "Pricing vulnerable options in incomplete markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 25(2), pages 135-170, February.
    7. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, vol. 31(2), pages 351-367, May.
    8. Xingchun Wang, 2016. "The Pricing of Catastrophe Equity Put Options with Default Risk," International Review of Finance, International Review of Finance Ltd., vol. 16(2), pages 181-201, June.
    9. Xu, Xinzhong & Taylor, Stephen J., 1994. "The Term Structure of Volatility Implied by Foreign Exchange Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(1), pages 57-74, March.
    10. Lung-Fu Chang & Mao-Wei Hung, 2006. "Valuation of vulnerable American options with correlated credit risk," Review of Derivatives Research, Springer, vol. 9(2), pages 137-165, September.
    11. Arora, Navneet & Gandhi, Priyank & Longstaff, Francis A., 2012. "Counterparty credit risk and the credit default swap market," Journal of Financial Economics, Elsevier, vol. 103(2), pages 280-293.
    12. 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.
    13. Christoffersen, Peter & Jacobs, Kris & Ornthanalai, Chayawat & Wang, Yintian, 2008. "Option valuation with long-run and short-run volatility components," Journal of Financial Economics, Elsevier, vol. 90(3), pages 272-297, December.
    14. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    15. Wang, Xingchun, 2016. "Catastrophe equity put options with target variance," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 79-86.
    16. Klein, Peter, 1996. "Pricing Black-Scholes options with correlated credit risk," Journal of Banking & Finance, Elsevier, vol. 20(7), pages 1211-1229, August.
    17. 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.
    18. Siu, Tak Kuen & Yang, Hailiang & Lau, John W., 2008. "Pricing currency options under two-factor Markov-modulated stochastic volatility models," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 295-302, December.
    19. Jingzhi Huang & Liuren Wu, 2004. "Specification Analysis of Option Pricing Models Based on Time- Changed Levy Processes," Finance 0401002, University Library of Munich, Germany.
    20. Guanying Wang & Xingchun Wang & Yongjin Wang, 2014. "Rare Shock, Two-Factor Stochastic Volatility and Currency Option Pricing," Applied Mathematical Finance, Taylor & Francis Journals, vol. 21(1), pages 32-50, March.
    21. 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.
    22. Slim, Skander, 2016. "On the source of stochastic volatility: Evidence from CAC40 index options during the subprime crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 63-76.
    23. repec:bla:jfinan:v:59:y:2004:i:3:p:1405-1440 is not listed on IDEAS
    24. Lihui Tian & Guanying Wang & Xingchun Wang & Yongjin Wang, 2014. "Pricing Vulnerable Options with Correlated Credit Risk Under Jump‐Diffusion Processes," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(10), pages 957-979, October.
    25. 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.
    26. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
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    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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