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Explicit formula for the valuation of catastrophe put option with exponential jump and default risk

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  • Koo, Eunho
  • Kim, Geonwoo

Abstract

This paper concerns a catastrophe put option with default risk. Catastrophe events are described by the exponential jump model, and the default event of the option issuer is specified by the intensity based model with a stochastic intensity. Under this model, we derive the explicit analytical pricing formula of a catastrophe put option with default risk by using the multidimensional Girsanov theorem repeatedly. We also observe the effects of default risk on the prices of a catastrophe put option through the numerical experiment.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:101:y:2017:i:c:p:1-7
    DOI: 10.1016/j.chaos.2017.05.012
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    References listed on IDEAS

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    1. Ning Cai & S. G. Kou, 2011. "Option Pricing Under a Mixed-Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 57(11), pages 2067-2081, November.
    2. 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.
    3. Jaimungal, Sebastian & Wang, Tao, 2006. "Catastrophe options with stochastic interest rates and compound Poisson losses," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 469-483, June.
    4. Valenti, Davide & Spagnolo, Bernardo & Bonanno, Giovanni, 2007. "Hitting time distributions in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 311-320.
    5. Chang, Lung-fu & Hung, Mao-wei, 2009. "Analytical valuation of catastrophe equity options with negative exponential jumps," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 59-69, February.
    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.
    7. G. Bonanno & D. Valenti & B. Spagnolo, 2005. "Role of Noise in a Market Model with Stochastic Volatility," Papers cond-mat/0510154, arXiv.org, revised Oct 2006.
    8. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    9. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    10. 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.
    11. Wang, Xingchun, 2016. "Catastrophe equity put options with target variance," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 79-86.
    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. Djilali Ait Aoudia & Jean-François Renaud, 2016. "Pricing Occupation-Time Options in a Mixed-Exponential Jump-Diffusion Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 23(1), pages 1-21, March.
    14. Lin, X. Sheldon & Wang, Tao, 2009. "Pricing perpetual American catastrophe put options: A penalty function approach," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 287-295, April.
    15. Cox, Samuel H. & Fairchild, Joseph R. & Pedersen, Hal W., 2004. "Valuation of structured risk management products," Insurance: Mathematics and Economics, Elsevier, vol. 34(2), pages 259-272, April.
    16. 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.
    17. S. G. Kou & Hui Wang, 2004. "Option Pricing Under a Double Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 50(9), pages 1178-1192, September.
    18. Bernardo Spagnolo & Davide Valenti, 2008. "Volatility Effects on the Escape Time in Financial Market Models," Papers 0810.1625, arXiv.org.
    19. Yu, Jun, 2015. "Catastrophe options with double compound Poisson processes," Economic Modelling, Elsevier, vol. 50(C), pages 291-297.
    20. Djilali Ait Aoudia & Jean-Franc{c}ois Renaud, 2016. "Pricing occupation-time options in a mixed-exponential jump-diffusion model," Papers 1603.09329, arXiv.org.
    21. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    22. G. Bonanno & D. Valenti & B. Spagnolo, 2006. "Role of noise in a market model with stochastic volatility," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 53(3), pages 405-409, October.
    23. 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.
    24. Klein, Peter, 1996. "Pricing Black-Scholes options with correlated credit risk," Journal of Banking & Finance, Elsevier, vol. 20(7), pages 1211-1229, August.
    25. Jiang, I-Ming & Yang, Sheng-Yung & Liu, Yu-Hong & Wang, Alan T., 2013. "Valuation of double trigger catastrophe options with counterparty risk," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 226-242.
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    Cited by:

    1. Junkee Jeon & Geonwoo Kim, 2021. "Power Exchange Option with a Hybrid Credit Risk under Jump-Diffusion Model," Mathematics, MDPI, vol. 10(1), pages 1-12, December.
    2. 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.
    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. Zaevski, Tsvetelin S. & Kounchev, Ognyan & Savov, Mladen, 2019. "Two frameworks for pricing defaultable derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 309-319.
    5. Geonwoo Kim, 2020. "Valuation of Exchange Option with Credit Risk in a Hybrid Model," Mathematics, MDPI, vol. 8(11), pages 1-11, November.

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