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Closed-form pricing formula for exchange option with credit risk

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  • Kim, Geonwoo
  • Koo, Eunho

Abstract

In this paper, we study the valuation of Exchange option with credit risk. Since the over-the-counter (OTC) markets have grown rapidly in size, the counterparty default risk is very important and should be considered for the valuation of options. For modeling of credit risk, we use the structural model of Klein [13]. We derive the closed-form pricing formula for the price of the Exchange option with credit risk via the Mellin transform and provide the experiment results to illustrate the important properties of option with numerical graphs.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:91:y:2016:i:c:p:221-227
    DOI: 10.1016/j.chaos.2016.06.005
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    References listed on IDEAS

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    1. Gerald Cheang & Carl Chiarella, 2011. "Exchange Options Under Jump-Diffusion Dynamics," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(3), pages 245-276.
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    6. Klein, Peter, 1996. "Pricing Black-Scholes options with correlated credit risk," Journal of Banking & Finance, Elsevier, vol. 20(7), pages 1211-1229, August.
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    10. 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.
    11. 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.
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    Cited by:

    1. 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).
    2. Ma, Chaoqun & Ma, Zonggang & Xiao, Shisong, 2019. "A closed-form pricing formula for vulnerable European options under stochastic yield spreads and interest rates," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 59-68.
    3. Donghyun Kim & Ji-Hun Yoon, 2023. "Analytic Method for Pricing Vulnerable External Barrier Options," Computational Economics, Springer;Society for Computational Economics, vol. 61(4), pages 1561-1591, April.
    4. 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.
    5. Jeon, Junkee & Kim, Geonwoo, 2019. "An integral equation approach for optimal investment policies with partial reversibility," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 73-78.
    6. Jeon, Junkee & Kim, Geonwoo, 2022. "Pricing European continuous-installment currency options with mean-reversion," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    7. Jeon, Junkee & Kim, Geonwoo, 2019. "Pricing European continuous-installment strangle options," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    8. 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.
    9. 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.
    10. Ma, Zonggang & Ma, Chaoqun & Wu, Zhijian, 2020. "Closed-form analytical solutions for options on agricultural futures with seasonality and stochastic convenience yield," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    11. 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).
    12. Zaevski, Tsvetelin S. & Kounchev, Ognyan & Savov, Mladen, 2019. "Two frameworks for pricing defaultable derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 309-319.
    13. Geonwoo Kim, 2020. "Valuation of Exchange Option with Credit Risk in a Hybrid Model," Mathematics, MDPI, vol. 8(11), pages 1-11, November.
    14. Junkee Jeon & Geonwoo Kim, 2020. "An Integral Equation Approach to the Irreversible Investment Problem with a Finite Horizon," Mathematics, MDPI, vol. 8(11), pages 1-10, November.
    15. 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.

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