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Analytical Valuation of Vulnerable Exchange Options with Stochastic Volatility in a Reduced-Form Model

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  • Junkee Jeon

    (Department of Applied Mathematics, Kyung Hee University, Yongin 17104, Republic of Korea)

  • Geonwoo Kim

    (School of Natural Sciences, Seoul National University of Science and Technology, Seoul 01811, Republic of Korea)

Abstract

This paper investigates the valuation of vulnerable exchange options with two underlying assets that follow a two-factor volatility model. We employ a reduced-form model incorporating a Poisson process with stochastic intensity. The proposed reduced-form model depends on a stochastic intensity process that is guaranteed to remain positive and includes both systemic and idiosyncratic risks. Using measure change techniques and characteristic functions, we obtain an explicit pricing formula for vulnerable exchange options within the proposed framework. We also provide numerical examples demonstrating the sensitivity of option prices to significant parameters.

Suggested Citation

  • Junkee Jeon & Geonwoo Kim, 2024. "Analytical Valuation of Vulnerable Exchange Options with Stochastic Volatility in a Reduced-Form Model," Mathematics, MDPI, vol. 12(24), pages 1-11, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:24:p:3879-:d:1540475
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    References listed on IDEAS

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    1. 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.
    2. Xingchun Wang, 2022. "Pricing European basket warrants with default risk under stochastic volatility models," Applied Economics Letters, Taylor & Francis Journals, vol. 29(3), pages 253-260, February.
    3. Peter Christoffersen & Steven Heston & Kris Jacobs, 2009. "The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well," Management Science, INFORMS, vol. 55(12), pages 1914-1932, December.
    4. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    5. Robert A. Jarrow & Stuart M. Turnbull, 2008. "Pricing Derivatives on Financial Securities Subject to Credit Risk," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 17, pages 377-409, World Scientific Publishing Co. Pte. Ltd..
    6. 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.
    7. Shengjie Yue & Chaoqun Ma & Xinwei Zhao & Chao Deng, 2023. "Pricing power exchange options with default risk, stochastic volatility and stochastic interest rate," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(5), pages 1431-1456, March.
    8. Robert A. Jarrow & Fan Yu, 2008. "Counterparty Risk and the Pricing of Defaultable Securities," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 20, pages 481-515, World Scientific Publishing Co. Pte. Ltd..
    9. 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.
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