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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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