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

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 proce...

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Bibliographic Details
Published in:Mathematics (Basel) 2024-12, Vol.12 (24), p.3879
Main Authors: Jeon, Junkee, Kim, Geonwoo
Format: Article
Language:English
Subjects:
Brownian motion
Characteristic functions
Credit risk
Default
exchange option
Parameter sensitivity
reduced-form model
stochastic volatility
Valuation
Volatility
vulnerable option
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12243879