Analytical Pricing Vulnerable Options with Stochastic Volatility in a Two-Factor Stochastic Interest Rate Model

Junkee Jeon and Geonwoo Kim ()
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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

Mathematics, 2025, vol. 13, issue 15, 1-15

Abstract: This paper develops an analytical pricing formula for vulnerable options with stochastic volatility under a two-factor stochastic interest rate model. We consider the underlying asset price following the Heston stochastic volatility model, while the interest rate is modeled as the sum of two processes. Using the joint characteristic function approach and measure change techniques, we derive an explicit pricing formula for a vulnerable European option. We also conduct numerical experiments to examine the effects of various model parameters on option values. This study provides a more realistic framework for pricing OTC derivatives by incorporating credit risk, stochastic volatility, and stochastic interest rates simultaneously.

Keywords: vulnerable option; stochastic interest rate; stochastic volatility; characteristic function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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