Valuation of Euro-Convertible Bonds in a Markov-Modulated, Cox–Ingersoll–Ross Economy

Yu-Min Lian, Jun-Home Chen () and Szu-Lang Liao
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Yu-Min Lian: Department of Business Administration, Fu Jen Catholic University, No. 510, Zhongzheng Rd., Xinzhuang Dist., New Taipei City 242062, Taiwan
Jun-Home Chen: Department of Business Administration, National Chin-Yi University of Technology, No. 57, Sec. 2, Zhongshan Rd., Taiping Dist., Taichung 411030, Taiwan
Szu-Lang Liao: Department of Money and Banking, National Chengchi University, No. 64, Sec. 2, Zhinan Rd., Wenshan Dist., Taipei City 116302, Taiwan

Mathematics, 2025, vol. 13, issue 13, 1-14

Abstract: This study investigates the valuation of Euro-convertible bonds (ECBs) using a novel Markov-modulated cojump-diffusion (MMCJD) model, which effectively captures the dynamics of stochastic volatility and simultaneous jumps (cojumps) in both the underlying stock prices and foreign exchange (FX) rates. Furthermore, we introduce a Markov-modulated Cox–Ingersoll–Ross (MMCIR) framework to accurately model domestic and foreign instantaneous interest rates within a regime-switching environment. To manage computational complexity, the least-squares Monte Carlo (LSMC) approach is employed for estimating ECB values. Numerical analyses demonstrate that explicitly incorporating stochastic volatilities and cojumps significantly enhances the realism of ECB pricing, underscoring the novelty and contribution of our integrated modeling approach.

Keywords: Euro-convertible bond (ECB); Markov-modulated cojump-diffusion (MMCJD) model; cojump; Markov-modulated Cox–Ingersoll–Ross (MMCIR) model; least-squares Monte Carlo (LSMC) method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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