Semi-Markov-modulated exponential-affine bond prices

Tak Kuen Siu and Robert J. Elliott

Quantitative Finance, 2025, vol. 25, issue 11, 1813-1829

Abstract: This paper introduces two semi-Markov-modulated short rate processes and discusses the pricing of a zero-coupon bond. Specifically, a semi-Markov-modulated Hull-White (HW) model and a semi-Markov-modulated Cox-Ingersoll-Ross (CIR) model for short-term interest rates are proposed. Under the semi-Markov-modulated HW model, the mean-reverting level and the volatility of short rate process are modulated by a continuous-time, finite-state, semi-Markov chain. Under the semi-Markov-modulated CIR model, only the mean-reverting level is modulated by the semi-Markov chain. Using forward measures, stochastic flows of diffeomorphisms and fundamental matrix solutions of linear matrix differential equations, semi-analytical approximate formulas for the bond price are obtained under the two short rate processes. The formulas are of semi-Markov-modulated exponential affine forms. Numerical studies, comparisons and sensitivity analyses are provided and discussed.

Date: 2025
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DOI: 10.1080/14697688.2025.2506771

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