On Markov‐modulated Exponential‐affine Bond Price Formulae

Abstract

We consider the bond valuation problem when the short rate process is described by a Markovian regime‐switching Hull–White model or a Markovian regime‐switching Cox–Ingersoll–Ross model. In each of the two short rate models, we establish a Markov‐modulated exponential‐affine bond price formula with coefficients given in terms of fundamental matrix solutions of linear matrix differential equations.

Keywords:

• Exponential affine form
• bond valuation
• regime‐switching forward measure
• fundamental matrix solution

Acknowledgements

We would like to thank the referee for many helpful, valuable and insightful comments and suggestions. Robert Elliott would like to thank SSHRC for its continued support.