Bond pricing formulas for Markov-modulated affine term structure models

Marianito R. Rodrigo; Rogemar S. Mamon

doi:10.3934/jimo.2020089

Article Contents

2021, Volume 17, Issue 5: 2685-2702. Doi: 10.3934/jimo.2020089

This issue Previous Article A combined scalarization method for multi-objective optimization problems Next Article Lookback option pricing problem of mean-reverting stock model in uncertain environment

Bond pricing formulas for Markov-modulated affine term structure models

Marianito R. Rodrigo^1, and
Rogemar S. Mamon^2, ,

1.
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, New South Wales, Australia
2.
Department of Statistical and Actuarial Sciences, University of Western Ontario, London, Ontario, Canada, and, Division of Physical Sciences and Mathematics, University of the Philippines Visayas, Miag-ao, Iloilo, Philippines

^* Corresponding author: Rogemar S. Mamon, Department of Statistical and Actuarial Sciences, University of Western Ontario, London, Ontario, Canada. E-mail: rmamon@stats.uwo.ca
^* Corresponding author: Rogemar S. Mamon, Department of Statistical and Actuarial Sciences, University of Western Ontario, London, Ontario, Canada. E-mail: rmamon@stats.uwo.ca

Received: September 30, 2019

Revised: January 31, 2020

Early access: April 2020

Published: September 2021

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Abstract

This article provides new developments in characterizing the class of regime-switching exponential affine interest rate processes in the context of pricing a zero-coupon bond. A finite-state Markov chain in continuous time dictates the random switching of time-dependent parameters of such processes. We present exact and approximate bond pricing formulas by solving a system of partial differential equations and minimizing an error functional. The bond price expression exhibits a representation that shows how it is explicitly impacted by the rate matrix and the time-dependent coefficient functions of the short rate models. We validate the bond pricing formulas numerically by examining a regime-switching Vasicek model.

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Mathematics Subject Classification: Primary: 91B28, 35A22; Secondary: 65R20, 35K05.

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