Regime-switching affine term structures

Andreas Celary, Paul Eisenberg and Zehra Eksi
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Andreas Celary: Institute for Statistics and Mathematics, WU-University of Economics and Business, Vienna, Austria
Paul Eisenberg: Institute for Statistics and Mathematics, WU-University of Economics and Business, Vienna, Austria
Zehra Eksi: Institute for Statistics and Mathematics, WU-University of Economics and Business, Vienna, Austria

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Abstract: We consider an HJM model setting for Markov-chain modulated forward rates. The underlying Markov chain is assumed to induce regime switches on the forward curve dynamics. Our primary focus is on the interest rate and energy futures markets. After deriving HJM-drift conditions for the two markets, we prove under the assumption of affine structure for the term structure that the forward curves are solutions to specific systems of ODEs that can be solved explicitly in many cases. This allows for a tractable model setting, and we present an algorithm for obtaining consistent forward curve models within our framework. We conclude by presenting some simple numerical examples.

Date: 2023-02
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