Pricing a Defaultable Zero-Coupon Bond under Imperfect Information and Regime Switching

Ashwaq Ali Zarban, David Colwell and Donna Mary Salopek ()
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Ashwaq Ali Zarban: School of Mathematics and Statistics, UNSW Sydney, Sydney 2052, Australia
David Colwell: Business School, UNSW Sydney, Sydney 2052, Australia
Donna Mary Salopek: School of Mathematics and Statistics, UNSW Sydney, Sydney 2052, Australia

Mathematics, 2024, vol. 12, issue 17, 1-19

Abstract: We propose a pricing formula for a defaultable zero-coupon bond with imperfect information under a regime switching model using a structural form of credit risk modelling. This paper provides explicit representations of risky debt under regime switching with a constant interest rate and risky debt under regime switching with a regime switching interest rate. While the value of the firm’s equity is observed continuously, we assume that the total value of the firm is only observed at discrete times, such as the dates of the release of the firm’s annual reports, or quarterly reports. This uncertainty about the true value of the firm results in credit spreads that do not approach zero as the debt approaches maturity, which is a problem with many structural models. The firm’s value is typically decomposed into its equity and debt; however, we consider the asset–to–equity ratio, an accounting ratio used to examine a firm’s financial well-being. The parameters in our model are regime switching, where the regime can be thought of as the state of the economy. A Markov chain with a constant transition rate matrix produces the regime switching.

Keywords: risky debt; imperfect information; interest rate; regime switching (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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