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

Author

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  • Ashwaq Ali Zarban

    (School of Mathematics and Statistics, UNSW Sydney, Sydney 2052, Australia
    These authors contributed equally to this work.)

  • David Colwell

    (Business School, UNSW Sydney, Sydney 2052, Australia
    These authors contributed equally to this work.)

  • Donna Mary Salopek

    (School of Mathematics and Statistics, UNSW Sydney, Sydney 2052, Australia
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Ashwaq Ali Zarban & David Colwell & Donna Mary Salopek, 2024. "Pricing a Defaultable Zero-Coupon Bond under Imperfect Information and Regime Switching," Mathematics, MDPI, vol. 12(17), pages 1-19, September.
  • Handle: RePEc:gam:jmathe:v:12:y:2024:i:17:p:2740-:d:1469922
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    References listed on IDEAS

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    1. Donatien Hainaut & David B. Colwell, 2016. "A structural model for credit risk with switching processes and synchronous jumps," The European Journal of Finance, Taylor & Francis Journals, vol. 22(11), pages 1040-1062, September.
    2. Ericsson, Jan & Reneby, Joel, 1999. "A Note on Contingent Claims Pricing with Non-Traded Assets," SSE/EFI Working Paper Series in Economics and Finance 314, Stockholm School of Economics, revised 01 Jul 2002.
    3. John Lau & Tak Siu, 2008. "Pricing Risky Debts Under a Markov-modudated Merton Model with Completely Random Measures," Computational Economics, Springer;Society for Computational Economics, vol. 31(3), pages 255-288, April.
    4. Bianca Hilberink & L.C.G. Rogers, 2002. "Optimal capital structure and endogenous default," Finance and Stochastics, Springer, vol. 6(2), pages 237-263.
    5. Duffie, Darrell & Lando, David, 2001. "Term Structures of Credit Spreads with Incomplete Accounting Information," Econometrica, Econometric Society, vol. 69(3), pages 633-664, May.
    6. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    7. Dionne, Georges & Gauthier, Geneviève & Hammami, Khemais & Maurice, Mathieu & Simonato, Jean-Guy, 2011. "A reduced form model of default spreads with Markov-switching macroeconomic factors," Journal of Banking & Finance, Elsevier, vol. 35(8), pages 1984-2000, August.
    8. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    9. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    10. Yinghui Dong & Kam C. Yuen & Guojing Wang & Chongfeng Wu, 2016. "A Reduced-Form Model for Correlated Defaults with Regime-Switching Shot Noise Intensities," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 459-486, June.
    11. Klein, Peter, 1996. "Pricing Black-Scholes options with correlated credit risk," Journal of Banking & Finance, Elsevier, vol. 20(7), pages 1211-1229, August.
    12. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    13. Chao Xu & Yinghui Dong & Guojing Wang, 2019. "The pricing of defaultable bonds under a regime-switching jump-diffusion model with stochastic default barrier," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(9), pages 2185-2205, May.
    14. Zhou, Chunsheng, 2001. "The term structure of credit spreads with jump risk," Journal of Banking & Finance, Elsevier, vol. 25(11), pages 2015-2040, November.
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