IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i17p2740-d1469922.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/17/2740/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/17/2740/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. 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.
    3. Bianca Hilberink & L.C.G. Rogers, 2002. "Optimal capital structure and endogenous default," Finance and Stochastics, Springer, vol. 6(2), pages 237-263.
    4. Duffie, Darrell & Lando, David, 2001. "Term Structures of Credit Spreads with Incomplete Accounting Information," Econometrica, Econometric Society, vol. 69(3), pages 633-664, May.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2011, January-A.
    2. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 5, July-Dece.
    3. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    4. Haipeng Xing & Yang Yu, 2018. "Firm’s Credit Risk in the Presence of Market Structural Breaks," Risks, MDPI, vol. 6(4), pages 1-16, December.
    5. Nan Chen & S. G. Kou, 2009. "Credit Spreads, Optimal Capital Structure, And Implied Volatility With Endogenous Default And Jump Risk," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 343-378, July.
    6. Dong-Mei Zhu & Jiejun Lu & Wai-Ki Ching & Tak-Kuen Siu, 2019. "Option Pricing Under a Stochastic Interest Rate and Volatility Model with Hidden Markovian Regime-Switching," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 555-586, February.
    7. Duffie, Darrell, 2005. "Credit risk modeling with affine processes," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2751-2802, November.
    8. Abel Elizalde, 2006. "Credit Risk Models II: Structural Models," Working Papers wp2006_0606, CEMFI.
    9. Nystrom, Kaj & Skoglund, Jimmy, 2006. "A credit risk model for large dimensional portfolios with application to economic capital," Journal of Banking & Finance, Elsevier, vol. 30(8), pages 2163-2197, August.
    10. Su-Lien Lu & Kuo-Jung Lee, 2021. "Investigating the Determinants of Credit Spread Using a Markov Regime-Switching Model: Evidence from Banks in Taiwan," Sustainability, MDPI, vol. 13(17), pages 1-25, August.
    11. Leonard Tchuindjo, 2007. "Pricing of Multi-Defaultable Bonds with a Two-Correlated-Factor Hull-White Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(1), pages 19-39.
    12. Vedolin, Andrea, 2012. "Uncertainty and leveraged Lucas Trees: the cross section of equilibrium volatility risk premia," LSE Research Online Documents on Economics 43091, London School of Economics and Political Science, LSE Library.
    13. Perrakis, Stylianos & Zhong, Rui, 2015. "Credit spreads and state-dependent volatility: Theory and empirical evidence," Journal of Banking & Finance, Elsevier, vol. 55(C), pages 215-231.
    14. René Garcia & Richard Luger & Eric Renault, 2000. "Asymmetric Smiles, Leverage Effects and Structural Parameters," Working Papers 2000-57, Center for Research in Economics and Statistics.
    15. Hilscher, Jens & Raviv, Alon, 2014. "Bank stability and market discipline: The effect of contingent capital on risk taking and default probability," Journal of Corporate Finance, Elsevier, vol. 29(C), pages 542-560.
    16. Wen Su, 2021. "Default Distances Based on the CEV-KMV Model," Papers 2107.10226, arXiv.org, revised May 2022.
    17. Jobst, Andreas A., 2014. "Measuring systemic risk-adjusted liquidity (SRL)—A model approach," Journal of Banking & Finance, Elsevier, vol. 45(C), pages 270-287.
    18. Chava, Sudheer & Jarrow, Robert, 2008. "Modeling loan commitments," Finance Research Letters, Elsevier, vol. 5(1), pages 11-20, March.
    19. Alexander David & Pietro Veronesi, 1998. "Option Prices with Uncertain Fundamentals: Theory and Evidence on the Dynamics of Implied Volatilities," CRSP working papers 485, Center for Research in Security Prices, Graduate School of Business, University of Chicago.
    20. Chen, An-Sing & Chu, Hsiang-Hui & Hung, Pi-Hsia & Cheng, Miao-Sih, 2020. "Financial risk and acquirers' stockholder wealth in mergers and acquisitions," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2024:i:17:p:2740-:d:1469922. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.