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Pricing defaultable bonds: a middle-way approach between structural and reduced-form models

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  • Lara Cathcart
  • Lina El-Jahel

Abstract

In this paper we present a valuation model that combines features of both the structural and reduced-form approaches for modelling default risk. We maintain the cause and effect or 'structural' definition of default and assume that default is triggered when a state variable reaches a default boundary. However, in our model, the state variable is not interpreted as the assets of the firm, but as a latent variable signalling the credit quality of the firm. Default in our model can also occur according to a doubly stochastic hazard rate. The hazard rate is a linear function of the state variable and the interest rate. We use the Cox et al. (A theory of the term structure of interest rates. Econometrica, 1985, 53(2), 385-407) term structure model to preclude the possibility of negative probabilities of default. We also horse race the proposed valuation model against structural and reduced-form default risky bond pricing models and find that term structures of credit spreads generated using the middle-way approach are more in line with empirical observations.

Suggested Citation

  • Lara Cathcart & Lina El-Jahel, 2006. "Pricing defaultable bonds: a middle-way approach between structural and reduced-form models," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 243-253.
    • Handle: RePEc:taf:quantf:v:6:y:2006:i:3:p:243-253
    DOI: 10.1080/14697680600670754
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    References listed on IDEAS

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    Cited by:

    1. Alain Monfort & Jean-Paul Renne, 2013. "Default, Liquidity, and Crises: an Econometric Framework," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 11(2), pages 221-262, March.
    2. Davide Radi & Vu Phuong Hoang & Gabriele Torri & Hana Dvořáčková, 2021. "A revised version of the Cathcart & El-Jahel model and its application to CDS market," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 669-705, December.
    3. M. C. Calvo-Garrido & S. Diop & A. Pascucci & C. V'azquez, 2019. "PDE models for the valuation of a non callable defaultable coupon bond under an extended JDCEV model," Papers 1905.01099, arXiv.org.
    4. Ballestra, Luca Vincenzo & Pacelli, Graziella, 2014. "Valuing risky debt: A new model combining structural information with the reduced-form approach," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 261-271.
    5. Hyong-Chol O & Dong-Hyok Kim & Jong-Jun Jo & Song-Hun Ri, 2013. "Integrals of Higher Binary Options and Defaultable Bond with Discrete Default Information," Papers 1305.6988, arXiv.org, revised Oct 2013.
    6. Hyong-Chol O. & Jong-Chol Kim & Il-Gwang Jon, 2017. "Numerical analysis for a unified 2 factor model of structural and reduced form types for corporate bonds with fixed discrete coupon," Papers 1709.06517, arXiv.org, revised Aug 2018.
    7. Giulia Livieri & Davide Radi & Elia Smaniotto, 2023. "Pricing Transition Risk with a Jump-Diffusion Credit Risk Model: Evidences from the CDS market," Papers 2303.12483, arXiv.org.
    8. Mark Craddock & Eckhard Platen, 2001. "Benchmark Pricing of Credit Derivatives Under a Standard Market Model," Research Paper Series 60, Quantitative Finance Research Centre, University of Technology, Sydney.
    9. Hyong-Chol O & Song-Yon Kim & Dong-Hyok Kim & Chol-Hyok Pak, 2013. "Comprehensive Unified Models of Structural and Reduced Form Models for Defaultable Fixed Income Bonds (Part 1: One factor-model, Part 2:Two factors-model)," Papers 1309.1647, arXiv.org, revised Sep 2013.
    10. Angie Elkhodiry & Joseph Paradi & Luis Seco, 2011. "Using equity options to imply credit information," Annals of Operations Research, Springer, vol. 185(1), pages 45-73, May.
    11. Ballestra, Luca Vincenzo & Pacelli, Graziella & Radi, Davide, 2020. "Modeling CDS spreads: A comparison of some hybrid approaches," Journal of Empirical Finance, Elsevier, vol. 57(C), pages 107-124.
    12. Chen, Li & Ma, Yong & Xiao, Weilin, 2022. "Pricing defaultable bonds under Hawkes jump-diffusion processes," Finance Research Letters, Elsevier, vol. 47(PB).

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