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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," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 11(2), pages 221-262, March.
    2. 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.
    3. 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.
    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. Gordon Gemmill, 2002. "Testing Merton's Model for Credit Spreads on Zero-Coupon Bonds," Working Papers wp02-08, Warwick Business School, Finance Group.
    7. 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.

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