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

Authors: Lara Cathcart a; Lina El-Jahel a
Affiliation:   a Tanaka Business School, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
DOI: 10.1080/14697680600670754
Publication Frequency: 8 issues per year
Published in: journal Quantitative Finance, Volume 6, Issue 3 June 2006 , pages 243 - 253
Formats available: HTML (English) : PDF (English)
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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.
Keywords: Stochastic term structure; Defaultable bond; Credit spread; Probability of default; Hazard rate
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