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

• Published in: Quantitative finance Vol. 6; no. 3; pp. 243 - 253
• Main Authors: Cathcart, Lara, El-Jahel, Lina
• Format: Journal Article
• Language: English
• Published: Bristol Routledge 01.06.2006; Taylor and Francis Journals; Taylor & Francis Ltd
• Series: Quantitative Finance
• Subjects: Bond markets; Credit spread; Default; Defaultable bond; Hazard rate; Interest rates; Prices; Probability of default; Risk; Stochastic models; Stochastic term structure; Studies; Valuation
• ISSN: 1469-7688; 1469-7696
• DOI: 10.1080/14697680600670754

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.