Pricing nondiversifiable credit risk in the corporate Eurobond market

The price of defaultable or credit-risky bonds differs from the equivalent maturity price of a risk-free bond for a well identified number of factors: the positive probability of default prior to the bond maturity, the estimated loss given default, that depends on the adopted assumption on the recovery rate for that class, see Duffie and Singleton [Duffie, D., Singleton, K.J., 1999. Modeling term structures of defaultable bonds. Rev. Financ. Stud. 12, 687-720] for several models of recovery rates, the probability that the bond issuer will migrate from the current rating class to a lower class. In this study we apply two well-known modelling approaches, due to Jarrow et al. [Jarrow, R.A., Lando, D., Turnbull, S.M., 1997. A Markov model for the term structure of credit risk spreads. Rev. Financ. Stud. 10, 481-523] and Schönbucher [Schönbucher, P.J., 2002. A tree implementation of a credit spread model for credit. J. Comput. Finance 6 (2), 175-196] to price specifically two risk sources affecting the evolution of bond prices over time: the risk to move from a current risk class to a different one over the bond residual life, and the risk associated with comovements of the credit spread curves and the risk-free term structure. The former is referred to as transition risk, the latter as correlation risk. The analysis is conducted extending appropriately to a multinomial setting the classical discrete binomial model of the term structure formulated by Black et al. [Black, F., Derman, E., Toy, W., 1990. A one-factor model of interest rates and its application to treasury bond options. Financ. Analysts J. (January/February), 33-39], applied previously by Abaffy et al. [Abaffy, J., Bertocchi, M., Dupačová, J., Moriggia, V., 2000. On generating scenarios for bond portfolios. Bull. Czech Econom. Soc. 11, 3-27, and references ibidem] and many other authors in literature. The generalised model, with transition [by Jarrow et al.] and correlation risk [by Schönbucher], is applied to a large dataset of corporate spreads to evaluate the sensitivity of the isolated risk sources on the fair price of risky bonds traded in the Eurobond market.