Valuing risky debt: A new model combining structural information with the reduced-form approach

• Published in: Insurance, mathematics & economics mathematics & economics, 2014-03, Vol.55, p.261-271
• Main Authors: Ballestra, Luca Vincenzo, Pacelli, Graziella
• Format: Article
• Language: English
• Subjects: Assets; Credit risk; Credit spread; Credit spreads; Default; Default intensity; Default risk; Differential equations; Economic models; Hybrid model; Macroeconomics; Market analysis; Mathematical problems; Reduced-form model; Risk management; Spread; Stochastic processes; Structural model; Studies
• ISSN: 0167-6687; 1873-5959
• DOI: 10.1016/j.insmatheco.2014.02.002

A new model of credit risk is proposed in which the intensity of default is described by an additional stochastic differential equation coupled with the process of the obligor’s asset value. Such an approach allows us to incorporate structural information as well as to capture the effect of external factors (e.g. macroeconomic factors) in a both parsimonious and economically consistent way. From the practical standpoint, the proposed model offers great flexibility and allows us to obtain credit spread curves of many different shapes, including double humped term structures. Furthermore, an approximate closed-form solution is derived, which is accurate, easy to implement, and allows for an efficient calibration to realized credit spreads. Numerical experiments are presented showing that the novel approach provides a very satisfactory fitting to market data and outperforms the model developed by Madan and Unal (2000). •We propose a new hybrid model of credit risk.•The dynamics of external (e.g. macroeconomic) variables is taken into account.•An efficient closed-form approximate solution is derived.•The model offers great flexibility to describe credit spreads.•The model outperforms the model by Madan and Unal (2000).