Fixed Income and Credit Risk: Structural and Reduced-Form Models

Abstract

Credit risk—the risk that a borrower will fail to meet contractual obligations—is the most fundamental risk in finance, preceding even equity risk in the capital structure hierarchy. The systematic analysis of credit risk in corporate bonds and loans accelerated after Merton’s (1974) foundational application of option pricing theory to corporate default: viewing equity as a call option on the firm’s assets and corporate debt as a position in the risk-free bond minus a put option on the firm’s assets provides the first theoretical model of credit spreads as compensation for default risk. This structural approach—relating default probability to observable firm characteristics (asset volatility, leverage, asset value)—was extended by Black and Cox (1976), Leland (1994), and others. Reduced-form models (Jarrow and Turnbull, 1995; Duffie and Singleton, 1999) take default intensity as an exogenous stochastic process, fitting term structures of credit spreads more flexibly than structural models. This paper reviews structural and reduced-form credit risk models, the credit default swap market that has revolutionized credit risk trading, credit spread determinants, and the contagion dynamics that make credit risk systemic.