Arbitrage-Free Credit Pricing Using Default Probabilities and Risk Sensitivities

Abstract

The relation between physical probabilities (rating) and risk-neutral probabilities (pricing) is derived in a large market with a quasi-factor structure. Factor sensitivities and default probabilities can be estimated for all kinds of credits on historical rating data. Since factor prices are obtainable from market data, the model allows the pricing of non-marketable credits and structured products thereof. The model explains various empirical observations: Credit spreads of equally rated borrowers differ, spreads are wider than implied by expected losses, and expected returns on CDOs must be greater than their rating matched, single-obligor securities due to the inherent systematic risk.

Keywords: Arbitrage pricing theory (APT), Collateralized debt obligation (CDO), Esscher's change of measure, Physical and risk-neutral default probability, Generalized linear mixed model (GLMM)

JEL Classification: G12, G33