A Modified Reduced-Form Model with Time-Varying Default and Recovery Rates and Its Applications in Pricing Convertible Bonds

Abstract

Reduced-form models of default risk require estimates of the recovery rate, or equivalently, the loss given default. In many cases, this is simply set at a fixed recovery rate of 40%. But the 40% rate is often far from the realized recovery amount in practice, and empirical research shows that recoveries are negatively related to ex ante default probabilities and the rate varies over time. In this article, the authors incorporate a regression-based estimate of the current recovery rate from historical data, modeling it as a function of the default probability and, potentially, macroeconomic data such as growth of the S&P Index. They then build this relationship into a lattice structure and show how it can be applied to price convertible bonds.