The Credit Market Handbook: Advanced Modeling Issues

CHAPTER 1

Estimating Default Probabilities Implicit in Equity Prices

Tibor Janosi,^a Robert Jarrow,^b,* and Yildiray Yildirim^c

This chapter uses a reduced-form credit risk model to estimate default probabilities implicit in equity prices. For a cross section of firms, a time-series regression of monthly equity returns is estimated. We show that it is feasible to infer the firm's probability of default implicit in equity returns. However, the existence of price bubbles and the difficulty in modeling equity price risk premium confound the estimation of these default probabilities, generating potentially biased estimates with large standard errors. Comparing these default intensities with those obtained from historical data or implicitly from debt prices confirms this result.

1. INTRODUCTION

Given the recent exponential growth in the credit derivatives market (see Risk Magazine, 2000), credit risk modeling and estimation have become topics of interest. The theoretical literature is quite extensive (see Bielecki and Rutkowski, 2000, for a review). The empirical literature estimating reduced-form credit risk models has concentrated on using debt prices (see Duffie, 1999; Duffie and Singleton, 1997; Duffie et al., 2000; Janosi et al., 2002; Madan and Unal, 1998), credit derivative prices (see Hull and White, 2000, 2001), or bankruptcy histories (see Altman, 1968; Chava and Jarrow, 2002; Shumway, 2001; Zmijewski, 1984). Equity prices have only been used to estimate default parameters ...