A Class of Discrete Transformation Survival Models With Application to Default Probability Prediction

Abstract

Corporate bankruptcy prediction plays a central role in academic finance research, business practice, and government regulation. Consequently, accurate default probability prediction is extremely important. We propose to apply a discrete transformation family of survival models to corporate default risk predictions. A class of Box-Cox transformations and logarithmic transformations is naturally adopted. The proposed transformation model family is shown to include the popular Shumway model and the grouped relative risk model. We show that a transformation parameter different from those two models is needed for default prediction using a bankruptcy dataset. In addition, we show using out-of-sample validation statistics that our model improves performance. We use the estimated default probability to examine a popular asset pricing question and determine whether default risk has carried a premium. Due to some distinct features of the bankruptcy application, the proposed class of discrete transformation survival models with time-varying covariates is different from the continuous survival models in the survival analysis literature. Their similarities and differences are discussed.

KEY WORDS:

• Corporate bankruptcy prediction
• Credit risk
• Logistic regression
• Proportional hazards
• Survival analysis

Acknowledgments

We thank the editors and two anonymous reviewers for their valuable comments.

Notes

¹Basel II is an international business standard that requires financial institutions to maintain enough cash reserves to cover risks incurred by operations.

website: http://wrds-web.wharton.upenn.edu/wrds/

equal-weighted return.

Data are available at Professor Kenneth R. French's website.