Handbook of Finance: Valuation, Financial Modeling, and Quantitative Tools

Chapter 26. Credit Risk Modeling Using Reduced-Form Models

MARK J. P. ANSON, PhD, JD, CPA, CFA, CAIA

President and Executive Director of Nuveen Investment Services

FRANK J. FABOZZI, PhD, CFA, CPA

Professor in the Practice of Finance, Yale School of Management

REN-RAW CHEN, PhD

Associate Professor of Finance, Rutgers University

MOORAD CHOUDHRY, PhD

Head of Treasury, KBC Financial Products, London

Abstract: Reduced-form models are one of two models used to model credit risk, the other being structural models. Both reduced-form and structural models are arbitrage free and employ the risk-neutral measure to price securities. The principal difference between the two models is that in structural models default is endogenous, while in reduced-form models it is exogenous. An advantage of reduced-form models is that specifying defaults exogenously greatly simplifies the problem because it ignores the constraint of defining what causes default and simply looks at the default event itself.

Keywords: reduced-form model, structural model, Poisson process, intensity parameter, Cox process, default time, Jarrow-Turnbull model, migration risk, Duffie-Singleton model, probability curve, spread-based models, hazard models

The two most popular approaches employed by commercial vendors of credit risk models are the structural approach and the reduced-form approach. The models suggested by these two approaches are used to value credit default swaps, the most popular type of credit derivative instrument. The structural ...