CREDIT RISK MODELING
David Lando (Copenhagen Business School)

Objectives

This course is an introduction to the key areas of credit risk analysis emphasizing the basic model structure, and the empirical implications of the models for corporate bond markets, default, recovery, and for markets for credit derivatives. We start with the basic Merton model, building on the Black-Scholes model, and generalize it to more realistic settings, including settings with dynamic capital structure. Time permitting, applications dealing with the evolution of ratings will be discussed. The course will then turn to the intensity-based framework which is useful for specifying dynamic models of credit spreads, for pricing credit default swaps, and for pricing collateralized debt obligations. The fourth day of the course will be devoted to the modeling of corporate bond yield spreads, CDS premia, and the different factors which contribute to credit spreads, such as risk premia for bearing default risk, illiquidity, and incomplete information. The last session will cover methods for analyzing correlated defaults, putting special emphasis on the implications of correlation for the pricing of CDOs.

Intended for

Finance professionals and academics interested in the modelling of credit risk, especially in connection with the pricing of risky debt and credit risk derivatives.

Prerequisites

Finance theory or asset pricing at a first-year graduate level. Familiarity with stochastic calculus and continuous-time finance is strongly recommended. The course will be based on Chapters 2-5 and 8-9 of Credit Risk Modeling by David Lando (Princeton University Press, 2004).

Topics

Structural models. The Merton model and its extensions. The Black-Cox model. Implications for credit spreads. Incomplete information and credit spreads. Estimating asset value and asset volatility. Coupons. Empirical evidence.

Dynamic capital structure and ratings. Stationary leverage ratios: the Leland model, Leland-Toft, models based on EBIT, applications, and empirical implications. Ratings and statistical analysis of rating processes.

Intensity models and CDS contracts. Intensity models of default. Recovery assumptions and empirical evidence. Credit default swaps. Relation to corporate bond spreads. CDS premia. Upfront payments. Implied default probabilities.

Risk premia, liquidity and other factors in credit spreads. The structure of risk premia. Implied vs. actual default probabilities. Liquidity components of credit spreads. Proxies for liquidity. Credit risk and swap spreads.

Correlated defaults and CDO modeling. Correlation in loan portfolios. The mixed binomial model. Factor intensity models. Large homogenous portfolio approximation. Application to pricing CDO tranches. The Gaussian copula. Simulating correlated defaults. Contagion.