Credit Risk Modeling: Default Probabilties

Jaime Frade

Department of Statistics Florida State Univeristy

Dr. XuFeng Niu STA5168

December 9, 2008

Outline

1 Introduction

Objective Preliminaries

Financial Definitions

Description of Data

Data: Predictor Variables

Historical Methods of Quantitatively Scoring

2 Logistic Regression Models

Saturated Logistic Regression Model Logistic Regression: Model 2

3 Comparsion and Prediction
4 Simulation and Validation

Comparsion: Barclay’s (Lehman) CDP Model Comparsion: Moody’s Model Prediction

5 Conclusion

Introduction

Credit Risk Methodolgy

In recent years more emphasis has shifted to the modeling and evaluation of credit risk. There are several forces behind this trend. First, credit markets have grown steadily and the credit derivatives market (CDS) has grown exponentially. Second, the understanding and the methodologies in managing and measuring other market risks, including interest rate risk, currency risk etc., have matured and are now assessed based on widely accepted principles, while credit risk is still a developing field.

Introduction Objective

\underline{Goal}

Built a quantative model that estimates the probability that a US issuer will default on public debt within a year, as a function of predictors that include financial ratios and equity market variables. The model is structured to balance timeliness and stability, and also allow company- or industry-level qualitative analysis.

The basic output of the model is a forward estimate of default probability. The model is uses logistic regression to derive the risk of insolvency within a year as a function of financial and market ratios.

Determine a logistic regression model After determining a statisitcally significant model, will show how to estimate probabilities from current data and intepret a logit model. Discuss the significance and relationship of the variables. Comparsion of the model with other currently accepted models. Apply validation techniques.

Introduction Preliminaries

Financial Definitions

\underline{Bonds:} A debt instrument issued for a period with the purpose of raising capital by borrowing for the issuer. \underline{Default:} The inability of a borrower to pay the interest or principal on a debt when it is due

\underline{Data}

Obtianed quarterly financial and market information from different issuers (ranging from publicly-traded US bank holding companies to industrial industries, etc) during 1998-2008.

Issuers consisted of myriad of companies that have either defaulted or are currently stable The data for the predictors was obtained from the financial statements from each issuer.

Defaulted Bonds

Defaulted bonds were chosen industry and time independent. Airlines: Delta Air Lines Inc, Northwest Airlines Corporation, FLYi, Inc, Financial Insitutions: Lehman Brothers, Bear Stearns, WAMU Delphi Corporation, Levitz Home Furnishings, Inc, Winn-Dixie Stores Inc, Calpine Generating Co LLC \underline{Data:} Predictors should target explaining/correlating with the following

framework

The most commonly used typology of risk factors for issuers is the one regulators uses the CAMEL framework. The focus is on determining predictors that targeted the following general areas which affect default concerns.

Capital Adequacy: Amount of core capital to a issuer’s risk-weighted assets. Assets quality. Management quality. Earnings: most common index of earnings is the ratio of net income to total assets. Asset Liquidity.

\underline{Data:} Predictors

Working Capital: Retained Earnings: Earnings Before Debit and Interest (EBIT): Market Value of Equity Earnings Volatitly Sales: Total Liabilties: Total Assets:

Introduction Historical Methods of Quantitatively Scoring

Existing quantitative models for scoring issuers’ credit risk fall into two broad classes: statistical and structural.

Statistical Models: Use historical data on characteristics of issuer (for example, measures of earnings or liquidity) to determine the set of characteristics that best predict the occurrence of the selected outcome. The precise form of the relationship between the inputs and the outcome is specified by the particulars of the statistical model used. These models are historically specific: the model parameters depend on the data used to create the model. Structional Models: models are form and parameters are, in principle, specified by a theory of economic structure. Contingent claims models, which basis the equity of a firm as a call option.

Logistic Regression Models

Logistic Regression Models Saturated Logistic Regression Model

P(X = x) = \frac{e^{β_{0}+β_{1} x_{1}+β_{2} x_{2}+β_{3} x_{3}}}{1 + e^{β_{0}+β_{1} x_{1}+β_{2} x_{2}+β_{3} x_{3}}}

Logistic Regression Models Logistic Regression: Model 2

Comparsion and Prediction Simulation and Validation

Simulation and Validation Comparsion: Barclay’s (Lehman) CDP Model

Simulation and Validation Comparsion: Moody’s Model

Simulation and Validation Prediction

test1

Conclusion

test1

Jaime Frade (Florida State Univeristy)  Credit Risk Modeling: Default Probabilties  December 9, 2008  20 / 20