The probability of default models differ from regular credit scoring models in several ways. First of all, credit scoring models are usually applied to smaller credits—individuals or small businesses—whereas default models are applied to larger credits—corporations or countries. Credit scoring models are largely statistical, regressing instances of default against various risk indicators, such as an obligor’s income, home renter or owner status, years at a job, educational level, debt to income ratio, and so forth, something that will be shown later in this case. Structural default models, in contrast, directly model the default process and are typically calibrated to market variables, such as the obligor’s stock price, asset value, book value of debt, or the credit spread on its bonds. Default models have many applications within financial institutions. They are used to support credit analysis and for finding the probability that a firm will default, to value counterparty credit risk limits, or to apply financial engineering techniques in developing credit derivatives or other credit instruments.
The example illustrated next uses the Merton probability of default model. This model is used to solve the probability of default of a publicly-traded company with equity and debt holdings, and to account for its volatilities in the market (Figure 2.1). This model is currently used by KMV and Moody’s to perform credit risk analysis. This approach assumes that the book value of an asset and asset volatility are unknown and solved in the model, and that the company is relatively stable, and the growth rate of the company’s assets are stable over time (e.g., not in startup mode). The model uses several simultaneous equations in options valuation theory coupled with optimization to obtain the implied underlying asset’s market value and volatility of the asset in order to compute the probability of default and distance to default for the firm.
