The first category of credit risk models are the ones based on the original framework developed by Merton (1974) using the principles of option pricing (Black and Scholes, 1973).
* the default process of a company is driven by the value of the company’s assets and the risk of a firm’s default is therefore explicitly linked to the variability of the firm’s asset value.
* The basic intuition behind the Merton model is relatively simple: default occurs when the value of a firm’s assets (the market value of the firm) is lower than that of its liabilities.
* The payment to the debt holders at the maturity of the debt is therefore the smaller of two quantities: ...view middle of the document...
This lack of success has been attributed to different reasons.
* Merton’s model the firm defaults only at maturity of the debt, a scenario that is at odds with reality.
* Second, for the model to be used in valuing default-risky debts of a firm with more than one class of debt in its capital structure (complex capital structures), the priority/seniority structures of various debts have to be specified.
* Reasons for not being adapted widely in reality
The attempt to overcome the above mentioned shortcomings of structural-form models gave rise to reduced-form models:
Unlike structural-form models, reduced-form models do not condition default on the value of the firm, and parameters related to the firm’s value need not be estimated to implement them. In addition to that, reduced-form models introduce separate explicit assumptions on the dynamic of both PD and RR. These variables are modeled independently from the structural features of the firm, its asset volatility and leverage. Generally speaking, reduced-form models assume an exogenous RR that is independent from the PD.
credit risk models aimed at measuring the potential loss, with a predetermined confidence level, that a portfolio of credit exposures could suffer within a specified time horizon (generally one year).
The main output of a credit risk model is the probability density function (PDF) of the future losses on a credit portfolio. From the analysis of such loss distribution, a financial institution can estimate both the expected loss and the unexpected loss on its credit portfolio.
* The expected loss equals the (unconditional) mean of the loss distribution; it represents the amount the bank can expect to lose within a specific period of time (usually one year).
* On the other side, the unexpected loss represents the “deviation” from expected loss and measures the actual portfolio risk.
* This can in turn be measured as the standard deviation of the loss distribution. Such measure is relevant only in the case of a normal distribution and is therefore hardly useful for credit risk measurement: indeed, the distribution of credit losses is usually highly asymmetrical and...