Commercial Banking
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: the face value of the debt or the market value of the firm’s assets. * Assuming that the company’s debt is entirely represented by a zero-coupon bond, if the value of the firm at maturity is greater than the face value of the bond, then the bondholder gets back the face value of the bond. * However, if the value of the firm is less than the face value of the bond, the shareholders get nothing and the bondholder gets back the market value of the firm. The payoff at maturity to the bondholder is therefore equivalent to the face value of the bond minus a put option on the value of the firm, with a strike price equal to the face value of the bond and a maturity equal to the maturity of the bond. Following this basic intuition, Merton derived an explicit formula for risky bonds which can be used both to estimate the PD of a firm and to estimate the yield differential between a risky bond and a default-free bond.
If, for example, the firm’s value increases, then its PD tends to decrease while the expected RR at default increases (ceteris paribus). On the other side, if the firm’s debt increases, its PD increases while the expected RR at default decreases. Finally, if the firm’s asset volatility increases, its PD increases while the expected RR at default decreases, since the possible asset values can be quite low relative to liability levels.

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 fat-tailed. * This implies that the probability of large losses is higher than the one associated with a normal distribution. Financial institutions typically apply credit risk models to evaluate the “economic capital” necessary to face the risk associated with their credit portfolios. In such a framework, provisions for credit losses should cover expected losses6, while economic capital is seen as a cushion for unexpected losses.

Credit VaR models can largely be seen as reduced-form models, where the RR is typically taken as an exogenous constant parameter or a stochastic variable independent from PD

In finance and economics, systematic risk (sometimes called aggregate risk, market risk, or undiversifiable risk) is vulnerability to events which affect aggregate outcomes such as broad market returns, total economy-wide resource holdings, or aggregate income. In many contexts, events like earthquakes and major weather catastrophes pose aggregate risks—they affect not only the distribution but also the total amount of resources. If every possible outcome of a stochastic economic process is characterized by the same aggregate result (but potentially different distributional outcomes), then the process has no aggregate risk.

In contrast, idiosyncratic risk (sometimes called specific risk, unsystematic risk, residual risk, or diversifiable risk) is risk to which only specific agents or industries are vulnerable (and is uncorrelated with broad market returns).

Validating Rating Models:
- Qualitative Validation
- Quantitative Validation
- Discriminatory Power
- Back-Testing the Calibration
- Stability
- Benchmarking
- Stress Tests

Moral Hazard:
The problem: post-contractual opportunistic behaviour * Lenders cannot observe the actions of borrowers
(actions that are not in the interest of the lender risky projects)
The solution: monitoring of borrower performance

Adverse Selection:
The problem: Pre-contractual opportunistic behaviour * Lenders cannot distinguish between good and bad borrowers
(bad borrowers overstate their credit worthiness
The solution: Credit assessment
- loan officers interview the borrowers, suppliers, check balance sheet