Neural networks (NNs), in their simplest form, are similar to a linear regression (see Principle et al., 2000). The explained variable y is the response, while the explaining variables x are the covariates. The linear regression would be:
The easiest way to visualize accuracy is through a misclassification matrix. The matrix simply cross-tabulates the actual classification versus the predicted classification. The simplest classification uses two categories only, defaulters and non-defaulters. When modelling ratings, there are as many classes as there are different ratings. It is a square matrix. Correct classifications are along the […]
The option theoretic approach to default considers that the equity holders have a put option on the value of the firms assets, whose strike price is the debt. The rationale is that if the asset value falls below the value of debt, the equity holders are better off by giving the assets to the lenders […]
When looking forward at a future date, economic default occurs when the asset value drops below debt. The debt level triggering default is unclear since debt amortizes by fractions according to some schedule. KMV uses a debt value combining short-term debt at horizon plus a fraction of the long-term debt. The issue is to determine […]
Some variations of Mertons model existed before 1974, implying default when asset value goes under a preset value of debt, and others are extensions, progressively extending the scope of the model to other variables. The gamblers ruin model considers that a gambler plays with a cash reserve from which he pays negative payoffs and to […]
In the KMV universe of listed firms, it is always possible to use the modelled Edf. In the private firm universe, there are no equity prices. Few firms belong to the KMV universe of modelled individual asset returns, among those of banks portfolios. In addition, credit officers prefer to assign ratings using both quantitative criteria […]
Migration matrices group historical frequencies of transitions across risk classes over a specified horizon, for example 1 year. A migration frequency is the count of firms migrating from one risk class to another risk class, or the ratio of these firms to the original firms in the initial risk class. Starting from one risk class, […]
Transition probabilities map to final asset values, using the standardized distance to default model. Table 38.6 reproduces a transition matrix, with fictitious data. The row F provides all migrations from this credit state to all others, including the default state, the sum of the frequencies as a percentage along the row totalling 100%.
There are many contractual exposures since term loans represent a large fraction of outstanding loans. Most other products raise exposure measurement issues because the amount at risk is unknown in advance. For banking credit exposures, relevant distinctions are on-balance sheet versus off-balance sheet transactions. In most cases, there are always hard data that bound exposures […]
DERIVATIVE EXPOSURES Derivatives include currency and interest swaps, options and any combination of these building blocks. Swaps exchange interest flows based on different rates, or flows in different currencies. Options allow us to buy or sell an asset at a stated price. The credit risk of derivatives results from the buy and hold view applicable […]
