Contemporary credit analysis comprises the following three areas:

1. Credit valuation of individual borrowers, as expressed in probability of default, and in the risk-neutral probability of default needed for debt pricing;
2. Portfolio risk measurement, taking into account the correlation of defaults, resulting in determining the probability distribution of portfolio losses, and of changes in the portfolio value; and
3. Structuring and pricing of credit derivatives, such as credit default swaps or collateralized debt obligations.

The theory of derivative asset pricing (options pricing) of Black, Scholes, and Merton opened up means of quantitative assessment of creditworthiness and pricing of debt securities. By being able to derive values of corporate liabilities from the market price of equity and its volatility, it became possible to measure credit risk in terms of probabilities of default rather than ordinal ratings.

The paper “Philosophy of Credit Valuation”(Chapter 16), written in 1984, provides an extensive argument for such methodology, as opposed to the previously established approach. Traditional approaches to credit valuation, such as agency ratings, involve a detailed examination of company's operations, projection of cash flows, measures of leverage and coverage, an assessment of the firm's future earning power, and so on. An assessment of the company's future, however, has already been made by all market participants and is reflected in the firm's current market value. Both current and prospective investors constantly perform this analysis, and their actions set the price for the company's equity. If the value of the company's assets can be inferred from the market valuation of equity, it will take advantage of the information contained in market prices.

The firm's liabilities are all claims, in one form or another, on the firm's assets. The firm's asset value is the worth of the firm's ongoing business. If all liabilities were traded, the market value of assets could be obtained as the sum of the market value of liabilities. It is asking the question: How much would it cost, in today's markets, to become the sole owner of the firm's business? It would necessitate buying all the stock, all the preferreds, convertibles, and so on, and all the firm's outstanding bonds, to pay off the bank debt, current obligations, and other costs. The total cost is the current market value of the firm's assets.

Typically, only the equity has observable price. The asset value must be inferred from equity value alone. This can be done by the options pricing theory. Merton's equation can be solved for the firm's asset value, provided we are able to supply the following information: Equity market value, stock price volatility, a complete description of the firm's liability structure including the terms of the liabilities (such as convertibility and callability), and the cash flows (such as interest payments and dividends). The author's work in this area could not be included in this publication, because it is the property of KMV Corporation and its successor, Moody's Corporation.

The market value of assets changes as the firm's future prospects change. The volatility of the asset value reflects the firm's business risk. The asset volatility needs to be estimated simultaneously with asset value from stock price and stock volatility.

If the asset value falls below the default point, the firm does not have the resources to repay its debt obligations. The default point is the cumulative amount of obligations payable within the given time frame. The probability of default is then calculated as the probability that the asset value falls below the default point.

Such an approach based on a causal relationship between the state of the firm and the probability of the firm defaulting allows for utilizing market information. It provides frequent updates and early warning of deterioration (or improvement) of credit quality.

Besides the valuation of credit for individual borrowers, it is necessary to measure the risks of portfolios of debt securities. The portfolio risk cannot be inferred solely from knowledge of the probabilities of default for the individual loans in the portfolio; it necessitates taking into account the correlation of defaults, resulting from the dependences of the asset values among the firms. The values of the firms' businesses are correlated, because they depend on common factors such as the state of the economy, the industries they have in common, and their mutual business relationships.

There is a number of useful measures of portfolio risk characteristics—for example, the expected loss, standard deviation of loss (unexpected loss), value-at-risk, various measures of diversification and concentration, and tail risk contribution. All these characteristics are determined by the probability distribution of the portfolio value as of a given future date. This is the subject of the article “Loan Portfolio Value” (Chapter 19).

There are three types of such probability distributions:

1. The distribution of portfolio realized losses
2. The distribution of portfolio market value at horizon date due to credit migration
3. The risk-neutral portfolio distribution (needed for pricing portfolio derivatives, such as CDOs)

Typically, bank loan portfolios are large, containing hundreds or thousands of names. A question naturally arises: How does the loss behave for large portfolios? Is there an asymptotic distribution type?

This question can be answered in affirmative for homogeneous portfolios, that is portfolios that have the same amount outstanding in each loan, same default probability for each loan, same maturity of each loan, and the same asset correlations between any two borrowers. In the limit, the distribution function of the loss on a homogeneous loan portfolio has a particular form, given in the 1987 memoranda “Probability of Loss on Loan Portfolio” and 1989 “Limiting Loan Loss Probability Distribution” (Chapters 17 and 18). This formula, which was incorporated into Basel II, has been shown empirically to provide a good approximation to the loss distribution for large portfolios, provided that the parameters in the formula are estimated from the actual portfolio composition, default characteristics, and correlations.

The note “The Empirical Test of the Distribution of Loan Portfolio Losses” (Chapter 20) reports the results of a test of the portfolio loss distribution performed by Patrick McAllister of Federal Reserve Bank. The test is based on the realization that it is not possible to obtain a sufficiently long time series of loan losses on a single loan portfolio, and that the only meaningful way of testing the distribution of loan losses is by using a cross-sectional sample of data on many portfolios. The sample contained about 23,000 actual annual gross losses reported to the FRB by U.S. banks over a period of several years. The frequency of losses were plotted in a histogram and compared with that calculated from the formula for the asymptotic loan loss distribution. The agreement in the shape of the distribution is remarkable.

The asymptotic distribution was derived as the limit distribution for a homogeneous portfolio. The sample in the FRB study is certainly as nonhomogeneous as possible: Each of the bank portfolios in the sample is a mix of loans of different qualities, maturities, and amounts outstanding, with nonequal diversification or concentration in specific industries; in addition, they are portfolios of different banks. There is nevertheless a conformity with the theoretical distribution; as is the case with many limit theorems, the asymptotic laws often appear to apply beyond their strict assumptions.