Much of the energy in this area has arisen from dissatisfaction with traditional approaches to credit risk measurement and with the current regulatory model of the Bank for International Settlements (BIS). Finally, many of the new models are equally applicable to assessing off-balance sheet as well as on-balance sheet credit risk.
STRUCTURAL INCREASE IN BANKRUPTCIES
DISINTERMEDIATION
MORE COMPETITIVE MARGINS
DECLINING AND VOLATILE VALUES OF COLLATERAL
THE GROWTH OF OFF-BALANCE-SHEET DERIVATIVES
TECHNOLOGY
THE BIS RISK-BASED CAPITAL REQUIREMENTS
Specifically, internal models potentially offer better ways to value outstanding loans and credit risk-exposed instruments such as bonds (commercial and emerging market), as well as better ways to predict default risk exposures for borrowers and derivative counterparties. Before looking at some of these new approaches to credit risk measurement, a brief analysis of the more traditional approaches will enhance the contrast between the new and traditional approaches to credit risk measurement.
A BRIEF OVERVIEW OF KEY VAR CONCEPTS The Role of Capital
We can solve for σ of the loss distribution in Figure 1.2, but because it is not normal, we cannot specify the probability that the losses fall within the confidence interval EL− σ to EL+ σ unless we have information about the shape of special distribution. , for example, its skewness (lack of symmetry) and its kurtosis (probability of extreme loss outcomes). The lower the correlation between pairs of securities, the greater the benefits of diversification in reducing portfolio risk.
EXPERT SYSTEMS
State of the business cycle; an important element in determining credit risk exposure, particularly for cyclical industries. When loan rates rise beyond a certain point, good borrowers leave the loan market; they prefer to self-finance their investment projects (adverse selection).
ARTIFICIAL NEURAL NETWORKS
Each hidden unit calculates a weighted sum of all inputs and forwards the result to other hidden units. Moody and Utans (1994) find that neural networks outperform linear regression in accurately classifying corporate credit ratings.
RATING SYSTEMS
Agency for credit rating of required capital Zavarovalnica za life insurance NAIC Ratings Equivalent internal credit rating companies. However, such an asset may have recovery or salvage value, but not to such an extent that the write-off should be deferred, although partial recovery may occur in the future.
CREDIT SCORING SYSTEMS
Second, with the exception of the market value of equity in the leverage ratio, the model is essentially based on accounting ratios. For example, what is the economic significance of an exponentially transformed sum of the leverage ratio and the ratio of sales to total assets.
January 2002
Regulatory Total Capital =Credit Risk Capital Requirement +Market Risk Capital Requirement +Operational Risk Capital Requirement where. The capital requirement for credit risk depends on the bank's choice of the standardized approach or internal ratings-based (basic or advanced) models.
THE STANDARDIZED MODEL FOR CREDIT RISK
All other claims on non-OECD governments and banks carry a 100 percent risk weight under BIS I. For example, a bank with an AAA rating will receive a 20 percent risk weight (and a 1.6 percent capital requirement) regardless the sovereign's credit rating.
THE INTERNAL RATINGS-BASED MODELS FOR CREDIT RISK
An adjustment for granularity (i.e., the degree of risk concentration in one borrower) is then applied.40 The adjustment can be positive or negative and reflects the portfolio's undiversified idiosyncratic risk. The calculation of the portfolio granularity capital requirement is based on the property that the VAR of a granular portfolio consisting of n homogeneous loans is equal to the VAR for an infinitely fine-grained portfolio (assumed in the calculation of the basic risk weights) plus an adjustment factor that is inversely proportional with n. The proportionality constant is a function of PD, LGD and F (the systematic risk sensitivity of the exposures in the portfolio).
ASSESSMENT
Thus, the data requirements are so substantial that full implementation of the advanced IRB approach is far in the future, even for the most advanced banks. See Gordy (2000) and Appendix 6.2 for a discussion of the “expected tail loss” estimate.] BIS II does not address any of these concerns.
SUMMARY
First, without taking into account the relationship between the probability of bankruptcy of individual banks, BIS II cannot specify a system-wide threshold of bankruptcy risk [see Acharya (2001)]. However, there is evidence [see Jackson et al. 2001)] that banks hold capital above the regulatory minimum in response to market pressures; For example, to participate in the swap market, the bank's credit quality must be higher than would be caused by implementing either BIS I or II.50THUS, the regulatory capital requirements may be considered lower limits that do not obviate the need for more accurate measurement of credit risk.
TREATMENT OF RETAIL EXPOSURES UNDER THE INTERNAL RATINGS-BASED APPROACH
In order for loans to be considered "small", the bank must manage them as a large group of fairly homogeneous loans. The expression N(y), where y reflects the variables in equation (3.4), denotes the cumulative distribution function for a standard normal random variable (ie, the probability that a normal random variable with mean zero and variance one is less than or equal to y) and the expression G (z), where z reflects the term in parentheses in equation (3.12), denotes the inverse cumulative distribution function for a standard normal random variable (i.e., the value
The KMV and Moody’s Models
THE LINK BETWEEN LOANS AND OPTIONALITY
Moreover, just as five variables enter the classic Black-Scholes-Merton (BSM) model of stock put option valuation, the value of the default option (or, more generally, the value of a risky loan) will depend also from the value of five similar variables. The market value of a firm's assets (A) and the volatility of the market value of a firm's assets (σA) are not directly observable.
THE KMV CREDIT MONITOR MODEL 5
As can be seen in Figure 4.4, EDF is the shaded area of the asset value distribution below B. In addition, the S&P grade of the obligor was compared to EDF's KMV performance.
MOODY’S PUBLIC FIRM MODEL 30
The Merton model variant performs almost as well as the Moody's model for extremely poor quality companies. However, the Moody's model clearly outperforms approximately the bottom 10% of the population and is much better at distinguishing defaults in the middle segment of the credit sector.
MERTON’S VALUATION MODEL
Debt can thus be viewed as a short put option on the company's assets; the shareholders will "sell" the company's assets to the lenders (that is, exercise the put option and default on the debt) if the market value of the assets is less than the strike price of the put, which is the repayment value of the debt. The distance to default (DD) is the number of standard deviations of the asset probability distribution between the current asset value and the standard point.
KPMG’s Loan Analysis System and Kamakura’s Risk Manager
The equilibrium ratio—where the expected return on the risky asset equals the risk-free rate—can be used to eliminate the implied risk-neutral probability of default (also called the equivalent martingale rate). Two proprietary reduced-form models are then examined: KPMG's Loan Analysis System and Kamakura's Risk Manager.
DERIVING RISK-NEUTRAL PROBABILITIES OF DEFAULT
To break this rate down into its component parts, we must first calculate the one-year forward rate; that is, the price of a B-rated one-year zero-coupon corporate bond due in one year, indicated3 1y1. Solution for 1y1 gives a one-year forward rate on the one-year maturity B-rated corporate bond of 18.36 percent p.a.
THE LOSS INTENSITY PROCESS
For an explanation of the Poisson intensity process and the simulation of credit spreads using different parameter estimates, see Appendix 5.1. Many earlier reduced-form models focused on modeling default intensity, PD, to separate the two components of the credit spread, PD × LGD. Their simplistic assumptions that LGD was constant or proportional to bond value were hypothetical; observed recovery rates are variable and exhibit a cyclical component.
DETERMINANTS OF BOND SPREADS
Typically, they use corporate bond yields to solve for the credit spread.9 However, PD and LGD estimates will be biased if corporate bond yields are influenced by factors other than just the risk-free rate and the credit spread. Therefore, if the risky bond yields are decomposed into the riskless rate plus only the credit spread, the estimate of credit risk exposure will be biased upward.
KPMG’S LOAN ANALYSIS SYSTEM (LAS)
From period 2 onwards, the value of the loan is €100 as long as there is no default and €0 is recovered in the event of default. For example, in our example we assumed that the transition matrix was fixed over the two-year term of the loan.
KAMAKURA’S RISK MANAGER (KRM)
Estimates of credit spreads using the Jarrow model better fit the observed values at all maturities. Reduced-form models decompose risky bond yields into the risk-free interest rate and the credit risk premium.
UNDERSTANDING A BASIC INTENSITY PROCESS 2 8
Hnt. Substituting the parameters from our previous example into equation (5.7), if the A-rated firm defaults with probability 0.02 in the event of a systemic collapse occurring with a 1 percent probability, then the firm's default intensity increases to 0.0012, and it is expected to default once in the next 833 (as opposed to 1,000) years. Furthermore, if the B-rated firm defaults with a 50 percent probability if the systemic event occurs, then the firm's default intensity increases to 0.055 for one expected default in the next 18 (instead of 20) years.
CreditMetrics and Other Models
THE CONCEPT OF VALUE AT RISK ( VAR)
With respect to the latter, and in terms of dollars, there is a 1 percent chance that the value of the equity will increase tomorrow to a value of $80+2.33σ (or more), and a 1 percent chance that it will drops to a value of $80−2.33σ (or less). First, P, or the current market value of a loan, is not directly observable because most loans are not traded.
CREDITMETRICS
This means that the credit event occurs in the first year of the life of the loan (see Figure 6.2). The latter is the estimated recovery value of the loan [or one minus loss given default (LGD)] if the borrower defaults.14.
CAPITAL REQUIREMENTS
The expected shortfall, denoted by , is calculated as the average of the excess distribution of unexpected losses above the VAR.99 threshold, which is shown as $53.53. This would be the capital requirement for the average of the most extreme events (ie those in the 1% tail of the distribution).
TECHNICAL ISSUES AND PROBLEMS
It is useful to compare the effects of the MTM model versus the DM model by calculating the expected and, more importantly, the unexpected losses for the same example (the BBB loan) considered earlier. The simplest assumption is that recoveries are fixed and independent of the distribution of default probabilities.
CALCULATING THE FORWARD ZERO CURVE FOR LOAN VALUATION
Derivation of the government's one-year yield curve using the current risk-free zero yield curve. CreditMetrics adds a fixed credit spread (si) to the risk-free zero yield forward curve to obtain the risky debt forward yield curve, FYCR, shown in Figure 6.8.
ESTIMATING UNEXPECTED LOSSES USING EXTREME VALUE THEORY
The method presented in this appendix has been criticized, among other things, for its assumptions of deterministic interest rates (fixed yield curves) and constant credit spreads, si. The second criticism could be addressed by decomposing risky debt yield curves directly instead of decomposing. to put together the risk-free U.S. This means that nearly 21⁄2 times more capital would be needed to insure the bank against catastrophic credit losses compared to unexpected losses occurring up to the 99th percentile level, even when "fat tails" are taken into account.
The CreditPortfolio View Model and Other Models
DEALING WITH CYCLICAL FACTORS
A version of the first approach is taken by CreditPortfolio View4 in its newer product, CPV-Direct, as well as in the advanced versions of Credit-Metrics and other VAR models discussed in Chapter 6.5. The second approach is taken by CPV-Macro. In this chapter, we first illustrate the basic dynamics of the CPV-Macro model and then briefly describe CPV-Direct.
THE MACRO SIMULATION APPROACH: CPV-MACRO
The density, or mass, of the probabilities in the transition matrix moves increasingly in a southeasterly direction as a recession progresses.7. For the next period (t+1), the transition matrix will have to be similarly adjusted by multiplying the unconditional value of pby Rt+1, or.
CPV DIRECT
The stress scenario illustrates how the probability distribution of default is affected by the expectation of a deep recession. The probability weight of the tail in the high-default area is increased (relative to the “usual scenario” shown in Figure 7.4) to reflect the assumption that high-risk borrowers are more likely to default when economic conditions worsen.
CALCULATING CONDITIONAL MIGRATION MATRICES IN CREDITPORTFOLIO VIEW–MACRO 18
This is shown in the bottom right entry of the conditional transition matrix, shown in Table 7.2. 0.006 and ∆pCA=0.0024 to obtain the last row in the conditional transition matrix shown in Table 7.2.25. This is repeated for each row of the unconditional transition matrix.
Mortality Models and the CSFP Credit Risk Plus Model
MORTALITY ANALYSIS
Suppose that MMR1=0.01 is an estimate of the mortality rate and we want to use extreme actuarial principles of confidence in the stability of the estimate for out-of-sample pricing and forecasting. Extreme actuarial principles may require σ to be one-tenth the size of the mortality rate estimate (or σ =.001).
CSFP CREDIT RISK PLUS
The latter can then be used to calculate the capital requirement, as shown in FIGURE 8.3 Distribution of losses with default rate uncertainty and severity uncertainty. 40,000, also contained 100 loans with a historical average default rate FIGURE 8.6 Loss distribution for an individual loan portfolio.
MODEL COMPARISON
The key risk factor in Credit Risk Plus is the variable average default rate in the economy. We have already discussed the similarity of determinants of credit risk correlation in the context of risk factors.
COMPARATIVE STUDIES
For example, Table 9.2 shows that the Credit Risk Plus estimates of the 1 percent VAR for the small portfolio dropped from 6.9 to 2.2 when assuming a uniform 0 percent asset correlation. CreditMetrics (DM version) and Credit Risk Plus with KMV and CIBC's (Canadian Imperial Bank of Commerce) own internal model (Credit VAR1).
MODERN PORTFOLIO THEORY: AN OVERVIEW
Ri=the average return on the ith asset in the portfolio, Xi=the proportion of the asset portfolio invested in the ith. From equation (10.1), the average return on a portfolio of assets ( ) is simply a weighted (Xi) sum of the average return on the individual assets in that portfolio.
APPLYING MPT TO NONTRADED BONDS AND LOANS
The numerator in equation (11.6) is the covariance (COVGF) between the asset values of the two firms, GandF. The marginal risk contribution columns in Table 11.6 reflect the risk of adding each loan to a portfolio of the remaining 19 loans (the standard deviation risk of a 20-loan portfolio minus the standard deviation risk of a 19-loan portfolio).
MODELING DEFAULT CORRELATIONS USING REDUCED FORM MODELS
Correlations between loan default probabilities arise because common factors affect the timing of jumps in default probabilities across assets (loans). Correlations between default intensities result in a rapid increase in default risk in the immediate period (11.19) λ =vVc+V.
OTHER PORTFOLIO APPROACHES
As can be seen in Table 11.7, correlations increase as the credit quality of debtors declines (ie, mAandmBget higher). Some of the new models are not full MPT models (returns are often left unmodelled), but their importance lies in the connection they show between loan portfolio risk (VAR) and: (1) default correlations and (2) portfolio diversification.
VALUING A LOAN THAT MATURES AFTER THE CREDIT HORIZON IN THE KMV PORTFOLIO MANAGER MODEL
In particular, MPT-based models suggest that loan portfolios in which individual loan default risks are highly correlated should have higher capital requirements than loan portfolios of the same size, in which default risk correlations are relatively low.