The Estimation Risk and the IRB Supervisory Formula (original) (raw)
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Estimating Probabilities of Default
SSRN Electronic Journal, 2000
We conduct a systematic comparison of confidence intervals around estimated probabilities of default (PD), using several analytical approaches from large-sample theory and bootstrapped small-sample confidence intervals. We do so for two different PD estimation methods-cohort and duration (intensity)-using twenty-two years of credit ratings data. We find that the bootstrapped intervals for the duration-based estimates are surprisingly tight when compared with the more commonly used (asymptotic) Wald interval. We find that even with these relatively tight confidence intervals, it is impossible to distinguish notch-level PDs for investment grade ratings-for example, a PD AA-from a PD A+. However, once the speculative grade barrier is crossed, we are able to distinguish quite cleanly notch-level estimated default probabilities. Conditioning on the state of the business cycle helps; it is easier to distinguish adjacent PDs in recessions than in expansions.
Confidence intervals for probabilities of default
Journal of Banking & Finance, 2006
In this paper we conduct a systematic comparison of confidence intervals around estimated probabilities of default (PD) using several analytical approaches as well as parametric and nonparametric bootstrap methods. We do so for two different PD estimation methods, cohort and duration (intensity), with 22 years of credit ratings data. We find that the bootstrapped intervals for the durationbased estimates are relatively tight when compared to either analytic or bootstrapped intervals around the less efficient cohort estimator. We show how the large differences between the point estimates and confidence intervals of these two estimators are consistent with non-Markovian migration behavior. Surprisingly, even with these relatively tight confidence intervals, it is impossible to distinguish notch-level PDs for investment grade ratings, e.g. a PD AAÀ from a PD A+. However, once the speculative grade barrier is crossed, we are able to distinguish quite cleanly notch-level estimated PDs. Conditioning on the state of the business cycle helps: it is easier to distinguish adjacent PDs in recessions than in expansions.
Confidence Intervals for Corporate Default Rates
SSRN Electronic Journal, 2000
Rating agency default studies provide estimates of mean default rates over multiple time horizons but have never included estimates of the standard errors of the estimates. This is due at least in part to the challenge of accounting for the high degree of correlation induced by their cohort-based methodologies. In this paper, we present a method for estimating confidence intervals for corporate default rates derived through a bootstrapping approach. The work extends research in the academic literature on oneyear default rates ] to the multi-year horizon case. Our results indicate that historical mean speculative-grade default rates are generally measured fairly precisely, with standard errors less the 10% of the estimated means. Investment-grade default rates, however, are measured much less precisely, particularly for issuers rated single A or above. Precision increases at longer horizons. Of practical importance, the results indicate that Moody's long-term ratings satisfy the Basel II criteria for effectively distinguishing relative credit risk. This is true even for "lowdefault portfolio" portion of the rating scale -letter ratings Aaa, Aa, and single Abecause the default rates associated with these rating categories are significantly different from one another at the two-year and longer investment horizons.
2006
Users of default prediction models often desire to know how accurate the estimated probabilities are. There are a number of mechanisms for testing this, but one that has found favor due to its intuitive appeal is the examination of goodness of fit between expected and observed default rates.While large data sets are required to test these estimates, particularly when probabilities are small as in the case of higher credit quality borrowers, the question of how large often arises. In this short note, we demonstrate, based on simple statistical relationships, how a lower bound on the size of a sample may be calculated for such experiments.Wherewehaveafixedsamplesize, thisapproachalsoprovidesameansforsizingthe minimum difference between predicted and empirical default rates that should be observed in order to conclude that the assumed probability and the observed default rate differ. When firms are not independent (correlation is non-zero), adding more observations does not necessarily...
Performance of default-risk measures: the sample matters
Journal of Banking & Finance, 2020
This paper examines the predictive power of the main default-risk measures used by both academics and practitioners, including accounting measures, market-price-based measures and the credit rating. Given that some measures are unavailable for some firm types, pair wise comparisons are made between the various measures, using same-size samples in every case. The results show the superiority of market-based measures, although their accuracy depends on the prediction horizon and the type of default events considered. Furthermore, examination shows that the effect of withinsample firm characteristics varies across measures. The overall finding is of poorer goodness of fit for accurate default prediction in samples characterised by high book-to-market ratios and/or high asset intangibility, both of which suggest pricing difficulty. In the case of large-firm samples, goodness of fit is in general negatively related to size, possibly because of the "too-big-to-fail" effect.
The Default Risk Charge approach to regulatory risk measurement processes
Dependence Modeling
In the present paper we consider the Default Risk Charge (DRC) measure as an effective alternative to the Incremental Risk Charge (IRC) one, proposing its implementation by a quasi exhaustive-heuristic algorithm to determine the minimum capital requested to a bank facing the market risk associated to portfolios based on assets issued by several financial agents. While most of the banks use the Monte Carlo simulation approach and the empirical quantile to estimate this risk measure, we provide new computational approaches, exhaustive or heuristic, currently becoming feasible because of both the new regulation and to the high speed - low cost technology available nowadays. Concrete algorithms and numerical examples are provided to illustrate the effectiveness of the proposed techniques.
Forecasting probabilities of default and loss rates given default in the presence of selection
This paper offers a joint estimation approach for forecasting probabilities of default and loss rates given default in the presence of selection. The approach accommodates fixed and random risk factors. An empirical analysis identifies bond ratings, borrower characteristics and macroeconomic information as important risk factors. A portfolio-level analysis finds evidence that common risk measurement approaches may underestimate bank capital by up to 17 per cent relative to the presented model.
Loss Given Default: Estimating by analyzing the distribution of credit assets and Validation
The Basel II Accord offers banks the opportunity to estimate Loss Given Default (LGD) if they wish to calculate their own value for the capital required to cover credit losses in extreme circumstances. This paper will analyze the various methods of modeling LGD and will provide an alternative estimate of LGD using Merton's model for the valuation of assets. Four components will be developed in this document: estimation of the minimum value that could have a financial asset, estimation of the loss given default LGD, development of a practical component, and finally validation of the proposed model. JEL classification numbers: G17, G24, G32
Benchmarking quantitative default risk models: a validation methodology
Moody's Investors Service, 2000
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