Estimation of Operational Value-at-Risk in the Presence of Minimum Collection Thresholds ? (original) (raw)
Related papers
The recently finalized Basel II Capital Accord requires banks to adopt a procedure to estimate the operational risk capital charge. Under the Advanced Measurement Approaches, that are currently mandated for all large internationally active US banks, require the use of historic operational loss data. Operational loss databases are typically subject to a minimum recording threshold of roughly $10,000. We demonstrate that ignoring such thresholds leads to biases in corresponding parameter estimates when the threshold is ignored. Using publicly available operational loss data, we analyze the effects of model misspecification on resulting expected loss, Value-at-Risk, and Conditional Value-at-Risk figures and show that underestimation of the regulatory capital is a consequence of such model error. The choice of an adequate loss distribution is conducted via in-sample goodness-of-fit procedures and backtesting, using both classical and robust methodologies. --
A loss distribution for operational risk derived from pooled bank losses
The Basel II accord encourages banks to develop their own advanced measurement approaches (AMA). However, the paucity of loss data implies that an individual bank cannot obtain a probability distribution with any reliability. We propose a model, targeting the regulator initially, by obtaining a probability distribution for loss magnitude using pooled annual risk losses from the banks under the regulator's oversight. We start with summarized loss data from 63 European banks and adjust the probability distribution obtained for losses that go unreported by falling below the threshold level. Using our model, the regulator has a tool for understanding the extent of annual operational losses across all the banks under its supervision. The regulator can use the model on an ongoing basis to make comparisons in year-on-year changes to the operational risk profile of the regulated banking sector. The Basel II accord lays out three possibilities for calculating the minimum capital reserve required to cover operational risk losses: the basic approach, the standardized approach, and the advanced measurement approach (AMA). The latter is specific to an individual bank that uses its own approach to determine capital requirements for its different lines of business and for the bank as a whole. A typical AMA model uses a probability distribution for loss per incident of a certain category and another for the number of incidents in that category, although there are other modeling approaches as well. A problem with this approach then is the paucity of loss data available for any particular bank to obtain such distributions. We obtain a probability distribution for operational risk loss impact using summarized results of pooled operational risk losses from multiple banks. Doing so allows us to derive simple AMA models for the regulators using data from the banks they oversee. One possibility is that the regulator can obtain an estimate for the capital requirement for a 'typical' bank under its supervision. We use data from 63 banks that the distribution fits annual losses very well. Moreover, we adjust for the fact that the regulator sees only losses above a certain threshold, say €10,000.
Reasonableness and Correctness for Operational Value-at-Risk
Economic Analysis Letters
Calculating the amount of regulatory capital to cover unexpected losses due to operational events in the upcoming year has caused problems because of difficulties in fitting probability distributions to data. It is consequently difficult to judge an appropriate level of capital that reflects the risk profile of a financial institution. We provide theoretical and empirical analyses to link the calculated capital to the sum of losses using appropriate statistical approximations. We conclude that, in order to reasonably reflect the associated risk, the capital should be approximately half the sum of losses, with a wide bound for the ratio of capital to sum.
Journal of Governance and Regulation (print)
The management of operational risk in the banking industry has undergone significant changes over the last decade due to substantial changes in operational risk environment. Globalization, deregulation, the use of complex financial products and changes in information technology have resulted in exposure to new risks very different from market and credit risks. In response, Basel Committee for banking Supervision has developed a regulatory framework, referred to as Basel II, that introduced operational risk category and corresponding capital requirements. Over the past five years, major banks in most parts of the world have received accreditation under the Basel II Advanced Measurement Approach (AMA) by adopting the loss distribution approach (LDA) despite there being a number of unresolved methodological challenges in its implementation. Different approaches and methods are still under hot debate. In this paper, we review methods proposed in the literature for combining different da...
A note on the estimation of the frequency and severity distribution of operational losses
2006
The Basel II Capital Accord requires banks to determine the capital charge to account for operational losses. Compound Poisson process with Lognormal losses is suggested for this purpose. The paper examines the impact of possibly censored and/or truncated data on the estimation of loss distributions. A procedure on consistent estimation of the severity and frequency distributions based on incomplete data samples is presented. It is also demonstrated that ignoring the peculiarities of available data samples leads to inaccurate Valueat-Risk estimates that govern the operational risk capital charge.
Estimating Operational Risk Capital with Greater Accuracy, Precision and Robustness
2013
The largest US banks are required by regulatory mandate to estimate the operational risk capital they must hold using an Advanced Measurement Approach (AMA) as defined by the Basel II/III Accords. Most use the Loss Distribution Approach (LDA) which defines the aggregate loss distribution as the convolution of a frequency and a severity distribution representing the number and magnitude of losses, respectively. Estimated capital is a Value-at-Risk (99.9th percentile) estimate of this annual loss distribution. In practice, the severity distribution drives the capital estimate, which is essentially a very high quantile of the estimated severity distribution. Unfortunately, because the relevant severities are heavy-tailed AND the quantiles being estimated are so high, VaR always appears to be a convex function of the severity parameters, causing all widely-used estimators to generate biased capital estimates (apparently) due to Jensen's Inequality. The observed capital inflation is ...
Implications of Alternative Operational Risk Modeling Techniques
2005
Quantification of operational risk has received increased attention with the inclusion of an explicit capital charge for operational risk under the new Basle proposal. The proposal provides significant flexibility for banks to use internal models to estimate their operational risk, and the associated capital needed for unexpected losses. Most banks have used variants of value at risk models that estimate frequency, severity, and loss distributions. This paper examines the empirical regularities in operational loss data. Using loss data from six large internationally active banking institutions, we find that loss data by event types are quite similar across institutions. Furthermore, our results are consistent with economic capital numbers disclosed by some large banks, and also with the results of studies modeling losses using publicly available "external" loss data.
Measuring operational risk in financial institutions
Applied Financial Economics, 2012
The scarcity of internal loss databases tends to hinder the use of the advanced approaches for operational risk measurement (Advanced Measurement Approaches (AMA)) in financial institutions. As there is a greater variety in credit risk modelling, this article explores the applicability of a modified version of CreditRisk+ to operational loss data. Our adapted model, OpRisk+, works out very satisfying Values-at-Risk (VaR) at 95% level as compared with estimates drawn from sophisticated AMA models. OpRisk+ proves to be especially worthy in the case of small samples, where more complex methods cannot be applied. OpRisk+ could therefore be used to fit the body of the distribution of operational losses up to the 95%-percentile, while Extreme Value Theory (EVT), external databases or scenario analysis should be used beyond this quantile.
Statistical Models of Operational Loss
Handbook of Finance, 2008
The purpose of this chapter is to give a theoretical but pedagogical introduction to the advanced statistical models that are currently being developed to estimate operational risks, with many examples to illustrate their applications in the financial industry. The introductory part discusses the definitions of operational risks in finance and banking, then considers the problems surrounding data collection and the consequent impossibility of estimating the 99.9 th percentile of an annual loss distribution with even a remote degree of accuracy. Section 7.2 describes a wellknown statistical method for estimating the loss distribution parameters when the data are subjective and/or are obtained from heterogeneous sources. Section 7.3 explains why the Advanced Measurement Approaches (AMA) for estimating operational risk capital are, in fact, all rooted in the same "Loss Distribution Approach" (LDA). The only differences are in the data used to estimate parameters (scorecard vs historical loss experience) and that, under certain assumptions, an analytic formula for estimating the unexpected loss may be used in place of simulation. In section 7.4, various generalizations of this formula are deduced from different assumptions about the loss frequency and severity, and the effect of different parameter estimation methods on the capital charge is discussed. We derive a simple formula for the inclusion of insurance cover, showing that the capital charge should be reduced by a factor (1 − r)