A Note on the Estimation of the Frequency and Severity Distribution of Operational Losses (original) (raw)
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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.
2012
The Basel II accord requires banks to put aside a capital buffer against unexpected operational losses, resulting from inadequate or failed internal processes, people and systems or from external events. Under the sophisticated Advanced Measurement Approach banks are given the opportunity to develop their own model to estimate operational risk. This report focus on a loss distribution approach based on a set of real data. First a comprehensive data analysis was made which suggested that the observations belonged to a heavy tailed distribution. An evaluation of commonly used distributions was performed. The evaluation resulted in the choice of a compound Poisson distribution to model frequency and a piecewise defined distribution with an empirical body and a generalized Pareto tail to model severity. The frequency distribution and the severity distribution define the loss distribution from which Monte Carlo simulations were made in order to estimate the 99.9% quantile, also known as the the regulatory capital. Conclusions made on the journey were that including all operational risks in a model is hard, but possible, and that extreme observations have a huge impact on the outcome.
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)
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...
Estimation of operational value-at-risk in the presence of minimum collection thresholds
The Basel II Capital Accord of 2004 sets guidelines on operational risk capital requirements to be adopted by internationally active banks by around year-end 2007. Operational loss databases are subject to a minimum recording threshold of roughly 10,000(internal)and10,000 (internal) and 10,000(internal)and1 million (external) – an aspect often overlooked by practitioners. We provide theoretical and empirical evidence that ignoring these thresholds leads to underestimation of the VaR and CVaR figures within the Loss Distribution Approach. We emphasize that four crucial components of a reliable operational loss actuarial model are: (1) non-homogenous Poisson process for the loss arrival process, (2) flexible loss severity distributions, (3) accounting for the incomplete data, and (4) robustness analysis of the model.
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. --
Using Loss Data to Quantify Operational Risk
SSRN Electronic Journal, 2003
Management and quantification of operational risk has been impeded by the lack of internal or external data on operational losses. We consider newly available data collected from public information sources, and show how such data can be used to quantify operational risk for large internationally active banks. We find that operational losses are an important source of risk for such banks, and that the capital charge for operational risk will often exceed the charge for market risk. Although operational risk capital will vary depending on the size and scope of a bank's activities, our results are consistent with the 2-7 billion dollars in capital some large internationally active banks are currently allocating for operational risk.
Routledge eBooks, 2017
The rapid growth of the banking business requires banks to adapt quickly and to be supported by reliable risk management. In contrast to the market and credit risks, an operational risk is the first risk type known by the banks, but the least understood compared to market and credit risks. Basel II (International Committee for setting up bank risk management) defines an operational risk as the arising risk from the failure of internal processes, people, systems, or external events. Basel II also sets the standard and internal calculation modelling that must be applied by the banks. This research discusses the method for a bank to measure the operational risk capital cost accurately with the Advanced Measurement Approach (AMA), that requires historical data (Loss Event Database) regarding operational loss events. This advanced approach uses mathematics and probabilistic calculation, that highly likely provides an accurate result. This research found that the Loss Distribution Approach has high accuracy for calculating operational risk on every event of the eight bank business lines. It is known that the largest fraud is derived from internal bank operation.
Bayesian inference method has been presented in this paper for the modeling of operational risk. Bank internal and external data are divided into defined loss cells and then fitted into probability distribution. The distribution parameters and their uncertainties are estimated from posterior distributions derived using the Bayesian inference. Loss frequency is fitted into Poisson distributions. While the Poisson parameters, in a similar way, are defined by a posterior distribution developed using Bayesian inference. Bank operation loss typically has some low frequency but high magnitude loss data. These, heavy tail low frequency loss data are divided into several buckets where the bucket frequencies are defined by the experts. A probability distribution, as defined by the internal and external data, is used for these data. A Poisson distribution is used for the bucket frequencies. However instead of using any distribution of the Poisson parameters, point estimations are used. Monte Carlo simulation is then carried out to calculate the capital charge of the internal as well as the heavy tail high profile low frequency losses. The output of the Monte Carlo simulation defines the capital requirement that has to be allocated to cover potential operational risk losses for the next year.