Operational Risk Quantification: Addressing the Risk Dependencies in LDA (original) (raw)
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Operational-Risk Dependencies and the Determination of Risk Capital
SSRN Electronic Journal, 2000
With the advent of Basel II, risk-capital provisions need to also account for operational risk. The specification of dependence structures and the assessment of their effects on aggregate risk-capital are still open issues in modeling operational risk. In this paper, we investigate the potential consequences of adopting the restrictive Basel's Loss Distribution Approach (LDA), as compared to strategies that take dependencies explicitly into account. Drawing on a real-world database, we fit alternative dependence structures, using parametric copulas and nonparametric tail-dependence coefficients, and discuss the implications on the estimation of aggregate risk capital. We find that risk-capital estimates may increase relative to that derived for the LDA when accounting explicitly for the presence of dependencies. This phenomenon is not only be due to the (fitted) characteristics of the data, but also arise from the specific Monte Carlo setup in simulation-based risk-capital analysis.
Aggregation issues in operational risk
The Journal of Operational Risk, 2008
In this paper we study copula-based models for aggregation of operational risk capital across business lines in a bank. A commonly used method of summation of the value-at-risk (VaR) measures, that relies on a hypothesis of full correlation of losses, becomes inappropriate in the presence of dependence between business lines and may lead to over-estimation of the capital charge. The problem can be further aggravated by the persistence of heavy tails in operational loss data; in some cases, the subadditivity property of value-at-risk may fail and the capital charge becomes underestimated. We use α-stable heavy-tailed distributions to model the loss data and then apply the copula approach in which the marginal distributions are consolidated in the symmetric and skewed Student tcopula framework. In our empirical study, we compare VaR and conditional VaR estimates with those obtained under the full correlation assumption. Our results demonstrate significant reduction in capital when a t-copula is employed. However, the capital reduction is significantly smaller than in cases where a moderately heavy-tailed or thin-tailed distribution is calibrated to loss data. We also show that for confidence levels below 94% VaR exhibits the super-additivity property.
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...
Flexible dependence modeling of operational risk losses and its impact on total capital requirements
Journal of Banking & Finance, 2014
Operational risk data, when available, are usually scarce, heavy-tailed and possibly dependent. In this work, we introduce a model that captures such real-world characteristics and explicitly deals with heterogeneous pairwise and tail dependence of losses. By considering flexible families of copulas, we can easily move beyond modeling bivariate dependence among losses and estimate the total risk capital for the seven-and eightdimensional distributions of event types and business lines. Using real-world data, we then evaluate the impact of realistic dependence modeling on estimating the total regulatory capital, which turns out to be up to 38% smaller than what the standard Basel approach would prescribe.
Modeling Correlations in Operational Risk
Acta Physica Polonica A, 2018
The key demand for banks' economic capital methodology is to ensure that the model covers all relevant sources of risk in the right way. Operational risk models treat the arising losses as stochastic variables. One of the problems encountered in modeling is the need of taking into account correlations between events. It is possible to build models for correlated events based on copula functions. But the problem is that the losses are related to isolated events and simple applications of copulas are not allowed. The authors present a new algorithm that shows a modied application of copulas to calculating operational risk. The calculations were done on real data that allows for examining the correlation impact on risk measurement. As an additional evaluation of the algorithm a reference model based on the ParetoLévy copulas was used.
Using Weighted Distributions to Model Operational Risk
ASTIN Bulletin, 2016
The quantification of operational risk has to deal with various concerns regarding data, much more than other types of risk which banks and insurers are obliged to manage. One of the main questions that worries both researchers and practitioners is the bias in the data on the operational losses amounts recorded. We support the assertions made by several authors and defend that this concern is serious when modeling operational losses data and, typically, is presented in all the databases. We show that it's possible, based on mild assumptions on the internal procedures put in place to manage operational losses, to make parametric inference using loss data statistics, that is, to estimate the parameters for the losses amounts, taking in consideration the bias that, not being considered, generates a two fold error in the estimators for the mean loss amount and the total loss amount, the former being overvalued and the last undervalued. In this paper, we do not consider the existence...
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.
International Journal of Risk …, 2008
The management of Operational Risks has always been difficult due to the high number of variables to work with and their complex multivariate distribution. A Copula is a statistic tool which has been recently used in finance and engineering to build flexible joint distributions in order to model a high number of variables. The goal of this paper is to propose its use to model Operational Risks, by showing its benefits with an empirical example.
New Results on the Correlation Problem in Operational Risk
Econometrics: Econometric & Statistical Methods - Special Topics eJournal, 2014
Internal models of operational risk are all built based on the same guidelines provided by the regulators. However, we observe a broad range of practices among banks concerning modeling choices and calibration methods. It is thus relevant to discuss the relative importance of the main drivers and modeling choices of the operational risk capital charge. Many studies in the literature have focused on the modeling of the tails in the severity distributions. In this paper, we use a class of analytical models for operational risk in order to assess the relative importance of all parameters of the model. In particular, we show that the bank’s capital charge is not very sensitive to the dispersion in correlations, the average level of correlations being a much more critical parameter of the operational risk capital charge. We show that the assumption of uniform correlations is robust, contrary to what is often advised by internal auditors or regulators.
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.