Implementing loss distribution approach for operational risk

Shevchenko, Pavel V.

doi:10.1002/asmb.812

Cited by 37 publications

(27 citation statements)

References 54 publications

(104 reference statements)

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“…So far, the operational risk literature could not present clear evidence favoring one approach over the other. For instance, using a simulation study, Shevchenko (2010) shows that for light-tail lognormal severity distributions, the shifting approach might induce significant bias in comparison to the truncation approach, but this bias becomes insignificant for heavy-tail lognormal distributions. Meanwhile, simulation studies performed by Cavallo et al (2012) under the shifting approach reveal that the overstatement or understatement of the severity of an individual loss in the extreme right tail depends on the characteristics of the data sample.…”

Section: Introductionmentioning

confidence: 99%

Estimation of Truncated Data Samples in Operational Risk Modeling

Ergashev

Pavlikov²,

Uryasev

et al. 2015

J of Risk & Insurance

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This article addresses challenges of estimating operational risk regulatory capital when a loss sample is truncated from below at a data collection threshold. Recent operational risk literature reports that the attempts to estimate loss distributions by the maximum likelihood method are not always successful under the truncation approach that accounts for the existence of censored losses—the likelihood surface is sometimes ascending with no global solution. The literature offers an alternative called the shifting approach, which estimates the loss distribution without taking into account censored losses. We present a necessary and sufficient condition for the existence of the global solution to the likelihood maximization problem under the truncation approach when the true loss distribution is lognormal, and derive a practically explicit expression for the global solution. We show by a simulation study that, as the sample size increases, the capital bias by the truncation approach declines while the bias by the shifting approach does not.

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Section: Introductionmentioning

confidence: 99%

Estimation of Truncated Data Samples in Operational Risk Modeling

Ergashev

Pavlikov²,

Uryasev

et al. 2015

J of Risk & Insurance

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show abstract

“…There are several modeling issues that should be resolved to use this approach in practice, a detailed review on the quantitative properties of estimation can be found in [19], [20], [21], [22], [23], [23], [24] and in addition in some important heavy tailed settings (large consequence, rare occurance) closed form representations of such models in [25], [16] and [15].…”

Section: A Brief Background On Loss Distributional Approach (Lda) Modelsmentioning

confidence: 99%

“…A severity distribution function F is said to have a dominantly varying tail if it satisfies the asymptotic condition that 20) for any u ∈ (0, 1). An alternative equivalent relationship is to consider…”

Section: Remark 217 (Implications For Capital Approximations)mentioning

confidence: 99%

Understanding operational risk capital approximations: First and second orders

Peters¹,

Targino²,

Shevchenko³

2013

JGR

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We set the context for capital approximation within the framework of the Basel II / III regulatory capital accords. This is particularly topical as the Basel III accord is shortly due to take effect. In this regard, we provide a summary of the role of capital adequacy in the new accord, highlighting along the way the significant loss events that have been attributed to the Operational Risk class that was introduced in the Basel II and III accords. Then we provide a semi-tutorial discussion on the modelling aspects of capital estimation under a Loss Distributional Approach (LDA). Our emphasis is to focuss on the important loss processes with regard to those that contribute most to capital, the so called "high consequence, low frequency" loss processes.This leads us to provide a tutorial overview of heavy tailed loss process modelling in OpRisk under Basel III, with discussion on the implications of such tail assumptions for the severity model in an LDA structure. This provides practitioners with a clear understanding of the features that they may wish to consider when developing OpRisk severity models in practice.From this discussion on heavy tailed severity models, we then develop an understanding of the impact such models have on the right tail asymptotics of the compound loss process and we provide detailed presentation of what are known as first and second order tail approximations for the resulting heavy tailed loss process. From this we develop a tutorial on three key families of risk measures and their equivalent second order asymptotic approximations: Value-at-Risk (Basel III industry standard); Expected Shortfall (ES) and the Spectral Risk Measure. These then form the capital approximations.We then provide a few example case studies to illustrate the accuracy of these asymptotic captial approximations, the rate of the convergence of the assymptotic result as a function of the LDA frequency and severity model parameters, the sensitivity of the capital approximation to the model parameters and the sensitivity to model miss-specification.Key words: Basel II/III; Capital Approximation; Loss Distributional Approach; Capital Approximation; Value-at-Risk; Expected Shortfall; Spectral Risk Measure; Subexponential; Regularly Varying. The Changing Landscape of Capital AccordsIn juristictions in which active regulation is applied to the banking sector throughout the world, the modelling of Operational Risk (OpRisk) has progressively taken a prominent place in financial quantitative measurement. This has occurred as a result of Basel II and now Basel III regulatory requirements. For example in the context of banking regulation in Australia, the basic framework of Basel II/III is summarized in Figure 1. In this juristiction one observes that a large amount of the developments in quantitative methodology for estimation of OpRisk capital, development of OpRisk frame- There have been both numerical and simulation based approaches adopted as well as analytical mathematical developments of closed form approximatio...

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“…If details of the insurance policies are known (e.g. top cover limit, excess amount, etc), see Shevchenko (2009), then it should not be difficult to account for insurance recoveries, when the annual loss distribution over next reporting year is estimated via simulation of the frequencies and severities. Often, event times are needed to calculate the insurance recoveries and these are easily simulated for Poisson processes considered in this paper.…”

Section: Modelmentioning

confidence: 99%

“…There are various important aspects of operational risk modeling discussed in the literature, e.g. Chavez-Demoulin et al (2006), Cruz (2002Cruz ( , 2004 and Shevchenko (2009) to mention a few. One of the challenges in modelling operational risk is the lack of complete data -often a bank's internal data are not reported below a certain level (typically of the order of €10,000).…”

Section: Introductionmentioning

confidence: 99%

Modeling operational risk data reported above a time-varying threshold

Shevchenko¹,

Temnov²

2009

JOP

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Typically, operational risk losses are reported above a threshold. Fitting data reported above a constant threshold is a well known and studied problem. However, in practice, the losses are scaled for business and other factors before the fitting and thus the threshold is varying across the scaled data sample. A reporting level may also change when a bank changes its reporting policy. We present both the maximum likelihood and Bayesian Markov chain Monte Carlo approaches to fitting the frequency and severity loss distributions using data in the case of a time varying threshold. Estimation of the annual loss distribution accounting for parameter uncertainty is also presented.

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Implementing loss distribution approach for operational risk

Cited by 37 publications

References 54 publications

Estimation of Truncated Data Samples in Operational Risk Modeling

Estimation of Truncated Data Samples in Operational Risk Modeling

Understanding operational risk capital approximations: First and second orders

Modeling operational risk data reported above a time-varying threshold

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