Anna Chernobai

Applying Robust Methods to Operational Risk Modeling

We use robust statistical methods to analyze operational loss data. Commonly used classical estimators of model parameters may be sub-optimal under minor departures of data from the model assumptions. Operational loss data are characterized by a very heavy right tail of the loss distribution attributed to several “low frequency/high severity” events. Classical estimators may produce biased estimates of parameters leading to unreasonably high estimates of mean, variance and the operational risk VAR and CVARmeasures. The main objective of robust methods is to focus the analysis on the fundamental properties of the bulk of the data, without being distorted by outliers. We argue that further comparison of results obtained under the classical and robust procedures can serve as a basis for the VAR sensitivity analysis and can lead to an understanding of the economic role played by these extreme events. An empirical study with 1980–2002 public operational loss data reveals that the highest 5% of losses account for up to 76% of the operational risk capital charge.

Aggregation issues in operational risk

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, which relies on a hypothesis of full correlation of losses, becomes inappropriate in the presence of dependence between business lines and may lead to overestimation 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 VaR 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 t-copula framework. In our empirical study, we compare VaR and conditional VaR estimates with those obtained under the full correlation assumption. Our results demonstrate a 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, when historical weekly data is used, VaR exhibits the superadditivity property for confidence levels below 94% and that, when the loss distribution approach is used, the superadditivity of VaR is observed at a higher confidence level (98%).

Composite goodness-of-fit tests for left-truncated loss samples

In many loss models the recorded data are left-truncated with an unknown number of missing data. We derive the exact formulae for several goodness-of-fit statistics that should be applied to such models. We additionally propose two new statistics to test the fit in the upper quantiles, applicable to models where the accuracy of the upper tail estimate is crucial, as in models addressing the Value-at-Risk and ruin probabilities. We apply the tests on a variety of distributions fitted to the external operational loss and the natural catastrophe insurance claim data, subject to the recording thresholds of

Heavy-tailed distributional model for operational losses

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Is Selection Bias Inherent in Housing Transactions? An Equilibrium Approach

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Empirical Examination of Operational Loss Distributions

We examine the statistical properties of operational losses obtained from a large European bank using an actuarial-type framework. The simplistic assumption of a Poisson frequency distribution fails and we show that the frequency process follows closely a non-homogeneous Poisson process with a deterministic intensity of the form of a continuous cdf-like function. Further, operational losses are modeled using a variety of distributions. We address the problems of (1) reporting bias; (2) supplementing internal data with external data; (3) tail estimation; and (4) mixing the distributions of the body and the tail, and propose practical solutions to such problems. Finally, our empirical findings are consistent with other studies reporting very heavy-tailed loss distributions with the tail index below unity.

Modelling Catastrophe Claims with Left-Truncated Severity Distributions (Extended Version)

We develop an equilibrium model for residential housing transactions in an economy with houses that differ in their quality and households that differ in their planned holding horizon. We show that, in equilibrium, a clientele effect persists, with long‐horizon buyers overwhelmingly choosing higher quality properties and short‐horizon buyers settling for lower quality properties. This clientele effect creates a sample selection bias: the properties that are on the market are predominantly of lower quality. Since these are the preferred choice of short‐horizon buyers, they demonstrate a faster turnover. Both the clientele effect and the selection bias are more pronounced with an increase in the variance of house quality and in the variance of the planned holding horizon. Our theoretical model supports empirical evidence on the existence of such bias in home price indices and explains it by the differences in ex ante holding horizons.

Operational IT Failures, IT Value Destruction, and Board-Level IT Governance Changes

Until very recently, it has been believed that banks are exposed to two main types of risks: credit risk (the counterparty failure risk) and market risk (the risk of loss due to changes in market indicators, such as interest rates and exchange rates), in the order of importance. The remaining financial risks have been put in the category of other risks, operational risk being one of them. Recent developments in the financial industry have shown that the importance of operational risk has been largely under-estimated. Newly defined capital requirements set by the Basel Committee for Banking Supervision in 2004, require financial institutions to estimate the capital charge to cover their operational losses [6].

Business Complexity and Risk Management: Evidence from Operational Risk Events in U.S. Bank Holding Companies

In this paper, we present a procedure for consistent estimation of the severity and frequency distributions based on incomplete insurance data and demonstrate that ignoring the thresholds leads to a serious underestimation of the ruin probabilities. The event frequency is modelled with a non-homogeneous Poisson process with a sinusoidal intensity rate function. The choice of an adequate loss distribution is conducted via the in-sample goodness-of-fit procedures and forecasting, using classical and robust methodologies.

Estimation of operational value-at-risk in the presence of minimum collection threshold: An empirical study

This paper presents an empirical study of changes that firms implement in their board-level IT governance (ITG) upon experiencing operational IT failures. Consistent with the separation of oversight from management decisions, board-level ITG is responsible for monitoring managerial IT decisions and policies for controlling IT resources. We expect that operational IT failures indicating inadequacies in board monitoring of controls over IT resources would result in a negative stock market reaction and, in turn, induce firms to improve their board-level ITG. Our expectation is confirmed based on a sample of 110 operational IT failures from U.S. public financial firms. Specifically, our results demonstrate that subsequent to experiencing operational IT failures, firms make improvements to the IT competency level of their boards, and the improvements are proportional to the degree of negative market reaction. However, those improvements are only on the executive side of the board, namely: an increase in the IT experience of internal (executive) directors and an increased turnover rate of CIOs serving on the board. Furthermore, the likelihood of CIO turnover is lower in IT-intensive firms where such turnover could be more disruptive. Our results contribute to understanding the critical connection between operational IT failures and board-level ITG.