Loss Distribution Approach for Operational Risk Capital Modelling Under Basel II: Combining Different Data Sources for Risk Estimation

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 data sources (internal data, external data and scenario analysis) which is one of the regulatory requirement for AMA.

[1]  Gareth W. Peters,et al.  Dynamic Operational Risk: Modeling Dependence and Combining Different Sources of Information , 2009, 0904.4074.

[2]  Jean-Philippe Peters,et al.  Modeling Operational Risk Based on Multiple Experts’ Opinion , 2009 .

[3]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[4]  Stuart A. Klugman,et al.  Loss Models: From Data to Decisions , 1998 .

[5]  M. Neil,et al.  Modeling operational risk in financial institutions using hybrid dynamic Bayesian networks , 2009 .

[6]  Norman Fenton,et al.  Using Bayesian Networks to Model Expected and Unexpected Operational Losses , 2005, Risk analysis : an official publication of the Society for Risk Analysis.

[7]  R. Yager.  On the dempster-shafer framework and new combination rules , 1987, Inf. Sci..

[8]  W. Ferguson.  Solvency: Models, Assessment and Regulation , 2009 .

[9]  Paul Glasserman,et al.  Monte Carlo Methods in Financial Engineering , 2003 .

[10]  Pavel V. Shevchenko,et al.  Modelling Operational Risk Using Bayesian Inference , 2011 .

[11]  Jon C. Helton,et al.  Mathematical representation of uncertainty , 2001 .

[12]  Pavel V. Shevchenko,et al.  The Quantification of Operational Risk Using Internal Data, Relevant External Data and Expert Opinion , 2007 .

[13]  Paul Embrechts,et al.  For example, , 2022 .

[14]  L. H. Miller.  Table of Percentage Points of Kolmogorov Statistics , 1956 .

[15]  G. Boole.  An Investigation of the Laws of Thought: On which are founded the mathematical theories of logic and probabilities , 2007 .

[16]  Thierry Roncalli,et al.  Loss Distribution Approach in Practice , 2007 .

[17]  T. Ferguson.  A Bayesian Analysis of Some Nonparametric Problems , 1973 .

[18]  Amandha Ganegoda,et al.  A scaling model for severity of operational losses using generalized additive models for location scale and shape (GAMLSS) , 2012, Annals of Actuarial Science.

[19]  Gianluca Antonini,et al.  Challenges and pitfalls in measuring operational risk from loss data , 2009 .

[20]  M. Merz,et al.  Stochastic Claims Reserving Methods in Insurance , 2008 .

[21]  Kari Sentz,et al.  Combination of Evidence in Dempster-Shafer Theory , 2002 .

[22]  Bakhodir Ergashev.  A Theoretical Framework for Incorporating Scenarios into Operational Risk Modeling , 2011 .

[23]  B. Rost.  Basel Committee On Banking Supervision , 2010 .

[24]  Arthur P. Dempster,et al.  Upper and Lower Probabilities Induced by a Multivalued Mapping , 1967, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[25]  Jeremy E. Oakley,et al.  Uncertain Judgements: Eliciting Experts' Probabilities , 2006 .

[26]  A. Kolmogoroff.  Confidence Limits for an Unknown Distribution Function , 1941 .

[27]  Marco Moscadelli,et al.  The Modelling of Operational Risk: Experience with the Analysis of the Data Collected by the Basel Committee , 2004 .

[28]  Marcelo Cruz.  Modeling, Measuring and Hedging Operational Risk , 2002 .

[29]  Kabir K. Dutta,et al.  A Tale of Tails: An Empirical Analysis of Loss Distribution Models for Estimating Operational Risk Capital , 2006 .

[30]  J. Corcoran.  Modelling Extremal Events for Insurance and Finance , 2002 .

[31]  Harry H. Panjer,et al.  Operational Risk : Modeling Analytics , 2006 .

[32]  Greg N. Gregoriou.  Operational Risk Toward Basel III: Best Practices and Issues in Modeling, Management, and Regulation , 2009 .

[33]  Svetlozar T. Rachev,et al.  Operational Risk: A Guide to Basel II Capital Requirements, Models, and Analysis , 2007 .

[34]  Marcelo Cruz,et al.  Operational Risk Modelling and Analysis: Theory and Practice , 2004 .

[35]  Michael K. Ong.  The Basel Handbook: A Guide for Financial Practitioners , 2003 .

[36]  Robert C. Williamson,et al.  Probabilistic arithmetic. I. Numerical methods for calculating convolutions and dependency bounds , 1990, Int. J. Approx. Reason..

[37]  Scott Ferson,et al.  Constructing Probability Boxes and Dempster-Shafer Structures , 2003 .

[38]  T. Fine,et al.  Towards a Frequentist Theory of Upper and Lower Probability , 1982 .

[39]  Paul Embrechts,et al.  Additivity properties for Value-at-Risk under Archimedean dependence and heavy-tailedness , 2009 .

[40]  Arthur P. Dempster,et al.  A Generalization of Bayesian Inference , 1968, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[41]  J. Berger.  Statistical Decision Theory and Bayesian Analysis , 1988 .

[42]  Alois Gisler,et al.  A Course in Credibility Theory and its Applications , 2005 .

[43]  Christine M. Anderson-Cook,et al.  Book review: quantitative risk management: concepts, techniques and tools, revised edition, by A.F. McNeil, R. Frey and P. Embrechts. Princeton University Press, 2015, ISBN 978-0-691-16627-8, xix + 700 pp. , 2017, Extremes.

[44]  Carolyn Moclair,et al.  The structural modeling of operational risk via Bayesian inference: combining loss data with expert opinions , 2006 .

[45]  Michael Kalkbrener,et al.  LDA at work: Deutsche Bank's approach to quantifying operational risk , 2006 .

[46]  Ronald R. Yager,et al.  Arithmetic and Other Operations on Dempster-Shafer Structures , 1986, Int. J. Man Mach. Stud..

[47]  Mario V. Wuthrich,et al.  A 'Toy' Model for Operational Risk Quantification Using Credibility Theory , 2007 .

[48]  P. Embrechts,et al.  Quantitative models for operational risk: Extremes, dependence and aggregation , 2006 .

[49]  P. Walley.  Statistical Reasoning with Imprecise Probabilities , 1990 .

[50]  P. V. Shevchenko,et al.  The Structural Modelling of Operational Risk Via Bayesian Inference: Combining Loss Data with Expert Opinions , 2006, 0904.1067.

[51]  Weekly Bulletin,et al.  OFFICE OF THE COMPTROLLER OF THE CURRENCY , 1995 .

[52]  Louis N Ntasin.  Operational Risks: Modeling Analytics , 2007 .