Implementing loss distribution approach for operational risk

Applied Stochastic Models in Business and Industry

Volumn 26, Issue 3, 2010, Pages 277-307

  Shevchenko, Pavel V ^a  

^a CSIRO   (Australia)

Author keywords

Basel II; Bayesian inference; Dependence modeling; Loss distribution approach; Operational risk

Indexed keywords

BASEL II; BAYESIAN INFERENCE; DEPENDENCE MODELING; LOSS DISTRIBUTION; OPERATIONAL RISKS;

INFERENCE ENGINES; LAWS AND LEGISLATION;

BAYESIAN NETWORKS;

EID: 77953592100     PISSN: 15241904     EISSN: 15264025     Source Type: Journal    
DOI: 10.1002/asmb.812     Document Type: Article

References (71)

1. Basel Committee on Banking Supervision. International Convergence of Capital Measurement and Capital Standards: A Revised Framework, Bank for International Settlements, Basel, 2006. Available from: www.bis.org.
2. King JL. Operational Risk: Measurements and Modelling. Wiley: New York, 2001.
3. Cruz MG. Modeling, Measuring and Hedging Operational Risk. Wiley: Chichester, 2002.
4. Cruz MG (ed.). Operational Risk Modelling and Analysis: Theory and Practice. Risk Books: London, 2004.
5. Panjer HH. Operational Risks: Modeling Analytics. Wiley: New York, 2006.
6. McNeil AJ, Frey R, Embrechts P. Quantitative Risk Management: Concepts, Techniques and Tools. Princeton University Press: Princeton, NJ, 2005.
7. Chernobai AS, Rachev ST, Fabozzi FJ. Operational Risk: A Guide to Basel II Capital Requirements, Models, and Analysis. Wiley: New Jersey, 2007.
8. Chavez-Demoulin V, Embrechts P, Nešlehová J. Quantitative models for operational risk: extremes, dependence and aggregation. Journal of Banking and Finance 2006; 30(9):2635-2658.
9. Frachot A, Moudoulaud O, Roncalli T. Loss distribution approach in practice. In The Basel Handbook: A Guide for Financial Practitioners, Ong M (ed.). Risk Books: London, 2004.
10. Aue F, Klakbrener M. Lda at work: Deutsche bank's approach to quatifying operational risk. The Journal of Operational Risk 2006; 1(4):49-95.
11. Klugman SA, Panjer HH, Willmot GE. Loss Models From Data to Decisions. Wiley: New York, 1998.
12. Sandström A. Solvency: Models, Assessment and Regulation. Chapman & Hall, CRC: Boca Raton, London, 2006.
13. Wüthrich MV, Merz M. Stochastic Claims Reserving Methods in Insurance. Wiley: New York, 2008.
14. Moscadelli M. The modelling of operational risk: experiences with the analysis of the data collected by the Basel committee. Working Paper No. 517, Bank of Italy, 2004.
15. Dutta K, Perry J. A tale of tails: an empirical analysis of loss distribution models for estimating operational risk capital. Working Paper No. 06-13, Federal Reserve Bank of Boston, 2006. Available from: http://www.bos.frb.org/ economic/wp/index.htm.
16. Bee M. On maximum likelihood estimation of operational loss distributions. Discussion Paper No. 3, Dipartimento di Economia, Universita degli Studi di Trento, 2005.
17. Chernobai A, Menn C, Trück S, Rachev ST. A note on the estimation of the frequency and severity distribution of operational losses. The Mathematical Scientist 2005; 30(2):87-97.
18. Mignola G, Ugoccioni R. Effect of a data collection threshold in the loss distribution approach. The Journal of Operational Risk 2006; 1(4):35-47.
19. Luo X, Shevchenko PV, Donnelly J. Addressing impact of truncation and parameter uncertainty on operational risk estimates. The Journal of Operational Risk 2007; 2:3-26.
20. Baud N, Frachot A, Roncalli T. How to avoid over-estimating capital charge for operational risk? OpRisk&Compliance, February 2003. Available from: www.opriskandcompliance.com.
21. Shevchenko PV, Temnov G. Modeling operational risk data reported above a time-varying threshold. The Journal of Operational Risk 2009; 4(2):19-42.
22. Basel Committee on Banking Supervision. Working Paper on the Regulatory Treatment of Operational Risk, Bank for International Settlements, September 2001. Avaialble from: www.bis.org.
23. Embrechts P, Klüppelberg C, Mikosch T. Modelling Extremal Events for Insurance and Finance. Springer: Berlin, 1997. Corrected fourth printing 2003.
24. Nešlehová J, Embrechts P, Chavez-Demoulin V. Infinite mean models and the LDA for operational risk. Journal of Operational Risk 2006; 1(1):3-25.
25. Degen M, Embrechts P, Lambrigger DD. The quantitative modeling of operational risk: between g-and-h and EVT. ASTIN Bulletin 2007; 37(2):265-291.
26. Gustafsson J, Nielsen JP, Pritchard P, Roberts D. Operational risk guided by kernel smoothing and continuous credibility: a practioners view. The Journal of Operational Risk 2006; 1(1):43-56.
27. Hess KT, Liewald A, Schmidt KD. An extension of Panjer's recursion. ASTIN Bulletin 2002; 32(2):283-297.
28. Gerhold S, Schmock U, Warnung R. A generalization of Panjer's recursion and numerically stable risk aggregation. Finance and Stochastics 2009; DOI: 10.1007/S00780-009-0104-1.
29. Sundt B. On some extensions of Panjer's class of counting distributions. ASTIN Bulletin 1992; 22(1):61-80.
30. Press WH, Teukolsky SA, Vetterling WT, Flannery BP. Numerical Recipes in C. Cambridge University Press: Cambridge, 2002.
31. Embrechts P, Frei M. Panjer recursion versus FFT for compound distributions. Mathematical Methods of Operations Research 2009; 69(3):497-508.
32. Schaller P, Temnov G. Efficient and precise computation of convolutions: applying FFT to heavy tailed distributions. Computational Methods in Applied Mathematics 2008; 8(2):187-200.
33. Luo X, Shevchenko PV. Computing tails of compound distributions using direct numerical integration. The Journal of Computational Finance 2009; unpublished.
34. Peters GW, Johansen AM, Doucet A. Simulation of the annual loss distribution in operational risk via Panjer recursions and Volterra integral equations for value-at-risk and expected shortfall estimation. The Journal of Operational Risk 2007; 2(3):29-58.
35. Böcker K, Klüppelberg C. Operational VAR: a closed-form approximation. Risk Magazine 2005; 12:90-93.
36. Böcker K, Sprittulla J. Operational VAR: meaningful means. Risk Magazine 2006; 12:96-98.
37. Ergashev B. Should risk managers rely on the maximum likelihood estimation method while quantifying operational risk? The Journal of Operational Risk 2008; 3:63-86.
38. Lehmann EL. Theory of Point Estimation. Wiley: New York, 1983.
39. Efron BF, Tibshirani RJ. An Introduction to the Bootstrap. Chapman and Hall: London, 1993.
40. Berger JO. Statistical Decision Theory and Bayesian Analysis (2nd edn). Springer: New York, 1985.
41. Peters GW, Sisson SA. Bayesian inference, Monte Carlo sampling and operational risk. The Journal of Operational Risk 2006; 1(3):27-50.
42. Robert CP, Casella G. Monte Carlo Statistical Methods (2nd edn). Springer Texts in Statistics. Springer: New York, 2004.
43. Gilks WR, Richardson S, Spiegelhalter DJ. Markov Chain Monte Carlo in Practice. Chapman & Hall: London, 1996.
44. Peters GW, Shevchenko PV, Wüthrich MV. Model uncertainty in claims reserving within Tweedie's compound Poisson models. ASTIN Bulletin 2009; 39(1):1-33.
45. Bedard M, Rosenthal JS. Optimal scaling of metropolis algorithms: heading towards general target distributions. The Canadian Journal of Statistics 2008; 36(4):483-503.
46. Davis E. Theory vs reality. OpRisk&Compliance, September 2006. Available from: www.opriskandcompliance. com/public/showPage.html?page=345305 [1 September 2006].
47. Shevchenko PV, Wüthrich MV. The structural modeling of operational risk via Bayesian inference: combining loss data with expert opinions. Journal of Operational Risk 2006; 1(3):3-26.
48. Bühlmann H, Gisler A. A Course in Credibility Theory and its Applications. Springer: Berlin, 2005.
49. Bühlmann H, Shevchenko PV, Wüthrich MV. A 'Toy' model for operational risk quantification using credibility theory. Journal of Operational Risk 2007; 2(1):3-19.
50. Federal Office of Private Insurance. Swiss Solvency Test, Technical Document, Bern, October 2006. Available from: www.bpv.admin.ch/themen/00506/ 00552.
51. Lambrigger DD, Shevchenko PV, Wüthrich MV. The quantification of operational risk using internal data, relevant external data and expert opinions. The Journal of Operational Risk 2007; 2:3-27.
52. Artzner P, Delbaen F, Eber JM, Heath D. Coherent measures of risk. Mathematical Finance 1999; 9:203-228.
53. Embrechts P, Nešlehová J, Wüthrich MV. Additivity properties for value-at-risk under Archimedean dependence and heavy-tailedness. Insurance: Mathematics and Economics 2009; 44:164-169.
54. Embrechts P, Lambrigger DD, Wüthrich MV. Multivariate extremes and the aggregation of dependent risks: examples and counter-examples. Extremes 2009; 12(2):107-127.
55. Frachot A, Roncalli T, Salomon E. The correlation problem in operational risk. Working Paper, Groupe de Recherche Opérationnelle, France, 2004.
56. Bee M. Copula-based multivariate models with applications to risk management and insurance. Working Paper, Dipartimento di Economia, Universita degli Studi di Trento, 2005. Avaialble from: URL: www.gloriamundi.org.
57. Lindskog F, McNeil A. Common Poisson shock models: application to insurance and credit risk modelling. ASTIN Bulletin 2003; 33:209-238.
58. Powojowski MR, Reynolds D, Tuenter HJH. Dependent events and operational risk. ALGO Research Quarterly 2002; 5(2):65-73.
59. Giacometti R, Rachev ST, Chernobai A, Bertocchi M. Aggregation issues in operational risk. The Journal of Operational Risk 2008; 3(3):3-23.
60. Embrechts P, Puccetti G. Aggregation operational risk across matrix structured loss data. The Journal of Operational Risk 2008; 3(2):29-44.
61. Böcker K, Klüppelberg C. Modelling and measuring multivariate operational risk with Lévy copulas. The Journal of Operational Risk 2008; 3(2):3-27.
62. Böcker K, Klüppelberg C. Multivariate models for operational risk. Quantitative Finance 2009; unpublished.
63. Joe H. Multivariate Models and Dependence Concepts. Chapman & Hall: London, 1997.
64. Nelson RB. An Introduction to Copulas. Springer: Berlin, 1999.
65. Cont R, Tankov P. Financial Modelling with Jump Processes. Chapman & Hall, CRC: Boca Raton, London, 2004.
66. Marshall CL. Measuring and Managing Operational Risks in Financial Institutions. Wiley: Singapore, 2001.
67. Peters GW, Shevchenko PV, Wüthrich MV. Dynamic operational risk: modeling dependence and combining different data sources of information. The Journal of Operational Risk 2009; 4(2):69-104.
68. Johnson NL, Kotz S, Balakrishnan N. Discrete Multivariate Distributions. Wiley: New York, 1997.
69. Shevchenko PV. Estimation of operational risk capital charge under parameter uncertainty. The Journal of Operational Risk 2008; 3(1):51-63.
70. Dalla Valle L. Bayesian copulae distributions, with application to operational risk management. Methodology and Computing in Applied Probability 2009; 11(1):95-115.
71. Mignola G, Ugoccioni R. Sources of uncertainty in modeling operational risk losses. The Journal of Operational Risk 2006; 1(2):33-50.