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Open AccessArticle

Practice Oriented and Monte Carlo Based Estimation of the Value-at-Risk for Operational Risk Measurement

1
Department of Statistics and Quantitative Methods, Milano-Bicocca University, 20126 Milano, Italy
2
Group Operational and Reputational Risks, UniCredit S.p.A., 20154 Milano, Italy
3
School of Mathematical and Statistical Sciences, Western University, London, ON N6A 5B7, Canada
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Research of the third author has been supported by the Natural Sciences and Engineering Research Council of Canada under the title “From Data to Integrated Risk Management and Smart Living: Mathematical Modelling, Statistical Inference, and Decision Making,” as well as by a Mitacs Accelerate Award from the national research organization Mathematics of Information Technology and Complex Systems, Canada, in partnership with Sun Life Financial, under the title “Risk Aggregation Beyond the Normal Limits.”
Risks 2019, 7(2), 50; https://doi.org/10.3390/risks7020050
Received: 22 March 2019 / Revised: 15 April 2019 / Accepted: 25 April 2019 / Published: 1 May 2019
(This article belongs to the Special Issue Risk, Ruin and Survival: Decision Making in Insurance and Finance)
We explore the Monte Carlo steps required to reduce the sampling error of the estimated 99.9% quantile within an acceptable threshold. Our research is of primary interest to practitioners working in the area of operational risk measurement, where the annual loss distribution cannot be analytically determined in advance. Usually, the frequency and the severity distributions should be adequately combined and elaborated with Monte Carlo methods, in order to estimate the loss distributions and risk measures. Naturally, financial analysts and regulators are interested in mitigating sampling errors, as prescribed in EU Regulation 2018/959. In particular, the sampling error of the 99.9% quantile is of paramount importance, along the lines of EU Regulation 575/2013. The Monte Carlo error for the operational risk measure is here assessed on the basis of the binomial distribution. Our approach is then applied to realistic simulated data, yielding a comparable precision of the estimate with a much lower computational effort, when compared to bootstrap, Monte Carlo repetition, and two other methods based on numerical optimization. View Full-Text
Keywords: advanced measurement approach; confidence interval; Monte Carlo; operational risk; value-at-risk advanced measurement approach; confidence interval; Monte Carlo; operational risk; value-at-risk
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Greselin, F.; Piacenza, F.; Zitikis, R. Practice Oriented and Monte Carlo Based Estimation of the Value-at-Risk for Operational Risk Measurement. Risks 2019, 7, 50.

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