Statistical Analysis of Operational Risk Data (eBook)

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2020 | 1st ed. 2020
IX, 84 Seiten
Springer International Publishing (Verlag)
978-3-030-42580-7 (ISBN)

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Statistical Analysis of Operational Risk Data - Giovanni De Luca, Danilo Carità, Francesco Martinelli
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This concise book for practitioners presents the statistical analysis of operational risk, which is considered the most relevant source of bank risk, after market and credit risk. The book shows that a careful statistical analysis can improve the results of the popular loss distribution approach. The authors identify the risk classes by applying a pooling rule based on statistical tests of goodness-of-fit, use the theory of the mixture of distributions to analyze the loss severities, and apply copula functions for risk class aggregation. Lastly, they assess operational risk data in order to estimate the so-called capital-at-risk that represents the minimum capital requirement that a bank has to hold. The book is primarily intended for quantitative analysts and risk managers, but also appeals to graduate students and researchers interested in bank risks.



Giovanni De Luca is a Professor of Economic Statistics and was coordinator of the bachelor degree in Statistics (until November 2019) at Parthenope University, Naples, Italy, where he has taught since 2003. He received his Ph.D. in Mathematical and Statistical Methods from the University of Perugia in 1997. From 1999 to 2002, he worked as an Assistant Professor at the University of Verona. His research interests include time series analysis and statistics for financial markets. Much of his work is focused on the modeling of the dependence structure among variables. He has also investigated mixture models for improving volatility prediction.

Danilo Carità obtained his Ph.D. in Economics, Sustainability and Statistics in 2018. He holds a bachelor's degree in Statistics and a master's degree in Quantitative Methods for Economics. He has participated in international conferences and contributed to the Econometric Research in Finance journal.

Francesco Martinelli is a senior financial quantitative analyst manager at UBI Banca. For 20 years, he has worked in the field of quantitative analysis applied to financial markets, in risk management, particularly market risk, credit risk, operational risk and counterparty risk sectors, asset management and the process of validation of internal models. He is also an expert on the estimation of the integrated macro-financial model.

Contents 6
List of Figures 8
List of Tables 10
1 The Operational Risk 11
1.1 Introduction 11
1.2 Models for Operational Risk 12
1.2.1 Basic Indicator Approach 14
1.2.2 Standardized Approach 14
1.2.3 Advanced Measurement Approach 15
1.3 Loss Distribution Approach 17
1.4 DIPO Consortium 18
References 20
2 Identification of the Risk Classes 21
2.1 Introduction 21
2.2 Distributional Tests 21
2.3 Application to DIPO Data 25
References 27
3 Severity Analysis 28
3.1 Introduction 28
3.2 Mixture of Three-Parameter Log-Normal Distributions 29
3.3 Extreme Value Theory 30
3.4 Application to DIPO Data 32
3.4.1 Mixture of k Log-Normal Distributions 32
3.4.2 Log-Normal–GPD Distribution 46
3.4.3 Comparison 56
References 59
4 Frequency Analysis 60
4.1 Introduction 60
4.2 Mixture of Poisson Distributions 60
4.2.1 The Poisson Distribution 60
4.2.2 Finite Poisson Mixture 61
4.3 Mixture of Negative Binomial Distributions 62
4.3.1 The Negative Binomial Distribution 62
4.3.2 Relationship with Poisson Distribution 63
4.3.3 Maximum Likelihood Estimation 65
4.3.4 Finite Negative Binomial Mixture 66
4.4 Application to DIPO Data 66
References 78
5 Convolution and Risk Class Aggregation 79
5.1 Introduction 79
5.2 Overall Loss Distribution 79
5.3 Risk Class Aggregation and Copula Functions 81
5.3.1 Tail Dependence 82
5.3.2 Elliptical Copulae 83
5.3.3 Archimedean Copulae 85
5.4 Value-at-Risk Estimates Considering t-Copula 86
References 90
6 Conclusions 91

Erscheint lt. Verlag 24.2.2020
Reihe/Serie SpringerBriefs in Statistics
SpringerBriefs in Statistics
Zusatzinfo IX, 84 p. 68 illus., 44 illus. in color.
Sprache englisch
Themenwelt Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
Wirtschaft Allgemeines / Lexika
Wirtschaft Betriebswirtschaft / Management
Schlagworte Capital-at-risk • convolution • Copula • extreme value theory • Frequency analysis • Identification of risk classes • Loss distribution approach • Mixture of distributions • Operational Risk • Overall loss distribution • Real-world data • Risk class aggregation • Severity analysis
ISBN-10 3-030-42580-0 / 3030425800
ISBN-13 978-3-030-42580-7 / 9783030425807
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