E-Book, Englisch, 155 Seiten
Reihe: BestMasters
Roccioletti Backtesting Value at Risk and Expected Shortfall
1. Auflage 2016
ISBN: 978-3-658-11908-9
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 155 Seiten
Reihe: BestMasters
ISBN: 978-3-658-11908-9
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
In this book Simona Roccioletti reviews several valuable studies about risk measures and their properties; in particular she studies the new (and heavily discussed) property of 'Elicitability' of a risk measure. More important, she investigates the issue related to the backtesting of Expected Shortfall. The main contribution of the work is the application of 'Test 1' and 'Test 2' developed by Acerbi and Szekely (2014) on different models and for five global market indexes.
Simona Roccioletti obtained her Master of Arts degree in Quantitative Asset and Risk Management at the University of Applied Sciences (bfi) Vienna, Austria.
Autoren/Hrsg.
Weitere Infos & Material
1;Acknowledgements;6
2;Contents;7
3;List of Figures;10
4;List of Tables;12
5;Abbreviations;13
6;Symbols;14
7;Abstract;15
8;Chapter 1 Introduction;16
9;Chapter 2 Risk Measures and their Properties;20
9.1;2.1 Definition of risk measure;20
9.2;2.2 Value at Risk;22
9.3;2.3 Expected Shortfall;24
9.4;2.4 Expectiles;26
9.5;2.5 Coherent risk measures;29
9.5.1;2.5.1 Coherence of VaR;31
9.5.2;2.5.2 Coherence of ES;33
9.5.3;2.5.3 Coherence of Expectiles;33
9.6;2.6 Risk Measures: a deeper view;34
9.6.1;2.6.1 Convexity;34
9.6.2;2.6.2 Comonotonic Additivity;36
9.6.3;2.6.3 Law Invariance;37
9.6.4;2.6.4 Robustness;38
10;Chapter 3 Elicitability;41
10.1;3.1 Evaluate Point Forecasts;41
10.1.1;3.1.1 Consistency;45
10.1.2;3.1.2 Back to Elicitability;47
10.2;3.2 Elicitability of VaR;50
10.3;3.3 Elicitability of ES;51
10.4;3.4 Elicitability of Expectiles;53
11;Chapter 4 Backtesting;56
11.1;4.1 The Backtesting Idea;57
11.2;4.2 Backtesting VaR;59
11.2.1;4.2.1 Unconditional Coverage Tests;61
11.2.2;4.2.2 Conditional Coverage Tests;63
11.2.3;4.2.3 Backtesting with Information Variables;67
11.2.4;4.2.4 Regulatory Framework;68
11.3;4.3 Backtesting ES;71
11.3.1;4.3.1 Test 1.;73
11.3.2;4.3.2 Test 2.;75
11.3.3;4.3.3 Test 3.;79
11.3.4;4.3.4 Power of the tests;81
12;Chapter 5 Empirical Analysis;83
12.1;5.1 Data;83
12.2;5.2 Models;84
12.2.1;5.2.1 Normal Distribution;85
12.2.2;5.2.2 Student’s t-distribution;86
12.2.3;5.2.3 Kernel Density Estimation;86
12.2.4;5.2.4 GARCH Models;89
12.3;5.3 Backtesting results;90
12.3.1;5.3.1 VaR results;92
12.3.2;5.3.2 ES results;99
13;Chapter 6 Conclusions;110
14;Appendix A MATLAB Code;112
14.1;A.1 MATLAB variables;112
14.2;A.2 ESTIMATION OF RISK MEASURES;115
14.2.1;A.2.1 Normal model;115
14.2.2;A.2.2 Student’s t model;116
14.2.3;A.2.3 Kernel model;117
14.2.4;A.2.4 Garch with normal innovations;118
14.2.5;A.2.5 Garch with Student’s t innovations;120
14.3;A.3 Value at Risk Tests;121
14.4;A.4 Expected Shortfall Tests;125
14.5;A.5 Monte Carlo p-values;127
15;Appendix B Figures;130
15.1;B.1 DAX;130
15.2;B.2 FTSE 100;135
15.3;B.3 NIKKEI;140
15.4;B.4 EURO STOXX 50;146
16;Bibliography;151
