VALUE AT RISK - EUROPEAN CENTRAL BANK W O R K I N G PA P E...

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EUROPEAN CENTRAL BANK WORKING PAPER SERIES ECB EZB EKT BCE EKP WORKING PAPER NO. 75 VALUE AT RISK MODELS IN FINANCE BY SIMONE MANGANELLI AND ROBERT F. ENGLE August 2001
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EUROPEAN CENTRAL BANK WORKING PAPER SERIES 1 Simone Manganelli, European Central Bank, Kaiserstraße 29, 60311 Frankfurt am Main, Germany. E-mail: [email protected] 2 Robert F. Engle, New York University and UCSD. E-mail: [email protected] WORKING PAPER NO. 75 VALUE AT RISK MODELS IN FINANCE BY SIMONE MANGANELLI 1 AND ROBERT F. ENGLE 2 August 2001
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ECB • Working Paper No 75 • August 2001 2 © European Central Bank, 2001 Address Kaiserstrasse 29 D-60311 Frankfurt am Main Germany Postal address Postfach 16 03 19 D-60066 Frankfurt am Main Germany Telephone +49 69 1344 0 Internet http://www.ecb.int Fax +49 69 1344 6000 Telex 411 144 ecb d All rights reserved. Reproduction for educational and non-commercial purposes is permitted provided that the source is acknowledged. The views expressed in this paper are those of the authors and do not necessarily reflect those of the European Central Bank. ISSN 1561-0810
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ECB • Working Paper No 75 • August 2001 3 Contents Abstract 4 Non-technical summary 5 1 Introduction 6 2 VaR Methodologies 7 2.1 Parametric Models 8 2.2 Nonparametric Methods 10 2.3 Semiparametric Models 12 3 Expected Shortfall 20 4 Monte Carlo Simulation 22 4.1 Sumulation Study of the Threshold Choice for EVT 22 4.2 Comparison of quantile methods performance 24 5 Conclusion 28 References 29 Appendix A: Tables 31 Appendix B: Figures 35 European Central Bank Working Paper Series 36
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Abstract Value at Risk (VaR) has become the standard measure that financial analysts use to quantify market risk. VaR is defined as the maximum potential change in value of a portfolio of financial instruments with a given probability over a certain horizon. VaR measures can have many applications, such as in risk management, to evaluate the performance of risk takers and for regulatory requirements, and hence it is very important to develop methodologies that provide accurate estimates. The main objective of this paper is to survey and evaluate the performance of the most popular univariate VaR methodologies, paying particular attention to their underlying assumptions and to their logical flaws. In the process, we show that the Historical Simulation method and its variants can be considered as special cases of the CAViaR framework developed by Engle and Manganelli (1999). We also provide two original methodological contributions. The first one introduces the extreme value theory into the CAViaR model. The second one concerns the estimation of the expected shortfall (the expected loss, given that the return exceeded the VaR) using a simple regression technique. The performance of the models surveyed in the paper is evaluated using a Monte Carlo simulation. We generate data using GARCH processes with different distributions and compare the estimated quantiles to the true ones. The results show that CAViaR models are the best performers with heavy-tailed DGP.
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This note was uploaded on 09/04/2010 for the course BUSINESS 1 taught by Professor Simonemanganelli1 during the Spring '10 term at Aarhus Universitet.

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VALUE AT RISK - EUROPEAN CENTRAL BANK W O R K I N G PA P E...

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