Bootstrap prediction intervals for VaR and ES in the context of GARCH models
In this paper, we propose a new bootstrap procedure to obtain prediction intervals of future Value at Risk (VaR) and Expected Shortfall (ES) in the context of univariate GARCH models. These intervals incorporate the parameter uncertainty associated with the estimation of the conditional variance of returns. Furthermore, they do not depend on any particular assumption on the error distribution. Alternative bootstrap intervals previously proposed in the literature incorporate the first but not the second source of uncertainty when computing the VaR and ES. We also consider an iterated smoothed bootstrap with better properties than traditional ones when computing prediction intervals for quantiles. However, this latter procedure depends on parameters that have to be arbitrarily chosen and is very complicated computationally. We analyze the finite sample performance of the proposed procedure and show that the coverage of our proposed procedure is closer to the nominal than that of the alternatives. All the results are illustrated by obtaining one-step-ahead prediction intervals of the VaR and ES of several real time series of financial returns.
|Date of creation:||May 2010|
|Date of revision:|
|Contact details of provider:|| Web page: http://portal.uc3m.es/portal/page/portal/dpto_estadistica|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Hansen, Bruce E, 1994.
"Autoregressive Conditional Density Estimation,"
International Economic Review,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-30, August.
- Hansen, B.E., 1992. "Autoregressive Conditional Density Estimation," RCER Working Papers 322, University of Rochester - Center for Economic Research (RCER).
- Tom Doan, . "RATS programs to replicate Hansen's GARCH models with time-varying t-densities," Statistical Software Components RTZ00086, Boston College Department of Economics.
- Suleyman Basak & Alex Shapiro, .
"Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices,"
Rodney L. White Center for Financial Research Working Papers
6-99, Wharton School Rodney L. White Center for Financial Research.
- Basak, Suleyman & Shapiro, Alexander, 2001. "Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices," Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 371-405.
- Suleyman Basak & Alexander Shapiro, 1999. "Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-032, New York University, Leonard N. Stern School of Business-.
- Suleyman Basak & Alex Shapiro, . "Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices," Rodney L. White Center for Financial Research Working Papers 06-99, Wharton School Rodney L. White Center for Financial Research.
- Hartz, Christoph & Mittnik, Stefan & Paolella, Marc, 2006. "Accurate value-at-risk forecasting based on the normal-GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2295-2312, December.
- Manfred Gilli & Evis këllezi, 2006. "An Application of Extreme Value Theory for Measuring Financial Risk," Computational Economics, Society for Computational Economics, vol. 27(2), pages 207-228, May.
- Hang Chan, Ngai & Deng, Shi-Jie & Peng, Liang & Xia, Zhendong, 2007. "Interval estimation of value-at-risk based on GARCH models with heavy-tailed innovations," Journal of Econometrics, Elsevier, vol. 137(2), pages 556-576, April.
- Peter Hall & Qiwei Yao, 2003. "Data tilting for time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 425-442.
- Yamai, Yasuhiro & Yoshiba, Toshinao, 2005. "Value-at-risk versus expected shortfall: A practical perspective," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 997-1015, April.
- Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
- Bams, Dennis & Lehnert, Thorsten & Wolff, Christian C.P., 2005.
"An evaluation framework for alternative VaR-models,"
Journal of International Money and Finance,
Elsevier, vol. 24(6), pages 944-958, October.
- Bams, Dennis & Lehnert, Thorsten & Wolff, Christian C, 2002. "An Evaluation Framework for Alternative VaR Models," CEPR Discussion Papers 3403, C.E.P.R. Discussion Papers.
- Carlo Acerbi & Dirk Tasche, 2001. "Expected Shortfall: a natural coherent alternative to Value at Risk," Papers cond-mat/0105191, arXiv.org.
- Carlo Acerbi & Dirk Tasche, 2002. "Expected Shortfall: A Natural Coherent Alternative to Value at Risk," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 31(2), pages 379-388, 07.
- Song Xi Chen, 2005. "Nonparametric Inference of Value-at-Risk for Dependent Financial Returns," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(2), pages 227-255.
- Peter Christoffersen & Sílvia Gonçalves, 2004. "Estimation Risk in Financial Risk Management," CIRANO Working Papers 2004s-15, CIRANO.
- Jeremy Berkowitz & Lutz Kilian, 1996.
"Recent developments in bootstrapping time series,"
Finance and Economics Discussion Series
96-45, Board of Governors of the Federal Reserve System (U.S.).
- Pascual, Lorenzo & Romo, Juan & Ruiz, Esther, 2006. "Bootstrap prediction for returns and volatilities in GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2293-2312, May.
When requesting a correction, please mention this item's handle: RePEc:cte:wsrepe:ws102814. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ana Poveda)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.