Value-at-Risk and Expected Shortfall when there is long range dependence
Empirical studies have shown that a large number of financial asset returns exhibit fat tails and are often characterized by volatility clustering and asymmetry. Also revealed as a stylized fact is Long memory or long range dependence in market volatility, with significant impact on pricing and forecasting of market volatility. The implication is that models that accomodate long memory hold the promise of improved long-run volatility forecast as well as accurate pricing of long-term contracts. On the other hand, recent focus is on whether long memory can affect the measurement of market risk in the context of Value-at- Risk (V aR). In this paper, we evaluate the Value-at-Risk (V aR) and Expected Shortfall (ESF) in financial markets under such conditions. We examine one equity portfolio, the British FTSE100 and three stocks of the German DAX index portfolio (Bayer, Siemens and Volkswagen). Classical V aR estimation methodology such as exponential moving average (EMA) as well as extension to cases where long memory is an inherent characteristics of the system are investigated. In particular, we estimate two long memory models, the Fractional Integrated Asymmetric Power-ARCH and the Hyperbolic-GARCH with different error distribution assumptions. Our results show that models that account for asymmetries in the volatility specifications as well as fractional integrated parametrization of the volatility process, perform better in predicting the one-step as well as five-step ahead V aR and ESF for short and long positions than short memory models. This suggests that for proper risk valuation of options, the degree of persistence should be investigated and appropriate models that incorporate the existence of such characteristic be taken into account.
|Date of creation:||Jan 2008|
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- Mike So, 2000. "Long-term memory in stock market volatility," Applied Financial Economics, Taylor & Francis Journals, vol. 10(5), pages 519-524.
- Peter M. Robinson & M. Henry, 1999.
"Long and short memory conditional heteroskedasticity in estimating the memory parameter of levels,"
LSE Research Online Documents on Economics
304, London School of Economics and Political Science, LSE Library.
- Robinson, P.M. & Henry, M., 1999. "Long And Short Memory Conditional Heteroskedasticity In Estimating The Memory Parameter Of Levels," Econometric Theory, Cambridge University Press, vol. 15(03), pages 299-336, June.
- Peter M. Robinson & Marc Henry, 1998. "Long and short memory conditional heteroscedasticity in estimating the memory parameter of levels," LSE Research Online Documents on Economics 2022, London School of Economics and Political Science, LSE Library.
- Stavros Degiannakis, 2004. "Volatility forecasting: evidence from a fractional integrated asymmetric power ARCH skewed-t model," Applied Financial Economics, Taylor & Francis Journals, vol. 14(18), pages 1333-1342.
- Olan Henry, 2002. "Long memory in stock returns: some international evidence," Applied Financial Economics, Taylor & Francis Journals, vol. 12(10), pages 725-729.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-62, November.
- Tim Bollerslev, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
EERI Research Paper Series
EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
- GIOT, Pierre & LAURENT, Sébastien, .
"Modelling daily Value-at-Risk using realized volatility and ARCH type models,"
CORE Discussion Papers RP
1708, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Giot, Pierre & Laurent, Sebastien, 2004. "Modelling daily Value-at-Risk using realized volatility and ARCH type models," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 379-398, June.
- Pierre Giot & Sébastien Laurent, 2002. "Modelling Daily Value-at-Risk Using Realized Volatility and ARCH Type Models," Computing in Economics and Finance 2002 52, Society for Computational Economics.
- Giot Pierre & Laurent Sebastien, 2001. "Modelling daily value-at-risk using realized volatility and arch type models," Research Memorandum 014, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- Herzberg, Markus & Sibbertsen, Philipp, 2004. "Pricing of options under different volatility models," Technical Reports 2004,62, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
- Granger, Clive W. J. & Ding, Zhuanxin, 1996. "Varieties of long memory models," Journal of Econometrics, Elsevier, vol. 73(1), pages 61-77, July.
- Giraitis, Liudas & Kokoszka, Piotr & Leipus, Remigijus, 2000. "Stationary Arch Models: Dependence Structure And Central Limit Theorem," Econometric Theory, Cambridge University Press, vol. 16(01), pages 3-22, February.
- repec:adr:anecst:y:1995:i:40:p:04 is not listed on IDEAS
- Liudas Giraitis & Piotr Kokoszka & Remigijus Leipus & Gilles Teyssière, 2000.
"Semiparametric Estimation of the Intensity of Long Memory in Conditional Heteroskedasticity,"
Statistical Inference for Stochastic Processes,
Springer, vol. 3(1), pages 113-128, January.
- Giraitis, Liudas & Kokoszka, Piotr & Leipus, Remigijus & Teyssière, Gilles, 1999. "Semiparametric estimation of the intensity of long memory in conditional heteroskedasticity," SFB 373 Discussion Papers 1999,81, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Giraitis, L. & Kokoszka, P. & Leipus, R. & Teyssiere, G., 1999. "Semiparametric Estimation of the Intensity of Long Memory in Conditional Heteroskedasticity," G.R.E.Q.A.M. 99a24, Universite Aix-Marseille III.
- Darryll Hendricks, 1996. "Evaluation of value-at-risk models using historical data," Economic Policy Review, Federal Reserve Bank of New York, issue Apr, pages 39-69.
- Billio, Monica & Pelizzon, Loriana, 2000. "Value-at-Risk: a multivariate switching regime approach," Journal of Empirical Finance, Elsevier, vol. 7(5), pages 531-554, December.
- Katsumi Shimotsu & Peter C.B. Phillips, 2000. "Local Whittle Estimation in Nonstationary and Unit Root Cases," Cowles Foundation Discussion Papers 1266, Cowles Foundation for Research in Economics, Yale University, revised Sep 2003.
- S»bastien Laurent and Jean-Philippe Peters, 2001. "G@RCH 2.0: An Ox Package for Estimating and Forecasting Various ARCH Models," Computing in Economics and Finance 2001 123, Society for Computational Economics.
- O. Scaillet, 2004. "Nonparametric Estimation and Sensitivity Analysis of Expected Shortfall," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 115-129.
- Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
- Ignacio N. Lobato & Peter M. Robinson, 1998. "A Nonparametric Test for I(0)," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 475-495.
- Bollerslev, Tim & Ole Mikkelsen, Hans, 1996.
"Modeling and pricing long memory in stock market volatility,"
Journal of Econometrics,
Elsevier, vol. 73(1), pages 151-184, July.
- Tom Doan, . "RATS program to replicate Bollerslev-Mikkelson(1996) FIEGARCH models," Statistical Software Components RTZ00173, Boston College Department of Economics.
- Chang Sik Kim & Peter C.B. Phillips, 2006. "Log Periodogram Regression: The Nonstationary Case," Cowles Foundation Discussion Papers 1587, Cowles Foundation for Research in Economics, Yale University.
- C. W. J. Granger & Zhuanxin Ding, 1995. "Some Properties of Absolute Return: An Alternative Measure of Risk," Annals of Economics and Statistics, GENES, issue 40, pages 67-91.
- Timotheos Angelidis & Stavros Degiannakis, 2007. "Backtesting VaR Models: An Expected Shortfall Approach," Working Papers 0701, University of Crete, Department of Economics.
- repec:adr:anecst:y:1995:i:40 is not listed on IDEAS
- Doornik Jurgen A & Ooms Marius, 2004. "Inference and Forecasting for ARFIMA Models With an Application to US and UK Inflation," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-25, May.
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