Daily Var Forecasts with Realized Volatility and Garch Models

• Autorzy: Barbara Będowska-Sójka
• Języki publikacji: EN

Abstrakty

EN

In this paper we evaluate alternative volatility forecasting methods under Value at Risk (VaR) modelling. We calculate one-step-ahead forecasts of daily VaR for the WIG20 index quoted on the Warsaw Stock Exchange within the period from 2007 to 2011. Our analysis extends the existing research by broadening the class of the models, including both the GARCH class models based on daily data and models for realized volatility based on intraday returns (HAR-RV, HAR-RV-J and ARFIMA). We find that the VaR estimates obtained from the models for daily returns and realized volatility give comparable results. Both long memory features and asymmetry are found to improve the VaR forecasts. However, when loss functions are considered, the models based on daily data allow minimizing regulatory loss function, whereas the models based on realized volatility allow minimizing the opportunity cost of capital.(original abstract)

Słowa kluczowe

EN

GARCH model; Forecasting

PL

Model GARCH; Prognozowanie

• Czasopismo: Argumenta Oeconomica
• Rocznik: 2015
• Numer: nr 1 (34)
• Strony: 157--173

Twórcy

autor

Barbara Będowska-Sójka

• Poznań University of Economics

Bibliografia

• Andersen, T. G., Bollerslev, T., Diebold, F. X., Ebens, H., The Distribution of Realized Stock Return Volatility, "Journal of Financial Economics" 61, pp. 43-76, 2001.
• Andersen, T. G., Bollerslev, T., Diebold, F. X., Labys, P., Modeling and Forecasting Realized Volatility, Econometrica 71, pp. 579-625, 2003.
• Andersen, T. G., Bollerslev, T., Diebold, F.X., Roughing It Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Returns Volatility, "The Review of Economics and Statistics" 89(4), pp. 701-720, 2007.
• Andersen, T. G., Bollerslev, T., Answering the Skeptics. Yes, Standard Volatility Models Do Provide Accurate Forecasts, "International Economic Review" 39 (4), pp. 885-905, 1998.
• Baillie, R., Bollerslev, T., Mikkelsen, H. O, Fractionally Integrated Generalized Autore-gressive Conditional Heteroskedasticity, "Journal of Econometrics", 74, pp. 3-30, 1996.
• Barndorff-Nielsen, O. E., Shephard, N., Econometric Analysis of Realised Volatility and Its Use in Estimating Stochastic Volatility Models, "Journal of the Royal Statistical Society", B, 64, pp. 253-280, 2002.
• Beck, A., Kim, Y. S. I., Rachev, S., Feindt, M., Fabozzi, F., Empirical Analysis of ARMA-GARCH Models in Market Risk Estimation on High-frequency US Data, "Studies in Nonlinear Dynamics and Econometrics" 17, 2, pp. 167-177, 2013.
• Będowska-Sójka, B., Kliber, A., Realized Volatility Versus GARCH and Stochastic Volatility Models. The Evidence from the WIG20 Index and the EUR/PLN Foreign Exchange Market, "Przegląd Statystyczny", 57, 4, pp. 105-127, 2010.
• Bollerslev, T., Generalized Autoregressive Conditional Heteroskedasticity, "Journal of Econometrics" 31, pp. 307-327, 1986.
• Corsi, F, Dacorogna, M., Müller, U., Zumbach, G., High Frequency Data do Improve Volatility and Risk Estimation, FCO.2000-03-18, Olsen Ltd. Research Group, 2009.
• Corsi, F., A Simple Approximate Long-memory Model of Realized Volatility, "Journal of Financial Econometrics" 7, No. 2, pp. 174-196, 2009.
• Engle, R. F., Manganelli, S., CAViaR. Conditional Autoregressive Value at Risk by Regression Quantiles, "Journal of Business and Economic Statistics", 22, pp. 367-381, 2004.
• Engle, R. F, Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation, Econometrica 50, pp. 987-1007, 1982.
• Fuertes, A-M., Izzeldin, M., Kalotychou, E., On Forecasting Daily Stock Volatility: The Role of Intraday Information and Market Conditions, "International Journal of Forecasting", 25(2), pp. 259-281, 2009.
• Fuertes, A-M., Olmo, J., Exploiting Intraday and Overnight Price Variation for Daily VaR Prediction, "Frontiers in Finance and Economics" 9, 2, pp. 1-31, 2012.
• Giot, P., Laurent, S., Modelling Daily Value-at-Risk Using Realized Volatility and ARCH Type Models, "Journal of Empirical Finance" 11,3, pp. 379-398, 2004.
• Glosten, L. R., Jagannathan, R., Runkle, D. E., On The Relation between The Expected Value and The Volatility of Nominal Excess Return on Stocks, "Journal of Finance" 48, pp. 1779-1801, 1993.
• Jajuga, K., Ogólny model dynamiki cen finansowych, "Dynamiczne Modele Ekonome-tryczne", Toruń, pp. 7-14, 2001.
• Kupiec, P., Techniques for Verifying the Accuracy of Risk Measurement Models, "Journal of Derivatives" 2, pp. 73-84, 1995.
• Laurent, S., G@rch 6.0 help, Timberlake Consultants Ltd., London, 2010.
• Lopez, J. A., Methods of Evaluating Value at Risk Estimates, Federal Reserve Bank of San Francisco Economic Review, pp. 3-17, 1999.
• Louzis, D. P., Xanthopoulos-Sisinis, S., Refenes, A., Are Realized Volatility Models Good Candidates for Alternative VaR Prediction Strategies, http://mpra.ub.uni-muenchen.de/30364/, 2011.
• Louzis, D. P., Xanthopoulos-Sisinis, S., Refenes, A., The Role of High-Frequency Intra-daily Data, Daily Range and Implied Volatility in Multi-Period Value-at-Risk Forecasting, "Journal of Forecasting" 32, pp. 561-576, 2013.
• Lunde, A., Hansen, P., A Forecast Comparison of Volatility Models: Does Anything Beat a GARCH(1,1)?, "Journal of Applied Econometrics", 20(7), pp. 873-889, 2005.
• McMillan, D. G., Speight, A. E. H., Evans, K. P., How Useful is Intraday Data for Evaluating Daily Value-at-Risk?: Evidence from three Euro Rates, "Journal of Multinational Financial Management" 18, pp. 488-503, 2008.
• McMillan, D. G., Speight, A. E. H., Value-at-Risk in Emerging Equity Markets: Comparative Evidence for Symmetric, Asymmetric, and Long-Memory GARCH Models, "International Review of Finance" 7, pp. 1-2, 2007
• Merton, R., On Estimating the Expected Return on the Market; an Exploratory Investigation, "Journal of Financial Economics" 8, pp. 323-361, 1980.
• Müller, U. A., Volatility Computed by Time Series Operators at High Frequency, Internal document UAM.1999-09-01, Olsen & Associates, Zurich, 1999.
• Piontek, K., Przegląd i porównanie metod oceny modeli VaR, Matematyczne i ekonome-tryczne metody oceny ryzyka finansowego, [in:] Chrzan, P., Prace Naukowe AE w Kato-wicach, Katowice, pp. 113-124, 2007.
• Pipien, M., Wykorzystanie rozkładów predyktywnych w prognozie VaR i rezerw kapitałowych związanych z ryzykiem rynkowym, ""Dynamiczne Modele Ekonometryczne", pp. 83-91, 2005.
• Taylor, S., Xu, X., The Incremental Volatility Information in One Million Foreign Exchange Quotations, "Journal of Empirical Finance" 4, pp. 317-340, 1997.
• Zumbach, G. O., Műller, U. A., Operators on Inhomogeneous Time Series, "International Journal of Theoretical and Applied Finance", 4(1), pp. 147-178, 2001.

Identyfikatory

DOI

10.15611/aoe.2015.1.06