Asai, Manabu and McAleer, Michael and Medeiros, Marcelo C. (2011) Asymmetry and Long Memory in Volatility Modelling. [ Documentos de trabajo del Instituto Complutense de Análisis Económico; nº 29, 2011, ] (Unpublished)
Available under License Creative Commons Attribution Non-commercial.
Official URL: http://eprints.ucm.es/13215/
A wide variety of conditional and stochastic variance models has been used to estimate latent volatility (or risk). In this paper, we propose a new long memory asymmetric volatility model which captures more flexible asymmetric patterns as compared with several existing models. We extend the new specification to realized volatility by taking account of measurement errors, and use the Efficient Importance Sampling technique to estimate the model. As an empirical example, we apply the new model to the realized volatility of S&P500 to show that the new specification of asymmetry significantly improves the goodness of fit, and that the out-of-sample forecasts and Value-at-Risk (VaR) thresholds are satisfactory. Overall, the results of the out-of-sample forecasts show the adequacy of the new asymmetric and long memory volatility model for the period including the global financial crisis.
|Item Type:||Working Paper or Technical Report|
The authors are most grateful to a Co-Editor, Associate Editor and two referees for very helpful comments and suggestions, and Marcel Scharth for efficient research assistance.
|Uncontrolled Keywords:||Asymmetric volatility, Long memory, Realized volatility, Measurement errors, Efficient importance sampling.|
|Subjects:||Social sciences > Economics > Econometrics|
|Series Name:||Documentos de trabajo del Instituto Complutense de Análisis Económico|
Andersen, T.G., Bollerslev, T., and F.X. Diebold (2010), “Parametric and Nonparametric Volatility Measurement”, in: L.P. Hansen and Y. A¨ıt-Sahalia (eds.), Handbook of Financial Econometrics, Amsterdam: North-Holland, pp. 67-138.
Andersen, T.G., T. Bollerslev, F.X. Diebold and P. Labys (2001), “The Distribution of. Realized Exchange Rate Volatility”, Journal of the American Statistical Association, 96, 42-55.
Asai, M. and M. McAleer (2005), “Dynamic Asymmetric Leverage in Stochastic Volatility Models”, Econometric Reviews, 24, 317-332.
Asai, M. and M. McAleer (2011), “Alternative Asymmetric Stochastic Volatility Models”, Econometric Reviews, 30, 548-564.
Asai, M. and M. McAleer (2009), “Multivariate Stochastic Volatility, Leverage and News Impact Surfaces”, Econometrics Journal, 12, 292-309.
Asai, M., M. McAleer and M. Medeiros (2011a), “Modelling and Forecasting Daily Volatility with Noisy Realized Volatility Measures”, to appear in Computational Statistics & Data Analysis.
Asai, M., M. McAleer and M. Medeiros (2011b), “Asymmetry and Long Memory in Volatility Modelling: Web-Appendix”, available at http://home.soka.ac.jp/~m-asai/ publications/Asai_McAleer_Medeiros(2011)-JFEC-Web-Appendix.pdf.
Asai, M., M. McAleer and J. Yu (2006), “Multivariate Stochastic Volatility: A Review”, Econometric Reviews, 25, 145-175.
Bandi, F.M. and R. Renò (2008), “Nonparametric Stochastic Volatility”, Unpublished paper, Graduate School of Business, University of Chicago.
Bandi, F.M. and J.R. Russell (2011), “Market Microstructure Noise, Integrated Variance Estimators, and the Accuracy of Asymptotic Approximations”, Journal of Econometrics, 160, 145-159.
Barndorff-Nielsen, O.E., and N. Shephard (2002), “Econometric Analysis of Realized Volatility and Its Use in Estimating Stochastic Volatility Models”, Journal of the Royal Statistical Society, Series B, 64, 253－280.
Barndorff-Nielsen, O.E., P.H. Hansen, A. Lunde and N. Shephard (2008), “Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise”, Econometrica, 76, 1481-1536.
Bollerslev, T. and H.O. Mikkeslen (1996), “Modeling and Pricing Long Memory in Stock Market Volatility”, Journal of Econometrics, 73, 151-184.
Bollerslev, T. and H. Zhou (2002), “Estimating Stochastic Volatility Diffusion Using Conditional Moments of Integrated Volatility”, Journal of Econometrics, 109, 33-65.
Bollerslev, T. and H. Zhou (2006), “Volatility Puzzles: A Simple Framework for Gauging Return-Volatility Regressions”, Journal of Econometrics, 131, 123-150.
Bollerslev, T., J. Litovinova and G. Tauchen (2006), “Leverage and Volatility Feedback Effects in High-Frequency Data”, Journal of Financial Econometrics, 4, 353-384.
Bollerslev, T., N. Sizova and G. Tauchen (2011), “Volatility in Equilibrium: Asymmetries and Dynamic Dependencies”, to appear in Review of Finance, doi: 10.1093/rof/rfr005.
Candelon, B., G. Colletaz, C. Hurlin, and S. Tokpavi (2011), “Backtesting Value-at-Risk: A GMM Duration-Based Approach”, Journal of Financial Econometrics, 9, 314-343.
Chen, X. and E. Ghysels (2008), “News - Good or Bad - and its Impact on Volatility Predictions over Multiple Horizons”, Unpublished paper, University of North Carolina at Chapel Hill.
Chernov, M., A.R. Gallant, E. Ghysels and G. Tauchen (2003), “Alternative Models for Stock Price Dynamics”, Journal of Econometrics, 116, 225-257.
Christoffersen, P. (1998), “Evaluating Interval Forecasts,” International Economic Review, 39, 841–62.
Christoffersen, P. and D. Pelletier (2004), “Backtesting Value-at-Risk: A Duration-Based Approach”, Journal of Financial Econometrics, 2, 84-108.
Comte, F. and E. Renault (1998), “Long Memory in Continuous-Time Stochastic Volatility Models”, Mathematical Finance, 8, 291-323.
Corsi, F. (2009), “A Simple Approximate Long-Memory Model of Realized Volatility,” Journal of Financial Econometrics, 7, 174-196.
Corsi, F. and R. Renò (2010), “HAR Volatility Modelling with Heterogeneous Leverage and Jumps”, Unpublished Paper, Università di Siena.
Danielsson, J. (1994), “Stochastic Volatility in Asset Prices: Estimation with Simulated Maximum Likelihood”, Journal of Econometrics, 64, 375-400.
Danielsson, J., and J.-F. Richard (1993), “Quadratic Acceleration for Simulated Maximum Likelihood Evaluation”, Journal of Applied Econometrics, 8, 153-173.
Diebold, F. X., and R. S. Mariano (1995), “Comparing Predictive Accuracy,” Journal of Business and Economic Statistics, 13, 253-263.
Durbin, J., and S.J. Koopman (1997), “Monte Carlo Maximum Likelihood Estimation for Non-Gaussian State Space Models”, Biometrika, 84, 669-684.
Eraker, B., M. Johannes, and N.G. Polson (2003), “The Impact of Jumps in Returns and Volatility”, Journal of Finance, 53, 1269-1300.
Ghysels, E., A.C. Harvey and E. Renault (1996), “Stochastic Volatility”, in C.R. Rao and G.S. Maddala (eds.), Statistical Methods in Finance, Amsterdam: North-Holland, pp. 119-191.
Hansen, P.R., J. Large and A. Lunde (2008), “Moving Average-based Estimators of Integrated Variance”, Econometric Reviews, 27, 79-111.
Harvey, D., S. Leybourne, and P. Newbold (1997), “Testing the Equality of Mean Squared Errors,” International Journal of Forecasting, 13, 281-291.
Harvey, A.C. and N. Shephard (1996), “Estimation of an Asymmetric Stochastic Volatility Model for Asset Returns”, Journal of Business and Economic Statistics, 14, 429-434.
Hull, J. and A. White (1987), “The Pricing of Options on Assets with Stochastic Volatility”, Journal of Finance, 42, 281-300.
Koopman, S.J., B. Jungbacker and E. Hol (2005), “Forecasting Daily Variablity of the S&P 100 Stock Index Using Historical Realized and Implied Volatility Measurements”, Journal of Empirical Finance, 12, 445-475.
Kuester, K., S. Mittnik and M.S. Paolella (2006), “Value-at-Risk Prediction: A Comparison of Alternative Strategies”, Journal of Financial Econometrics, 4, 53-89.
Liesenfeld, R., and J.-F. Richard (2003), “Univariate and Multivariate Stochastic Volatility Models: Estimation and Diagnostics”, Journal of Empirical Finance, 10, 505-531.
Liesenfeld, R., and J.-F. Richard (2006), “Classical and Bayesian Analysis of Univariate and Multivariate Stochastic Volatility Models”, Econometric Reviews, 25, 335-361.
Martens, M., D. van Dijk, and M. de Pooter (2009), “Forecasting S&P 500 Volatility: Long Memory, Level Sifts, Leverage Effects, Day-of-the-Week Seasonality, and Macroeconomic Announcements”, International Journal of Forecasting, 25, 282-303.
McAleer, M. (2005), “Automated Inference and Learning in Modeling Financial Volatility”, Econometric Theory, 21, 232-261.
McAleer, M. and M. Medeiros (2008), “Realized Volatility: A Review”, Econometric Reviews, 27, 10-45.
Nelson, D.B. (1990), “ARCH Models as Diffusion Approximations”, Journal of Econometrics, 45, 7–38.
Nelson, D.B. (1991), “Conditional Heteroskedasticity in Asset Returns: A New Approach”, Econometrica, 59, 347-370.
Patton, A. and K. Sheppard (2010), “Good Volatility, Bad Volatility: Signed Jumps and the Persistence of Volatility”, Unpublished Paper, Duke University.
Pong S., M.B. Shackelton, S.J. Taylor and X. Xu (2004), “Forecasting Currency Volatility: A Comparison of Implied Volatilities and AR(FI)MA models, Journal of Banking and Finance, 28, 2541-2563.
Shephard, N. and K. Sheppard (2010), “Realising the Future: Forecasting with High-Frequency Based Volatility (HEAVY) Models”, Journal of Applied Econometrics, 23, 197-231.
Taylor, S.J. (1982), “Financial Returns Modelled by the Product of Two Stochastic Processes - A Study of Daily Sugar Prices 1961-79”, in O. D. Anderson (Ed.), Time Series Analysis: Theory and Practice, 1, Amsterdam: North-Holland, pp. 203–226.
Todorov, V. (2009), “Estimation of Continuous-Time Stochastic Volatility Models with Jumps Using High-Frequency Data”, Journal of Econometrics, 148, 131-148.
Wiggins, J.B. (1987), “Option Values Under Stochastic Volatility: Theory and Empirical Estimates”, Journal of Financial Economics, 19, 351-372.
Yu, J. (2005), “On Leverage in a Stochastic Volatility Model”, Journal of Econometrics, 127, 165-178.
Zhang, L., P.A. Mykland and Y. Aït-Sahalia (2005), “A Tale of Two Time Scales: Determining Integrated Volatility with Noisy High Frequency Data”, Journal of the American Statistical Association, 100, 1394 – 1411.
|Deposited On:||06 Sep 2011 08:05|
|Last Modified:||06 Feb 2014 09:43|
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