Ranking and Combining Volatility Proxies for Garch and Stochastic Volatility Models

Visser, Marcel P. (2008): Ranking and Combining Volatility Proxies for Garch and Stochastic Volatility Models.

Abstract

Daily volatility proxies based on intraday data, such as the high-low range and the realized volatility, are important to the specification of discrete time volatility models, and to the quality of their parameter estimation. The main result of this paper is a simple procedure for combining such proxies into a single, highly efficient volatility proxy. The approach is novel in optimizing proxies in relation to the scale factor (the volatility) in discrete time models, rather than optimizing proxies as estimators of the quadratic variation. For the S&P 500 index tick data over the years 1988-2006 the procedure yields a proxy which puts, among other things, more weight on the sum of the highs than on the sum of the lows over ten-minute intervals. The empirical analysis indicates that this finite-grid optimized proxy outperforms the standard five-minute realized volatility by at least 40%, and the limiting case of the square root of the quadratic variation by 25%.

• Item Type: MPRA Paper
• Language: English
• Keywords: volatility proxy; realized volatility; quadratic variation; scale factor; arch/garch/stochastic volatility; variance of logarithm
• Subjects: G - Financial Economics > G1 - General Financial Markets; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C65 - Miscellaneous Mathematical Tools; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C52 - Model Evaluation, Validation, and Selection; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes

References

Alizadeh, S., Brandt, M.W. and Diebold, F.X. (2002). Range-based estimation of stochastic volatility models. The Journal of Finance, 57, number 3, 1047-1091.

Andersen, T.G., Bollerslev, T. and Diebold, F.X. (2008). Parametric and Nonparametric Volatility Measurement. In Handbook of Financial Econometrics (ed. Y. Ait-Sahalia). Forthcoming.

Andersen, T.G., Bollerslev, T., F.X., Diebold and Labys, P. (2001). The distribution of realized exchange rate volatility. Journal of the American Statistical Association, 96, number 453, 42-55.

Andersen, T.G., Bollerslev, T., F.X., Diebold and Labys, P. (2003). Modeling and forecasting realized volatility. Econometrica, 71, number 2, 579-625.

Barndorff-Nielsen, O.E. and Shephard, N. (2002). Estimating quadratic variation using realized variance. Journal of Applied Econometrics, 17, number 5, 457-477.

Barndorff-Nielsen, O.E. and Shephard, N. (2003). Realized power variation and stochastic volatility models. Bernoulli, 9, number 2, 243-65 and 1109-1111.

Barndorff-Nielsen, O.E. and Shephard, N. (2004). Power and Bipower Variation with Stochastic Volatility and Jumps. Journal of Financial Econometrics, 2, number 1, 1- 37.

Billingsley, P. (1999). Convergence of Probability Measures, 2nd edn. New York: John Wiley & Sons, Inc.

Christensen, K. and Podolskij, M. (2007). Realized range-based estimation of integrated variance. Journal of Econometrics.

Dacorogna, M.M., Gencay, R., Muller, U., Olsen, R.B. and Pictet, O.V. (2001). An Intro- duction to High-Frequency Finance. London: Academic Press.

Drost, F.C. and Nijman, T.E. (1993). Temporal aggregation of Garch processes. Economet- rica, 61, number 4, 909-927.

Drost, F.C. and Werker, B.J.M. (1996). Closing the GARCH gap: Continuous time GARCH modeling. Journal of Econometrics, 74, number 1, 31-57.

Engle, R.F. (2002). New frontiers for arch models. Journal of Applied Econometrics, 17, number 5, 425-446.

Hansen, P.R. and Lunde, A. (2005). A Realized Variance for the Whole Day Based on Intermittent High-Frequency Data. Journal of Financial Econometrics, 3, number 4, 525-554.

Hansen, P.R. and Lunde, A. (2006a). Consistent ranking of volatility models. Journal of Econometrics, 131, number 1-2, 97-121.

Hansen, P.R. and Lunde, A. (2006b). Realized variance and market microstructure noise. Journal of Business & Economic Statistics, 24, number 2, 127-161.

Martens, M. and van Dijk, D. (2007). Measuring volatility with the realized range. Journal of Econometrics, 138, number 1, 181-207.

McAleer, M. and Medeiros, M.C. (2008). Realized Volatility: A Review. Econometric Reviews, 27, number 1, 10-45.

Meddahi, N. and Renault, E. (2004). Temporal aggregation of volatility models. Journal of Econometrics, 119, number 2, 355-377.

Oomen, R.C.A. (2005). Properties of bias-corrected realized variance under alternative sampling schemes. Journal of Financial Econometrics, 3, number 4, 555-577.

Oomen, R.C.A. (2006). Properties of realized variance under alternative sampling schemes. Journal of Business & Economic Statistics, 24, number 2, 219-237.

Parkinson, M. (1980). The extreme value method for estimating the variance of the rate of return. Journal of Business, 53, 61-65.

Patton, A.J. and Sheppard, K. (2008). Evaluating Volatility Forecasts. In Handbook of Financial Time Series (eds T.G. Andersen, R.A. Davis, J.P. Kreiss and T. Mikosch). Springer. Forthcoming.

Visser, M.P. (2008). Garch parameter estimation using high-frequency data. MPRA paper no. 9076.

Zhang, L., Mykland, P.A. and A$-1 Ñt-Sahalia, Y. (2005). A tale of two time scales: Determining integrated volatility with noisy high-frequency data. Journal of the American Statistical Association, 100, number 472, 1394-1411.