Forecasting S&P 500 Daily Volatility using a Proxy for Downward Price Pressure

Visser, Marcel P. (2008): Forecasting S&P 500 Daily Volatility using a Proxy for Downward Price Pressure.

Abstract

This paper decomposes volatility proxies according to upward and downward price movements in high-frequency financial data, and uses this decomposition for forecasting volatility. The paper introduces a simple Garch-type discrete time model that incorporates such high-frequency based statistics into a forecast equation for daily volatility. Analysis of S&P 500 index tick data over the years 1988-2006 shows that taking into account the downward movements improves forecast accuracy significantly. The R2 statistic for evaluating daily volatility forecasts attains a value of 0.80, both for in-sample and out-of-sample prediction.

• Item Type: MPRA Paper
• Language: English
• Keywords: volatility proxy; downward absolute power variation; log-Garch; volatility asymmetry; leverage effect; SP500; volatility forecasting; high-frequency data
• Subjects: C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods ; Simulation Methods; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes; G - Financial Economics > G1 - General Financial Markets > G10 - General

References

Awartani, B.M.A. and Corradi, V. (2005). Predicting the volatility of the S&P-500 stock index via GARCH models: the role of asymmetries. International Journal of Forecasting, 21, number 1, 167-183.

Barndorff-Nielsen, O.E., Kinnebrock, S. and Shephard, N. (2008). Measuring downside risk - realised semivariance. CREATES Research Paper 2008-42, University of Aarhus.

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 Stochas- tic Volatility and Jumps. Journal of Financial Econometrics, 2, number 1, 1-37.

Berkes, I., Horvath, L. and Kokoszka, P. (2003). Garch processes: structure and estimation. Bernoulli, 9, number 2, 201-227.

Black, B. (1976). Studies of stock price volatility changes. In Proceedings of the 1976 Meetings of the American Statistical Association, Business and Economic Statistics, pp. 177-181.

Bollerslev, T., Litvinova, J. and Tauchen, G. (2006). Leverage and Volatility Feedback Effects in High-Frequency Data. Journal of Financial Econometrics, 4, number 3, 353-384.

Bollerslev, T. and Wooldridge, J.M. (1992). Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances. Econometric Reviews, 11, number 2, 143-172.

Bougerol, P. and Picard, N. (1992). Strict Stationarity of Generalized Autoregressive Processes. The Annals of Probability, 20, number 4, 1714-1730.

Brandt, M.W. and Jones, C.S. (2006). Volatility Forecasting With Range-Based EGARCH Models. Journal of Business & Economic Statistics, 24, number 4, 470-486.

Brockwell, P.J. and Davis, R.A. (1991). Time Series: Theory and Methods. Springer Series in Statistics, second edn. New York: Springer-Verlag.

Busch, T. (2005). A robust LR test for the GARCH model. Economics Letters, 88, 358-364.

Christie, A.C. (1982). The Stochastic Behavior of Common Stock Variances-Value, Leverage and Interest Rate Effects. Journal of Financial Economics, 10, number 4, 407-432.

Corsi, F. (2004). A Simple Long Memory Model of Realized Volatility. SSRN Paper.

de Vilder, R.G. and Visser, M.P. (2008). Ranking and Combining Volatility Proxies for Garch and Stochastic Volatility Models. MPRA paper no. 11001.

Diebold, F.X. and Mariano, R.S. (1995). Comparing Predictive Accuracy. Journal of Business & Economic Statistics, 13, number 3, 253-263.

Engle, R.F. and Gallo, G.M. (2006). A multiple indicators model for volatility using intra- daily data. Journal of Econometrics, 131, number 1-2, 2-27.

Engle, R.F. and Ng, V.K. (1993). Measuring and Testing the Impact of News on Volatility. The Journal of Finance, 48, number 5, 1749-1778.

Engle, R.F. and Patton, A.J. (2001). What good is a volatility model? Quantitative Finance, 1, number 2, 237-245.

Forsberg, L. and Ghysels, E. (2007). Why Do Absolute Returns Predict Volatility So Well? Journal of Financial Econometrics, 5, number 1, 31-67.

Geweke, J. (1986). Modelling the Persistence of Conditional Variances - Comment. Econo- metric Reviews, 5, number 1, 57-61.

Ghysels, E., Santa-Clara, P. and Valkanov, R. (2006). Predicting volatility: getting the most out of return data sampled at different frequencies. Journal of Econometrics, 131, number 1-2, 59-95.

Glosten, L.R., Jagannathan, R. and Runkle, D.E. (1993). On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks. The Journal of Finance, 48, number 5, 1779-1801.

Hansen, P.R. and Lunde, A. (2005). A forecast comparison of volatility models: does anything beat a GARCH(1,1)? Journal of Applied Econometrics, 20, number 7, 873-889.

Koopman, S.J., B., Jungbacker and Hol, E. (2005). Forecasting daily variability of the S&P 100 stock index using historical, realised and implied volatility measurements. Journal of Empirical Finance, 12, number 3, 445-475.

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

Mincer, J. and Zarnowitz, V. (1969). The Evaluation of Economic Forecasts. In Economic Forecasts and Expectation (ed. J. Mincer), National Bureau of Economic Research, pp. 3-46. Columbia University Press.

Muller, U.A., Dacorogna, M.M., Dave, R.D., Olsen, R.B., Pictet, O.V. and Weizsacker, J.E. (1997). Volatilities of Different Time Resolutions - Analyzing the Dynamics of Different Market Components. Journal of Empirical Finance, 4, number 2-3, 213-239.

Nelson, D.B. (1991). Conditional Heteroskedasticity in Asset Returns: A New Approach. Econometrica, 59, number 2, 347-370.

Pantula, S.G. (1986). Modelling the Persistence of Conditional Variances - Comment. Econometric Reviews, 5, number 1, 71-74.

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

Straumann, D. and T., Mikosch (2006). Quasi-maximum-likelihood estimation in condition- ally heteroscedastic time series: a stochastic recurrence equations approach. The Annals of Statistics, 34, number 5, 2449-2495.

Taylor, S.J. (1987). Forecasting the volatility of currency exchange rates. International Journal of Forecasting, 3, number 1, 159-170.

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

West, K.D. (1996). Asymptotic inference about predictive ability. Econometrica, 64, number 5, 1067-1084.