Forecasting Exchange Rate Volatility

Journal of Empirical Finance 19 (2012) 627–639

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Forecasting exchange rate volatility: The superior performance of conditional combinations of time series and option implied forecasts☆
Guillermo Benavides a,⁎, Carlos Capistrán b a b

Banco de México, Mexico
Bank of America Merrill Lynch, Mexico

article

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Article history:
Received 26 February 2010
Accepted 5 July 2012
Available online 16 July 2012
Keywords:
Composite forecasts
Forecast evaluation
GARCH
Implied volatility
Mexican peso–U.S. dollar exchange rate
Regime switching

abstract
This paper provides empirical evidence that combinations of option implied and time series volatility forecasts that are conditional on current information are statistically superior to individual models, unconditional combinations, and hybrid forecasts. Superior forecasting performance is achieved by both, taking into account the conditional expected performance of each model given current information, and combining individual forecasts. The method used in this paper to produce conditional combinations extends the application of conditional predictive ability tests to select forecast combinations. The application is for volatility forecasts of the Mexican peso–US dollar exchange rate, where realized volatility calculated using intraday data is used as a proxy for the (latent) daily volatility.
© 2012 Elsevier B.V. All rights reserved.

JEL classification:
C22
C52
C53
G10

1. Introduction
Even though several models are widely used by academics and practitioners to forecast volatility, nowadays there is no consensus about which method is superior in terms of forecasting accuracy (Andersen et al., 2006; Poon and Granger, 2003; Taylor, 2005). The vast majority of models can be classified in two classes: models based on time series, and models based on

References: Akgiray, V., 1989. Conditional heteroskedasticity in time series of stock returns: evidence and forecasts. J. Bus. 62, 55–80. Andersen, T.G., Bollerslev, T., 1998. Answering the skeptics: yes, standard volatility models do provide accurate forecasts. Int. Econ. Rev. 39, 885–905. Andersen, T., Bollerslev, T.P., Diebold, F.X., Labys, P., 1999. (Understanding, optimizing, using and forecasting) realized volatility and correlation. Working Paper, Northwestern University, Duke University and University of Pennsylvania, pp Andersen, T.G., Bollerslev, T., Christoffersen, P.F., Diebold, F.X., 2006. Volatility and correlation forecasting. In: Elliott, G., Granger, C.W.J., Timmermann, A. (Eds.), Handbook of Economic Forecasting Bates, J.M., Granger, C.W.J., 1969. The combination of forecasts. Oper. Res. Q. 20, 451–468. Becker, R., Clemens, A.E., 2008. Are combination forecasts of S&P 500 volatility statistically superior? Int. J. Forecast. 24, 122–133. Benavides, G., 2003. Price volatility forecasts for agricultural commodities: an application of historical volatility models, option implieds and composite approaches for futures prices of corn and wheat Benavides, G., 2006. Volatility forecasts for the Mexican Peso–US Dollar exchange rate: an empirical analysis of GARCH, option implied and composite forecasts models Black, F., Scholes, M.S., 1973. The pricing of options and corporate liabilities. J. Polit. Econ. 81, 637–654 May–June. Blair, B.J., Poon, S., Taylor, S.J., 2001. Forecasting S&P 100 volatility: the incremental information content of implied volatilities and high-frequency index returns. Bollerslev, T.P., 1986. Generalized autoregressive conditional heteroskedasticity. J. Econ. 31, 307–327. Bollerslev, T.P., Engle, R.F., Nelson, D.B., 1994. ARCH models. In: Engle, R.F., McFadden, D.L. (Eds.), Handbook of Econometrics, Vol. 4. Elsevier, Amsterdam. Bollerslev, T.P., Tauchen, G., Zhou, H., 2009. Expected stock returns and variance risk premia. Rev. Financ. Stud. 22, 4463–4492. Canina, L., Figlewski, S., 1993. The informational content of implied volatility. Rev. Financ. Stud. 6, 659–681. Clemen, R.T., 1989. Combining forecasts: a review and annotated bibliography. Int. J. Forecast. 5, 559–583. Cumby, R., Figlewski, S., Hasbrouck, J., 1993. Forecasting volatilities and correlations with EGARCH models. J. Deriv. 1, 51–63. Day, T.E., Lewis, C.M., 1992. Stock market volatility and the information content of stock index options. J. Econ. 52, 267–287. Deutsch, M., Granger, C.W.J., Terasvirta, T., 1994. The combination of forecasts using changing weights. Int. J. Forecast. 10, 47–57. Diebold, F.X., Mariano, R.S., 1995. Comparing predictive accuracy. J. Bus. Econ. Stat. 13, 253–263. Ederington, L., Guan, W., 2002. Is implied volatility an informationally efficient and effective predictor of future volatility? J. Risk 4, 3. Elliott, G., Timmermann, A., 2005. Optimal forecast combination weights under regime switching. Int. Econ. Rev. 46, 1081–1102. Engle, R.F., 1982. Autoregressive conditional heteroskedasticity with estimates of the variance of U.K. inflation. Econometrica 50, 987–1008. Engle, R.F., Ng, V.K., 1993. Measuring and testing the impact of news on volatility. J. Finance 48, 1749–1778. Fleming, J., 1998. The quality of market volatility forecasts implied by S&P 100 index option prices. J. Empir. Financ. 5, 317–345. Fleming, J., Ostdiek, B., Whaley, R.E., 1995. Predicting stock market volatility: a new measure. J. Futur. Mark. 15, 265–302. G. Benavides, C. Capistrán / Journal of Empirical Finance 19 (2012) 627–639 639 Garman, M.B., Kohlhagen, S.W., 1983. Foreign currency option values. J. Int. Money Finance 2, 231–237. Giacomini, R., White, H., 2006. Tests of conditional predictive ability. Econometrica 74, 1545–1578. Granger, C.W.J., 2003. Long memory process — an economist 's viewpoint. In: Gulats, C., et al. (Ed.), Advances in Statistics, Combinations, and Related Areas. World Scientific Publishers, pp Granger, C.W.J., Ramanathan, R., 1984. Improved methods of combining forecasts. J. Forecast. 3, 197–204. Guidolin, M., Timmermann, A., 2009. Forecasts of US Short-term interest rates: a flexible forecast combination approach. J. Econ. 150, 297–311. Guo, D., 1996. The predictive power of implied stochastic variance from currency options. J. Futur. Mark. 16, 915–942. Hansen, P.R., Lunde, A., 2005a. A forecast comparison of volatility models: does anything beat a GARCH(1,1)? J. Appl. Econ. 20, 873–889. Hansen, P.R., Lunde, A., 2005b. A realized variance for the whole day based on intermittent high frequency data. J. Financ. Econ. 3 (4), 525–554. Jorion, P., 1995. Predicting volatility in the foreign exchange market. J. Finance 50, 507–528. Lamoureux, C.G., Lastrapes, W.D., 1993. Forecasting stock return variance: toward an understanding of stochastic implied volatilities. Rev. Financ. Stud. 6, 293–326. Manfredo, M., Leuthold, R.M., Irwin, S.H., 2001. Forecasting cash price volatility of fed cattle, feeder cattle and corn: time series, implied volatility and composite approaches Newey, W., West, K., 1987. A simple positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55, 703–708. Noh, J., Engle, R.F., Kane, A., 1994. Forecasting volatility and option prices of the S&P 500 index. J. Deriv. 2, 17–30. Patton, A.J., 2011. Volatility forecast comparison using imperfect volatility proxies. J. Econ. 160 (1), 246–256 (January). Patton, A.J., Sheppard, K., 2009. Evaluating volatility and correlation forecasts. In: Andersen, T.G., Davis, R.A., Kreiss, J.P., Mikosch, T. (Eds.), Handbook of Financial Time Series Pesaran, M.H., Timmermann, A., 2007. Selection of estimation window in the presence of breaks. J. Econ. 137, 134–161. Pong, S., Shackleton, M., Taylor, S., Xu, X., 2004. Forecasting currency volatility: a comparison of implied volatilities and AR(FI)MA models. J. Bank. Financ. 28 (10), 2541–2563. Poon, S.H., Granger, C.W.J., 2003. Forecasting volatility in financial markets: a review. J. Econ. Lit. 41, 478–539. Szakmary, A., Ors, E., Kim, J.K., Davidson III, W.D., 2003. The predictive power of implied volatility: evidence from 35 futures markets. J. Bank. Financ. 27, 2151–2175. Taylor, S.J., 1986. Modeling Financial Time Series. Wiley. Taylor, S.J., 2005. Asset Price Dynamics, Volatility, and Prediction. Princeton University Press. Timmermann, A., 2006. Forecast combinations. In: Elliott, G., Granger, C.W.J., Timmermann, A. (Eds.), Handbook of Economic Forecasting. North Holland, Amsterdam. West, K.D., 1996. Asymptotic inference about predictive ability. Econometrica 64, 1067–1084. Xu, X., Taylor, S.J., 1995. Conditional volatility and the informational efficiency of the PHLX currency options market. J. Bank. Financ. 19, 803–821.