The Role of Implied Volatility in Forecasting Future Realized Volatility and Jumps in Foreign Exchange, Stock, and Bond Markets

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Abstract
We study the forecasting of future realized volatility in the stock, bond, and foreign exchange markets, as well as the continuous sample path and jump components of this, from variables in the information set, including implied volatility backed out from option prices. Recent nonparametric statistical techniques of Barndor-Nielsen & Shephard (2004, 2006) are used to separate realized volatility into its continuous and jump components, which enhances forecasting performance, as shown by Andersen, Bollerslev & Diebold (2005). We generalize the heterogeneous autoregressive (HAR) model of Corsi (2004) to include implied volatility as an additional regressor, and to the separate forecasting of the realized components. We also introduce a new vector HAR (VecHAR) model for the resulting simultaneous system, controlling for possible endogeneity issues in the forecasting equations. We show that implied volatility contains incremental information about future volatility relative to both continuous and jump components of past realized volatility. Indeed, in the foreign exchange market, implied volatility completely subsumes the information content of daily, weekly, and monthly realized volatility measures, when forecasting future realized volatility or its continuous component. In addition, implied volatility is an unbiased forecast of future realized volatility in the foreign exchange and stock markets. Perhaps surprisingly, the jump component of realized return volatility is, to some extent, predictable, and options appear to be calibrated to incorporate information about future jumps in all three markets.

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