The role of implied volatility in forecasting future realized volatility and jumps in foreign exchange, stock, and bond markets

We study the forecasting of future realized volatility in the foreign exchange, stock, and bond markets from variables in our information set, including implied volatility backed out from option prices. Realized volatility is separated into its continuous and jump components, and the heterogeneous autoregressive (HAR) model is applied with implied volatility as an additional forecasting variable. A vector HAR (VecHAR) model for the resulting simultaneous system is introduced, controlling for possible endogeneity issues. We find that implied volatility contains incremental information about future volatility in all three markets, relative to past continuous and jump components, and it is an unbiased forecast in the foreign exchange and stock markets. Out-of-sample forecasting experiments confirm that implied volatility is important in forecasting future realized volatility components in all three markets. Perhaps surprisingly, the jump component is, to some extent, predictable, and options appear calibrated to incorporate information about future jumps in all three markets.