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 the 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 …nd 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 con…rm 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. Keywords: Bipower variation, HAR, Heterogeneous Autoregressive Model, implied volatility, jumps, options, realized volatility, VecHAR, volatility forecasting. JEL classi…cation: C22, C32, F31, G1. 1 Introduction In both the theoretical and empirical …nance literatures, volatility is generally recognized as one of the most important determinants of risky asset values, such as exchange rates, stock and bond prices, and hence interest rates. Since any valuation procedure involves assessing the level and riskiness of future payo¤s, it is particularly the forecasting of future volatility from variables in the current information set that is important for asset pricing, derivative pricing, hedging, and risk management. A number of di¤erent variables are potentially relevant for volatility forecasting. In Corresponding author. Address: Department of Economics, Dunning Hall Room 307, 94 University Avenue, Queen’s University, Kingston, Ontario K7L 3N6, Canada. Email: [email protected]