## Abstract

The variance risk premium (VRP) is defined as the difference between the forecast of return variance (volatility) under the risk neutral measure and that under the physical measure. The former is obtained as a model-free implied volatility from the option prices and the latter is forecasted using the past daily or intraday returns. Recent empirical evidence suggests that the VRPs of stock indexes predict the excess return of those indexes and some other financial and macroeconomic variables. This paper examines the predictability of the VRP of the Nikkei 225 stock index by extending the method for forecasting the volatility under the physical measure. The first extension is to use the extended model for the realized volatility calculated using intraday returns. Specifically, the heterogeneous autoregressive (HAR) model is used with the realized kernel of the Nikkei 225 index calculated taking account of the bias caused by microstructure noise and the Japanese volatility index (VXJ), which is the model-free implied volatility from the prices of the Nikkei 225 options. The second extension is to combine the daily returns of the Nikkei 225 index and the monthly data on the index of industrial production (IIP) in Japan. This is accomplished by employing the MIDAS-GJR model where the daily volatility is divided into the monthly component that depends on the past monthly data on the IIP and the daily component that follows the GJR model. It is demonstrated the both extensions improve the predictability of the VRP for the IIP but it is not so for the returns of the Nikkei 225 index.