Estimating and forecasting instantaneous volatility through a duration model : An assessment based on VaR

Abstract

In order to forecast one-step ahead volatility, we calculated jump intensity by using estimated parameters of a duration model of price change. In this procedure, we do not assume any distribution on log-return. Although we do not make any distributional assumption, we may practically choose a suitable distribution e.g. Normal, student, etc, including empirical density, when we calculate a VaR (Value at Risk) with an instantaneous volatility to check the prediction performance. Furthermore, we compare the goodness of fit among assumed distributions of log-return. We find that fat tail distributions such as NIG, Laplace, are well fitted to the actual high frequency data listed on the Tokyo stock exchange 1st section from 4 Jan. 2001 to 28 June 2001High frequency data, Duration model, Instantaneous volatility, VaR