Modelling and Forecasting Intraday Market Risk with Application to Stock Indices

Abstract

On the afternoon of May 6, 2010 the Dow Jones Industrial Average (DJIA) plunged about 1000 points (about 9%) in a matter of minutes before rebounding almost as quickly. This was the biggest one day point decline on an intraday basis in the DJIA's history. An almost similar dramatic change in intraday volatility was observed on April 4, 2000 when the DJIA dropped by 4.8%. These historical events present a very compelling argument for the need for robust econometrics models which can forecast intraday asset volatility. There are numerous models available in the finance literature to model financial asset volatility. Various Autoregressive Conditional Heteroskedastic (ARCH) time series models are widely used for modelling daily (end of day) volatility of the financial assets. The family of basic GARCH models works well for modelling daily volatility but they are proven to be not as efficient for intraday volatility. The last two decades have seen some research augmenting the GARCH family of models to forecast intraday volatility, the Multiplicative Component GARCH (MCGARCH) model of Engle & Sokalska (2012) being the most recent of them. MCGARCH models the conditional variance as the multiplicative product of daily, diurnal, and stochastic intraday volatility of the financial asset. In this paper we use the MCGARCH model to forecast the intraday volatility of Australia's S&P/ASX-50 stock market index and the USA Dow Jones Industrial Average (DJIA) stock market index. We also use the model to forecast their intraday Value at Risk (VaR) and Expected Shortfall (ES). As the model requires a daily volatility component, we test a GARCH based estimate of the daily volatility component against the daily realized volatility (RV) estimates obtained from the Heterogeneous Autoregressive model for Realized Volatility (HARRV). The results in the paper show that 1 minute VaR forecasts obtained from the MCGARCH model using the HARRV based daily volatility component outperform the ones obtained using the GARCH based daily volatility component.