Modeling and Forecasting Financial Volatilities Using a Joint Model for Range and Realized Volatility

There exist many ways to measure financial asset volatility. In this paper, we introduce a new joint model for the high-low range of assets prices and realized measure of volatility: Realized CARR. In fact, the high-low range and realized volatility, both are efficient estimators of volatility. Hence, this new joint model can be viewed as a model of volatility. The model is similar to the Realized GARCH model of Hansen et al. (2012), and it can be estimated by the quasi-maximum likelihood method. Out-of-sample volatility forecasting using Standard and Poors 500 stock index (S&P), Dow Jones Industrial Average index (DJI) and National Association of Securities Dealers Automated Quotation (NASDAQ) 100 equity index shows that the Realized CARR model does outperform the Realized GARCH model.