Abstract
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.
Highlights
Modeling the volatility of financial asset returns is of fundamental importance to option pricing, assets portfolio and risk management
The model proposed by this paper can be used to calculate Value-at-Risk and Expected Shortfall which are helpful for financial risk managers and portfolio managers
The Realized GARCH model proposed by Hansen et al (2012) [7] is a joint model for daily return and realized volatility
Summary
Modeling the volatility of financial asset returns is of fundamental importance to option pricing, assets portfolio and risk management. Any of these realized measures of volatility contains much information about the current level of asset price volatility than the squared daily return This makes them widely used in the recent research of financial economics. The daily return is less subject to the market microstructure noise but contains less information of volatility, while the realized volatility is heavily contaminated by the noise but still includes much information In this context, recently, numerous researchers have devoted to study the joint model for daily returns and realized measure of volatility. It is a puzzle that the theory and the simulation results of the high-low range estimator perform well, while the empirical application performs poorly, due to its failure to capture the dynamic of volatilities For this reason, Chou (2005) proposed a range-based volatility model named CARR (Conditional Autoregressive Range model), which can appropriately model the dynamic of the high-low range [14].
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