Discrete time volatility models typically employ a latent scale factor to represent volatility. High frequency data may be used to construct proxies for these scale factors. Examples are the intraday high-low range and the realized volatility. This paper develops a method for ranking and...

This paper decomposes volatility proxies according to upward and downward price movements in high-frequency financial data, and uses this decomposition for forecasting volatility. The paper introduces a simple Garch-type discrete time model that incorporates such high-frequency based statistics...

High frequency data are often used to construct proxies for the daily volatility in discrete time volatility models. This paper introduces a calculus for such proxies, making it possible to compare and optimize them. The two distinguishing features of the approach are (1) a simple continuous...

A standard procedure for obtaining parameter values of a GARCH model for financial volatility is the quasi maximum likelihood estimator (QMLE) based on daily close-to-close returns. This paper generalizes the QMLE based on daily returns to a QMLE based on intraday high-frequency data. Volatility...

Estimation of the parameters of Garch models for financial data is typically based on daily close-to-close returns. This paper shows that the efficiency of the parameter estimators may be greatly improved by using volatility proxies based on intraday data. The paper develops a Garch quasi...