EWMA historical volatility estimators. (English) Zbl 1344.62009

Summary: In this paper different types of historical volatility estimators based on open-high-low-close (OHLC) values are studied. The estimators are broken down to the main building blocks and the correlation structure of these building blocks with time dependent variance (volatility squared) is investigated. The building blocks are estimated from the equity index (SPX in USA and DAX in Germany) and compared with a volatility index (VIX in USA and VDAX in Germany) which stands as a proxy for volatility, because the values of the volatility process are in general not available. In an empirical study it is observed that both the autocorrelation function of variance and the cross-correlation functions of building blocks with the variance decrease exponentially with the same degree. This dependence can be explained as exponentially decreasing “amount of information” and it naturally leads to use of exponentially decreasing weights in historical estimators. The proposed EWMA style estimators have higher predicting power over the commonly used estimators and in prediction beat the very popular GARCH(1,1).


62P05 Applications of statistics to actuarial sciences and financial mathematics
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
91B82 Statistical methods; economic indices and measures