Consistent High-Precision Volatility from High-Frequency Data

Estimates of daily volatility are investigated. Realized volatility can be computed from returns observed over time intervals of different sizes. For simple statistical reasons, volatility estimators based on high-frequency returns have been proposed, but such estimators are found to be strongly biased as compared to volatilities of daily returns. This bias originates from microstructure effects in the price formation. For foreign exchange, the relevant microstructure effect is the incoherent price formation, which leads to a strong negative first-order autocorrelation ρ 1 40% for tick-by-tick returns and to the volatility bias. On the basis of a simple theoretical model for foreign exchange data, the incoherent term can be filtered away from the tick-by-tick price series. With filtered prices, the daily volatility can be estimated using the information contained in highfrequency data, providing a high-precision measure of volatility at any time interval. 1Olsen & Associates Research Institute for Applied Economics Seefeldstrasse 233, 8008 Zürich, Switzerland. e-mail: [email protected], [email protected], [email protected] phone: +41-1/386 48 48 Fax: +41-1/422 22 82 2Zurich Re General Guisan Quai 26, 8022 Zürich, Switzerland. e-mail: [email protected]