Return-Based and Range-Based (Co)Variance Estimation - with an Application to Foreign Exchange Markets

48 Pages Posted: 14 Jan 2002

See all articles by Celso Brunetti

Celso Brunetti

Board of Governors of the Federal Reserve System

Peter M. Lildholdt

Bank of England - Monetary Analysis

Date Written: March 2002

Abstract

This paper analyzes and compares range-based and return-based variance/covariance estimates. We provide new results on the relative efficiency of the range. We show that the use of the range is compatible with time varying volatilities and we extend the range to a multivariate setup. A new estimator for the covariance, termed co-range, which is based on high and low prices, is proposed. The main properties of the new estimator are derived. Empirically, we find that range-based measures of variance, standard deviation, co-variance and correlation possess a much higher degree of persistence compared to conventional measures based on open/close prices.

Keywords: Co-range, foreign exchange rates, price range, high and low prices, covariance estimation, volatility dynamics

JEL Classification: C32, C49, G15

Suggested Citation

Brunetti, Celso and Lildholdt, Peter M., Return-Based and Range-Based (Co)Variance Estimation - with an Application to Foreign Exchange Markets (March 2002). Available at SSRN: https://ssrn.com/abstract=296875 or http://dx.doi.org/10.2139/ssrn.296875

Celso Brunetti (Contact Author)

Board of Governors of the Federal Reserve System ( email )

20th Street and Constitution Avenue NW
Washington, DC 20551
United States

Peter M. Lildholdt

Bank of England - Monetary Analysis ( email )

Threadneedle Street
London EC2R 8AH
United Kingdom

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