A No-Arbitrage Approach to Range-Based Estimation of Return Covariances and Correlations

We extend range-based volatility estimation to the multivariate case. In particular, we propose a range-based covariance estimator motivated by a key financial economic consideration, the absence of arbitrage, in addition to statistical considerations. We show that this estimator is highly efficient yet robust to market microstructure noise arising from bid-ask bounce and asynchronous trading.

[1]  R. C. Merton,et al.  On Estimating the Expected Return on the Market: An Exploratory Investigation , 1980 .

[2]  M. Parkinson.  The Extreme Value Method for Estimating the Variance of the Rate of Return , 1980 .

[3]  M. J. Klass,et al.  On the Estimation of Security Price Volatilities from Historical Data , 1980 .

[4]  Philip E. Gill,et al.  Practical optimization , 1981 .

[5]  S. Beckers,et al.  Variances of Security Price Returns Based on High , 1983 .

[6]  Walter N. Torous,et al.  The Maximum Likelihood Estimation of Security Price Volatility: Theory, Evidence, and Application to Option Pricing , 1984 .

[7]  K. French,et al.  Expected stock returns and volatility , 1987 .

[8]  Alan G. White,et al.  The Pricing of Options on Assets with Stochastic Volatilities , 1987 .

[9]  L. Rogers,et al.  Estimating Variance From High, Low and Closing Prices , 1991 .

[10]  Naoto Kunitomo,et al.  Improving the Parkinson Method of Estimating Security Price Volatilities , 1992 .

[11]  Joel Hasbrouck,et al.  The Dynamics of Discrete Bid and Ask Quotes , 1996 .

[12]  Joel Hasbrouck,et al.  Security Bid/Ask Dynamics with Discreteness and Clustering: Simple Strategies for Modeling and Estimation , 1998 .

[13]  T. Bollerslev,et al.  ANSWERING THE SKEPTICS: YES, STANDARD VOLATILITY MODELS DO PROVIDE ACCURATE FORECASTS* , 1998 .

[14]  Elizabeth Eskow,et al.  A Revised Modified Cholesky Factorization Algorithm , 1999, SIAM J. Optim..

[15]  D. Yang,et al.  Drift Independent Volatility Estimation Based on High, Low, Open, and Close Prices , 2000 .

[16]  Francis X. Diebold,et al.  Modeling and Forecasting Realized Volatility , 2001 .

[17]  Michael W. Brandt,et al.  Range-Based Estimation of Stochastic Volatility Models , 2001 .

[18]  F. Diebold,et al.  The Distribution of Realized Exchange Rate Volatility , 2000 .

[19]  F. Diebold,et al.  The distribution of realized stock return volatility , 2001 .

[20]  Fulvio Corsi,et al.  Efficient Estimation of Volatility Using High Frequency Data , 2002 .

[21]  Peter M. Lildholdt,et al.  Return-Based and Range-Based (Co)Variance Estimation - with an Application to Foreign Exchange Markets , 2002 .

[22]  Olivier Ledoit,et al.  A well-conditioned estimator for large-dimensional covariance matrices , 2004 .