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High-Frequency Covariance Estimates With Noisy and Asynchronous Financial Data
 

Summary: High-Frequency Covariance Estimates With Noisy
and Asynchronous Financial Data
Yacine AÏT-SAHALIA, Jianqing FAN, and Dacheng XIU
This article proposes a consistent and efficient estimator of the high-frequency covariance (quadratic covariation) of two arbitrary assets,
observed asynchronously with market microstructure noise. This estimator is built on the marriage of the quasi­maximum likelihood
estimator of the quadratic variation and the proposed generalized synchronization scheme and thus is not influenced by the Epps effect.
Moreover, the estimation procedure is free of tuning parameters or bandwidths and is readily implementable. Monte Carlo simulations
show the advantage of this estimator by comparing it with a variety of estimators with specific synchronization methods. The empirical
studies of six foreign exchange future contracts illustrate the time-varying correlations of the currencies during the 2008 global financial
crisis, demonstrating the similarities and differences in their roles as key currencies in the global market.
KEY WORDS: Covariance; Generalized synchronization method; Market microstructure noise; Quasi-Maximum Likelihood Estimator;
Refresh Time.
1. INTRODUCTION
The covariation between asset returns plays a crucial role in
modern finance. For instance, the covariance matrix and its in-
verse are the key statistics in portfolio optimization and risk
management. Many recent financial innovations involve com-
plex derivatives, like exotic options written on the minimum,
maximum or difference of two assets, or some structured fi-
nancial products, such as CDOs. All of these innovations are

  

Source: Aït-Sahalia, Yacine - Program in Applied and Comptutational Mathematics & Department of Economics, Princeton University
Fan, Jianqing - Department of Operations Research and Financial Engineering, Princeton University

 

Collections: Mathematics