BBB93653d01

BBB93653d01 - High-Frequency Covariance Estimates With...

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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 quasi–maximum 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 built upon, or in order to exploit, the correlation structure of two or more assets. As technological developments make high frequency data commonly available, much effort has been put into developing statistical inference methodologies for continu- ous time models with intra-day data, enabling us to capture the daily variation of some interesting statistics that were otherwise unobservable from daily or weekly data. Realized variance estimation is an example of such statis- tics. Unfortunately, unlike those low frequency time series that are homogeneously spaced, tick-by-tick transactions of differ- ent assets usually occur randomly and asynchronously; in ad- dition, with high frequency data comes market microstructure noise. These factors make it difficult to employ a Realized Covariance (RC) estimator directly. Popular estimators in the univariate variance case include Two Scales Realized Volatil- ity (TSRV) of Zhang, Mykland, and Aït-Sahalia ( 2005 ), the first consistent estimator for integrated volatility in the presence of noise, Multi-Scale Realized Volatility (MSRV), a modifica- tion of TSRV which achieves the best possible rate of conver- gence proposed by Zhang ( 2006 ), Realized Kernels (RK) by Barndorff-Nielsen et al. ( 2008a ) and the Pre-Averaging (PA) approach by Jacod et al. ( 2009 ), both of which contain sets of nonparametric estimators that can also achieve the best con- vergence rate. In contrast with these nonparametric estimators,
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This note was uploaded on 10/27/2011 for the course RAD 131 taught by Professor Ded during the Spring '11 term at Duke.

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BBB93653d01 - High-Frequency Covariance Estimates With...

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