Econometric analysis of multivariate realised QML: Estimation of the covariation of equity prices under asynchronous trading

The analysis of the intraday dynamics of correlations among high-frequency returns is challenging due to the presence of asynchronous trading and market microstructure noise. Both effects may lead to significant data reduction and may severely underestimate correlations if traditional methods for low-frequency data are employed. We propose to model intraday log-prices through a multivariate local-level model with score-driven covariance matrices and to treat asynchronicity as a missing value problem. The main advantages of this approach are: (i) all available data are used when filtering correlations, (ii) market microstructure noise is taken into account, (iii) estimation is performed through standard maximum likelihood methods. Our empirical analysis, performed on 1-second NYSE data, shows that opening hours are dominated by idiosyncratic risk and that a market factor progressively emerges in the second part of the day. The method can be used as a nowcasting tool for highfrequency data, allowing to study the real-time response of covariances to macro-news announcements and to build intraday portfolios with very short optimization horizons. . We are particularly grateful for suggestions we have received from Maria Elvira Mancino, Davide Delle Monache, Ivan Petrella, Fabrizio Venditti, Giampiero Gallo, Davide Pirino and participants to the IAAE 2017 conference in Sapporo, the 10 th SoFiE conference in New York and the VIECO 2017 conference in Wien. 1A large class of conditional covariance models have been proposed in the econometric literature and their use is widespread in risk and portfolio management at daily or lower frequencies. Popular multivariate dynamic time-series models include the class of multivariate extensions of the univariate GARCH model of Engle (1982) andBollerslev (1986) and the Dynamic Conditional Correlation (DCC) model of Engle (2002). A drawback of these models is that they are misspecified if data are recorded with observational noise and require synchronization in case data are irregularly spaced. As a consequence, they cannot be straightforwardly applied to intraday data, since high-frequency prices are contaminated by microstructure noise and assets are traded asynchronously. Both effects may lead to ignore a large portion of data and can significantly underestimate correlations. The problem of estimating and forecasting intraday volatilities and correlations is, however, of crucial importance in high-frequency finance. For instance, an high-frequency trader is interested in rebalancing the portfolio on an intraday basis and thus needs accurate shortterm covariance forecasts. Similarly, the study of the intraday dependencies of financial assets is useful to examine the reaction of the market to external information and has a theoretical relevance in market microstructure research.We contribute to the literature on intraday covariance estimation by proposing a modelling strategy that can handle both asynchronous trading and microstructure effects. High-frequency log-prices are modeled t...

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“…They thus assumed a diagonal covariance matrix for the noise. Shephard and Xiu (2017) made the same assumption.…”

Section: Time-varying Covariancesmentioning

confidence: 96%

A Score-Driven Conditional Correlation Model for Noisy and Asynchronous Data: An Application to High-Frequency Covariance Dynamics

Buccheri

Bormetti

Corsi

et al. 2020

Journal of Business & Economic Statistics

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“…The prominent works on this topic are the Fourier analysis approach of [40], the sampling design kernel method of [23] and the quasi-likelihood analysis of [44]. In addition, recently various approaches to deal with these issues simultaneously have been proposed by many authors; see, for example, [1,6,8,9,15,51].…”

Section: Introductionmentioning

confidence: 99%

Quadratic covariation estimation of an irregularly observed semimartingale with jumps and noise

Koike¹

2016

Bernoulli

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This paper presents a central limit theorem for a pre-averaged version of the realized covariance estimator for the quadratic covariation of a discretely observed semimartingale with noise. The semimartingale possibly has jumps, while the observation times show irregularity, nonsynchronicity, and some dependence on the observed process. It is shown that the observation times' effect on the asymptotic distribution of the estimator is only through two characteristics: the observation frequency and the covariance structure of the noise. This is completely different from the case of the realized covariance in a pure semimartingale setting.

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“…In Sections 3.2 and 3.3, the reasoning of recovering the pure rounded prices through the Kalman filter is explained. The Kalman filter is also adopted in the high‐frequency (co)variation estimation by Shephard and Xiu and Da and Xiu for different settings without rounding. Our integrated volatility estimator, which deals with both random noise and rounding, has an additional application of particle filter.…”

Section: The Combined Filtering Approachmentioning

confidence: 99%

A combined filtering approach to high‐frequency volatility estimation with mixed‐type microstructure noises

Tang

Zhang

2018

Appl Stoch Models Bus & Ind

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This paper introduces a solution that combines the Kalman and particle filters to the challenging problem of estimating integrated volatility using high-frequency data where the underlying prices are perturbed by a mixture of random noise and price discreteness. An explanation is presented of how the proposed combined filtering approach is able to correct for bias due to this mixed-type microstructure effect. Simulation and empirical studies on the tick-by-tick trade price data for four US stocks in the year 2009 show that our method has clear advantages over existing high-frequency volatility estimation methods. KEYWORDScombined filters, high-frequency data, integrated volatility, market microstructure noise, price discreteness INTRODUCTIONThe last 15 years have seen growing interest in volatility estimation using high-frequency data. One challenge when making inferences using high-frequency data is the presence of a market microstructure effect that causes the traditional realized volatility (RV) method to fail. 1 The market microstructure effect may be attributable to, among other causes, bid-ask bounce, adverse selection due to asymmetry of information for different traders, dealer's inventory control, and price discreteness. In contrast to those random effects that can be deemed measurement errors, the effect that stems from price discreteness is of a nonlinear nature. Although the work described in the existing literature has usually treated the two kinds of effect somewhat separately, they are both present in real data and pose a great challenge to volatility estimation using high-frequency data. Subsampling (eg, at an adhoc 5-minute frequency as suggested by Andersen et al 2 ) may mitigate the microstructure effect to a certain degree; however, it is one of the first principles of statistics that one should not throw away a large amount of data. In this paper, we address the problem by proposing an approach that combines the Kalman and particle filters.The study of price discreteness can be dated back to the 1980s. If one takes price discreteness as rounding errors, then explicitly characterizing the effect of rounding on the latent "true" asset returns becomes surprisingly difficult, except under specific parametric Brownian/geometric Brownian models (cf the work of Campbell et al 3 ). In particular, under the parametric Brownian/geometric Brownian setup for the latent "true" price, Ball, 4 Gottlieb and Kalay, 5 and Harris, 6 among others, studied the effect of price discreteness on estimation of the volatility of the latent true price process. For models other than those that take price discreteness as rounding errors and are related to volatility estimation, see, eg, the ordered probit model in the work of Hausman et al 7 and the barrier models in the works of Marsh and Rosenfeld 8 and Cho and Frees. 9Appl Stochastic Models Bus Ind. 2019;35:603-623.wileyonlinelibrary.com/journal/asmb

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Econometric analysis of multivariate realised QML: Estimation of the covariation of equity prices under asynchronous trading

Cited by 44 publications

References 91 publications

A Score-Driven Conditional Correlation Model for Noisy and Asynchronous Data: An Application to High-Frequency Covariance Dynamics

A Score-Driven Conditional Correlation Model for Noisy and Asynchronous Data: An Application to High-Frequency Covariance Dynamics

Quadratic covariation estimation of an irregularly observed semimartingale with jumps and noise

A combined filtering approach to high‐frequency volatility estimation with mixed‐type microstructure noises

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