Estimating spot volatility with high-frequency financial data

Zu, Yang; Boswijk, H. Peter

doi:10.1016/j.jeconom.2014.04.001

Cited by 80 publications

(53 citation statements)

References 54 publications

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“…Mancini et al . () and Zu and Boswijk () studied the problem of estimating spot volatility with the presence of microstructure noise. Although Mancini et al .…”

Section: Discussionmentioning

confidence: 99%

Non‐parametric Estimation of High‐frequency Spot Volatility for Brownian Semimartingale With Jumps

Fang

Zeng

et al. 2014

Journal Time Series Analysis

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The availability of high‐frequency financial data has led to substantial improvements in our understanding of financial volatility. Most existing literature focuses on estimating the integrated volatility over a fixed period. This article proposes a non‐parametric threshold kernel method to estimate the time‐dependent spot volatility and jumps when the underlying price process is governed by Brownian semimartingale with finite activity jumps. The threshold kernel estimator combines the threshold estimation for integrated volatility and the kernel filtering approach for spot volatility when the price process is driven only by diffusions without jumps. The estimator proposed is consistent and asymptotically normal and has the same rate of convergence as the estimator studied by Kristensen (2010) in a setting without jumps. The Monte Carlo simulation study shows that the proposed estimator exhibits excellent performance over a wide range of jump sizes and for different sampling frequencies. An empirical example is given to illustrate the potential applications of the proposed method.

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“…Mancini et al . () and Zu and Boswijk () studied the problem of estimating spot volatility with the presence of microstructure noise. Although Mancini et al .…”

Section: Discussionmentioning

confidence: 99%

Non‐parametric Estimation of High‐frequency Spot Volatility for Brownian Semimartingale With Jumps

Fang

Zeng

et al. 2014

Journal Time Series Analysis

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“…Fully nonparametric methods when volatility is instead a càdlàg process have been studied by Malliavin and Mancino [33,34] and Kristensen [32] in the absence of jumps, and by Zu and Boswijk [53], Hoffmann, Munk and Schmidt-Hieber [22] and Ogawa and Sanfelici [42] in the absence of jumps but with noisy observations. Related studies include the idea of rolling sample volatility estimators in Foster and Nelson [20], see also Andreou and Ghysels [4], the theory of spot volatility estimation developed in Bandi and Renò [7], and the kernel based methods of Fan and Wang [17], and Mykland and Zhang [40].…”

Section: Introductionmentioning

confidence: 99%

Spot volatility estimation using delta sequences

2015

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Abstract. We introduce a class of nonparametric spot volatility estimators based on delta sequences and conceived to include many of the existing estimators in the field as special cases. The full limit theory is first derived when unevenly sampled observations under infill asymptotics and fixed time-horizon are considered, and the state variable is assumed to follow a Brownian semimartingale.We then extend our class of estimators to include Poisson jumps or financial microstructure noise in the observed price process. As an application of our results, we relate the Fourier estimator to a specific delta sequence obtained with the Fejér function. The proposed estimators are applied to data from the S&P500 stock index futures market.

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“…Notably, our spot covariance matrix estimator (12) converges considerably faster than existing noise-robust spot volatility estimators based on the difference quotient of integrated volatility estimates (e.g. Zu and Boswijk, 2014). The two-step approach (12) with combinations over different frequencies strongly reduces the estimator's variance (compared to simpler methods).…”

Section: Asymptotic Propertiesmentioning

confidence: 94%

“…To account for noise, the predominant approach is to compute a difference quotient based on a noise-robust integrated volatility estimator, e.g., the (univariate) realized kernel, the pre-averaging estimator or the two-scale estimator. Here, examples include Mykland and Zhang (2008), Mancini et al (2015), Bos et al (2012) and Zu and Boswijk (2014). An alternative approach based on series estimators of non-stochastic spot volatility is introduced by Munk and Schmidt-Hieber (2010b), while Munk and Schmidt-Hieber (2010a) study optimal convergence rates in the aforementioned setting.…”

Section: Introductionmentioning

confidence: 99%

Estimating the Spot Covariation of Asset Prices—Statistical Theory and Empirical Evidence

Bibinger

Hautsch

Malec

et al. 2017

Journal of Business & Economic Statistics

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We propose a new estimator for the spot covariance matrix of a multi-dimensional continuous semi-martingale log asset price process which is subject to noise and non-synchronous observations. The estimator is constructed based on a local average of block-wise parametric spectral covariance estimates. The latter originate from a local method of moments (LMM) which recently has been introduced by . We prove consistency and a point-wise stable central limit theorem for the proposed spot covariance estimator in a very general setup with stochastic volatility, leverage effects and general noise distributions.Moreover, we extend the LMM estimator to be robust against autocorrelated noise and propose a method to adaptively infer the autocorrelations from the data. Based on simulations we provide empirical guidance on the effective implementation of the estimator and apply it to high-frequency data of a cross-section of Nasdaq blue chip stocks. Employing the estimator to estimate spot covariances, correlations and volatilities in normal but also unusual periods yields novel insights into intraday covariance and correlation dynamics.We show that intraday (co-)variations (i) follow underlying periodicity patterns, (ii) reveal substantial intraday variability associated with (co-)variation risk, and (iii) can increase strongly and nearly instantaneously if new information arrives.

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Estimating spot volatility with high-frequency financial data

Cited by 80 publications

References 54 publications

Non‐parametric Estimation of High‐frequency Spot Volatility for Brownian Semimartingale With Jumps

Non‐parametric Estimation of High‐frequency Spot Volatility for Brownian Semimartingale With Jumps

Spot volatility estimation using delta sequences

Estimating the Spot Covariation of Asset Prices—Statistical Theory and Empirical Evidence

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