Estimation of the instantaneous volatility

Alvarez, Alex; Panloup, Fabien; Pontier, Monique; Savy, Nicolas

doi:10.1007/s11203-011-9062-2

Cited by 37 publications

(32 citation statements)

References 19 publications

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“…Under the absence of jumps and microstructure noise, estimation of spot variance is discussed, among others, in Foster and Nelson (1996), Andreou and Ghysels (2002), Alvarez, Panloup, Pontier, and Savy (2008), Fan and Wang (2008) and Kristensen (2009). Kinnebrock (2008), Mykland and Zhang (2008) and Ogawa and Sanfelici (2008) consider estimation when price observations are contaminated with microstructure noise.…”

Section: Introductionmentioning

confidence: 99%

Spot Variance Path Estimation and Its Application to High-Frequency Jump Testing

Bos

Janus

Koopman

2012

Journal of Financial Econometrics

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This paper considers spot variance path estimation from datasets of intraday high frequency asset prices in the presence of diurnal variance patterns, jumps, leverage effects and microstructure noise. We rely on parametric and nonparametric methods. The estimated spot variance path can be used to extend an existing high frequency jump test statistic, to detect arrival times of jumps and to obtain distributional characteristics of detected jumps. The effectiveness of our approach is explored through Monte Carlo simulations. It is shown that sparse sampling for mitigating the impact of microstructure noise has an adverse affect on both spot variance estimation and jump detection. In our approach we can analyze high frequency price observations that are contaminated with microstructure noise without the need for sparse sampling, say at fifteen minute intervals. An empirical illustration is presented for the intraday EUR/USD exchange rates. Our main finding is that fewer jumps are detected when sampling intervals increase.

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Section: Introductionmentioning

confidence: 99%

Spot Variance Path Estimation and Its Application to High-Frequency Jump Testing

Bos

Janus

Koopman

2012

Journal of Financial Econometrics

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“… 3 This problem has also been studied by, for example, Fan and Wang (2008) and Alvarez et al (2012). Moreover, Jacod and Todorov (2010) and Li and Xiu (2016) included the estimation of spot volatility as an intermediate step to their main goals.…”

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confidence: 99%

Estimation of the Continuous and Discontinuous Leverage Effects

Aı̈t-Sahalia

Fan

Laeven

et al. 2017

Journal of the American Statistical Association

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This paper examines the leverage effect, or the generally negative covariation between asset returns and their changes in volatility, under a general setup that allows the log-price and volatility processes to be Itô semimartingales. We decompose the leverage effect into continuous and discontinuous parts and develop statistical methods to estimate them. We establish the asymptotic properties of these estimators. We also extend our methods and results (for the continuous leverage) to the situation where there is market microstructure noise in the observed returns. We show in Monte Carlo simulations that our estimators have good finite sample performance. When applying our methods to real data, our empirical results provide convincing evidence of the presence of the two leverage effects, especially the discontinuous one.

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“…There are quite a few articles concerning construction of pointwise confidence bands for spot volatility; see e.g. [2,38,42,44]. In contrast, only a few results are available on the behavior of uniform errors in spot volatility estimation: Kristensen [38] and Kanaya and Kristensen [34] give uniform convergence rates for kerneltype spot volatility estimators, while Fan and Wang [24] consider a Gumbel approximation for the distribution of uniform errors of kernel-type spot volatility estimators.…”

Section: Introductionmentioning

confidence: 99%

Gaussian approximation of maxima of Wiener functionals and its application to high-frequency data

Koike¹

2019

Ann. Statist.

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This paper establishes an upper bound for the Kolmogorov distance between the maximum of a highdimensional vector of smooth Wiener functionals and the maximum of a Gaussian random vector. As a special case, we show that the maximum of multiple Wiener-Itô integrals with common orders is well-approximated by its Gaussian analog in terms of the Kolmogorov distance if their covariance matrices are close to each other and the maximum of the fourth cumulants of the multiple Wiener-Itô integrals is close to zero. This may be viewed as a new kind of fourth moment phenomenon, which has attracted considerable attention in the recent studies of probability. This type of Gaussian approximation result has many potential applications to statistics.To illustrate this point, we present two statistical applications in high-frequency financial econometrics: One is the hypothesis testing problem for the absence of lead-lag effects and the other is the construction of uniform confidence bands for spot volatility.Let m * be an integer such that |ρ m * |Σ(θ m * ) = max 1≤m≤M |ρ m |Σ(θ m ). By assumption [A4], for each n ∈ N there is a number ϑ n ∈ G n such that |ϑ n − θ m * | ≤ υ n . Now noting (B.5), we havefor sufficiently large n. Let us denote by ⊖ the symmetric difference between two sets. Then we have

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Estimation of the instantaneous volatility

Cited by 37 publications

References 19 publications

Spot Variance Path Estimation and Its Application to High-Frequency Jump Testing

Spot Variance Path Estimation and Its Application to High-Frequency Jump Testing

Estimation of the Continuous and Discontinuous Leverage Effects

Gaussian approximation of maxima of Wiener functionals and its application to high-frequency data

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