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Fourier Spot Volatility Estimator: Asymptotic Normality and Efficiency with Liquid and Illiquid High-Frequency Data.

Mancino ME, Recchioni MC - PLoS ONE (2015)

Bottom Line: The recent availability of high frequency data has permitted more efficient ways of computing volatility.We address this issue by using the Fourier estimator of instantaneous volatility introduced in Malliavin and Mancino 2002.We prove a central limit theorem for this estimator with optimal rate and asymptotic variance.

View Article: PubMed Central - PubMed

Affiliation: Department of Economics and Management, University of Florence, Florence, Italy.

ABSTRACT
The recent availability of high frequency data has permitted more efficient ways of computing volatility. However, estimation of volatility from asset price observations is challenging because observed high frequency data are generally affected by noise-microstructure effects. We address this issue by using the Fourier estimator of instantaneous volatility introduced in Malliavin and Mancino 2002. We prove a central limit theorem for this estimator with optimal rate and asymptotic variance. An extensive simulation study shows the accuracy of the spot volatility estimates obtained using the Fourier estimator and its robustness even in the presence of different microstructure noise specifications. An empirical analysis on high frequency data (U.S. S&P500 and FIB 30 indices) illustrates how the Fourier spot volatility estimates can be successfully used to study intraday variations of volatility and to predict intraday Value at Risk.

No MeSH data available.


Related in: MedlinePlus

True and estimated variance path.The four graphs show the true variance, σ2(t), (solid line) and the Fourier estimated variance, , (dotted line) as a function of time for four realizations obtained with model (11)–(12) and a sampling interval of 2 minutes.
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pone.0139041.g003: True and estimated variance path.The four graphs show the true variance, σ2(t), (solid line) and the Fourier estimated variance, , (dotted line) as a function of time for four realizations obtained with model (11)–(12) and a sampling interval of 2 minutes.

Mentions: Secondly, we prove that the Fourier estimator provides accurate spot volatility estimates. We use the simulated data p(ti), ti = i/n, i = 0, 1, …, n, n = 23400, to estimate the variance σ2(t) on the time grid , j = 1, 2, …, 23400/120, Δ t = 120/23400 = 1/195. That is, we estimate the spot variance using a sampling interval of two minutes. In this exercise the log-prices, p(ti) are not affected by microstructure noise. Fig 3 shows four realizations of the true variance (solid line) and the corresponding estimates (dotted line) obtained with the Fourier estimator with N = n/2 and . It is worth noting that Fig 3 shows that the Fourier estimator approximates the true variance with a satisfactory accuracy over the entire interval. This property is a consequence of the fact that the Fourier method generates a global estimator. This accuracy is relevant for calibrating parametric models such as those of [29–31]. In fact, as shown in the empirical analysis, we can use the spot volatility estimates to reconstruct accurate standardized returns which could be used to efficiently estimate model parameters.


Fourier Spot Volatility Estimator: Asymptotic Normality and Efficiency with Liquid and Illiquid High-Frequency Data.

Mancino ME, Recchioni MC - PLoS ONE (2015)

True and estimated variance path.The four graphs show the true variance, σ2(t), (solid line) and the Fourier estimated variance, , (dotted line) as a function of time for four realizations obtained with model (11)–(12) and a sampling interval of 2 minutes.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4589382&req=5

pone.0139041.g003: True and estimated variance path.The four graphs show the true variance, σ2(t), (solid line) and the Fourier estimated variance, , (dotted line) as a function of time for four realizations obtained with model (11)–(12) and a sampling interval of 2 minutes.
Mentions: Secondly, we prove that the Fourier estimator provides accurate spot volatility estimates. We use the simulated data p(ti), ti = i/n, i = 0, 1, …, n, n = 23400, to estimate the variance σ2(t) on the time grid , j = 1, 2, …, 23400/120, Δ t = 120/23400 = 1/195. That is, we estimate the spot variance using a sampling interval of two minutes. In this exercise the log-prices, p(ti) are not affected by microstructure noise. Fig 3 shows four realizations of the true variance (solid line) and the corresponding estimates (dotted line) obtained with the Fourier estimator with N = n/2 and . It is worth noting that Fig 3 shows that the Fourier estimator approximates the true variance with a satisfactory accuracy over the entire interval. This property is a consequence of the fact that the Fourier method generates a global estimator. This accuracy is relevant for calibrating parametric models such as those of [29–31]. In fact, as shown in the empirical analysis, we can use the spot volatility estimates to reconstruct accurate standardized returns which could be used to efficiently estimate model parameters.

Bottom Line: The recent availability of high frequency data has permitted more efficient ways of computing volatility.We address this issue by using the Fourier estimator of instantaneous volatility introduced in Malliavin and Mancino 2002.We prove a central limit theorem for this estimator with optimal rate and asymptotic variance.

View Article: PubMed Central - PubMed

Affiliation: Department of Economics and Management, University of Florence, Florence, Italy.

ABSTRACT
The recent availability of high frequency data has permitted more efficient ways of computing volatility. However, estimation of volatility from asset price observations is challenging because observed high frequency data are generally affected by noise-microstructure effects. We address this issue by using the Fourier estimator of instantaneous volatility introduced in Malliavin and Mancino 2002. We prove a central limit theorem for this estimator with optimal rate and asymptotic variance. An extensive simulation study shows the accuracy of the spot volatility estimates obtained using the Fourier estimator and its robustness even in the presence of different microstructure noise specifications. An empirical analysis on high frequency data (U.S. S&P500 and FIB 30 indices) illustrates how the Fourier spot volatility estimates can be successfully used to study intraday variations of volatility and to predict intraday Value at Risk.

No MeSH data available.


Related in: MedlinePlus