Limits...
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

Comparison of the empirical cumulative distribution function and the standard normal one.Cumulative distribution functions of a sampled normal process (0,1) (blue line) and of the sampled process  (red line) with a sampling interval of 1 minute (March 4-7, 2013).
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4589382&req=5

pone.0139041.g009: Comparison of the empirical cumulative distribution function and the standard normal one.Cumulative distribution functions of a sampled normal process (0,1) (blue line) and of the sampled process (red line) with a sampling interval of 1 minute (March 4-7, 2013).

Mentions: We compute an estimate, , of the standardized return zt using the spot volatility estimated with the Fourier method as done in Subsection 4.1. The frequencies N and M for the Fourier estimator are chosen according to N = n/2 and . Fig 9 shows the empirical cumulative distribution function for and the expected cumulative distribution function (i.e. (0,1)), with Δ t = T/n = (1/390) seconds. Moreover, the BJ and the KS tests applied to the random sample do not reject the hypothesis at the significance level 0.05 and their p-values are 0.3, 0.6, respectively. The Fourier estimator shows a good performance in interpreting changes of volatilities despite the fact that the asset is illiquid. This finding is confirmed also by the second application, that is, the Value at Risk (VaR) prediction. This application has already been illustrated in Refs. [26, 28] to measure the performance of integrated volatility estimators and in Ref. [27] for the spot volatility estimators.


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

Mancino ME, Recchioni MC - PLoS ONE (2015)

Comparison of the empirical cumulative distribution function and the standard normal one.Cumulative distribution functions of a sampled normal process (0,1) (blue line) and of the sampled process  (red line) with a sampling interval of 1 minute (March 4-7, 2013).
© Copyright Policy
Related In: Results  -  Collection

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

pone.0139041.g009: Comparison of the empirical cumulative distribution function and the standard normal one.Cumulative distribution functions of a sampled normal process (0,1) (blue line) and of the sampled process (red line) with a sampling interval of 1 minute (March 4-7, 2013).
Mentions: We compute an estimate, , of the standardized return zt using the spot volatility estimated with the Fourier method as done in Subsection 4.1. The frequencies N and M for the Fourier estimator are chosen according to N = n/2 and . Fig 9 shows the empirical cumulative distribution function for and the expected cumulative distribution function (i.e. (0,1)), with Δ t = T/n = (1/390) seconds. Moreover, the BJ and the KS tests applied to the random sample do not reject the hypothesis at the significance level 0.05 and their p-values are 0.3, 0.6, respectively. The Fourier estimator shows a good performance in interpreting changes of volatilities despite the fact that the asset is illiquid. This finding is confirmed also by the second application, that is, the Value at Risk (VaR) prediction. This application has already been illustrated in Refs. [26, 28] to measure the performance of integrated volatility estimators and in Ref. [27] for the spot volatility estimators.

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