The Fourier-Malliavin Volatility (FMVol) MATLAB library
Abstract: This paper presents the Fourier-Malliavin Volatility (FMVol) estimation library for MATLAB. This library includes functions that implement Fourier- Malliavin estimators (see Malliavin and Mancino (2002, 2009)) of the volatility and co-volatility of continuous stochastic volatility processes and second-order quantities, like the quarticity (the squared volatility), the volatility of volatility and the leverage (the covariance between changes in the process and changes in its volatility). The Fourier-Malliavin method is fully non-parametric, does not require equally-spaced observations and is robust to measurement errors, or noise, without any preliminary bias correction or pre-treatment of the observations. Further, in its multivariate version, it is intrinsically robust to irregular and asynchronous sampling. Although originally introduced for a specific application in financial econometrics, namely the estimation of asset volatilities, the Fourier-Malliavin method is a general method that can be applied whenever one is interested in reconstructing the latent volatility and second-order quantities of a continuous stochastic volatility process from discrete observations.
- High-freqeuncy financial econometrics. Princeton University Press.
- Bloomfield, P. (2000). Fourier Analysis of Time Series. An Introduction. Wiley Series in Probability and Statistics.
- Christie, A. A. (1982). The stochastic behavior of common stock variances: Value, leverage and interest rate effects. Journal of Financial Economics, 10(4):407–432.
- Curato, I. (2019). Estimation of the stochastic leverage effect using the fourier transform method. Stochastic Processes and their Applications, 129(9):3207–3238.
- Measuring the leverage effect in a high-frequency framework. In Gregoriou, G., editor, The Handbook of High-Frequency Trading, pages 425–446. Elsevier.
- Stochastic leverage effect in high-frequency data: a fourier based analysis. Econometrics and Statistics, 23:53–82.
- Reduced heart rate volatility: an early predictor of death in trauma patients. Annals of Surgery, 240(3):547–556.
- Hannan, E. (1970). Multiple Time Series. John Wiley and Sons.
- Heston, S. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of Financial Studies, 6:327–343.
- Asymptotic results for the fourier estimator of the integrated quarticity. Decisions in Economics and Finance, 42(2):471–502.
- Malliavin, P. (1995). Integration and probability. Springer-Verlag.
- Fourier series method for measurement of multivariate volatilities. Finance and Stochastics, 4:49–61.
- A fourier transform method for nonparametric estimation of volatility. The Annals of Statistics, 37(4):1983–2010.
- Asymptotic normality for the spot volatility fourier estimator in the presence of microstructure noise contamination. Working Paper.
- Fourier spot volatility estimator: asymptotic normality and efficiency with liquid and illiquid high-frequency data. PloS one, 10(9):e0139041.
- Robustness of fourier estimator of integrated volatility in the presence of microstructure noise. Computational Statistics & Data Analysis, 52(6):2966–2989.
- Estimating covariance via fourier method in the presence of asynchronous trading and microstructure noise. Journal of Financial Econometrics, 9(2):367–408.
- Estimation of quarticity with high frequency data. Quantitative Finance, 12(4):607–622.
- Rate-efficient asymptotic normality of the fourier estimator of the leverage process. Statistics and Its Interface, 15(1):73–89.
- Mudelsee, M. (2014). Climate time series analysis: Classical statistical and bootstrap methods. Springer International Publishing.
- The impact of local temperature volatility on attention to climate change: Evidence from spanish tweets. Global Environmental Change, 69:102286.
- Mathematical modeling suggests that periodontitis behaves as a non-linear chaotic dynamical process. Journal of Periodontology, 84(10):e29–e39.
- Priestley, M. (1983). Spectral Analysis and Time Series. Academic Press.
- High-frequency volatility of volatility estimation free from spot volatility estimates. Quantitative Finance, 15(8):1331–1345.
- Toscano, G. (2022). The price-leverage covariation as a measure of the response of the leverage effect to price and volatility changes. Applied Stochastic Models in Business and Industry, 38(3):497–511.
- Volatility of volatility estimation: central limit theorems for the fourier transform estimator and empirical study of the daily time series stylized facts. Journal of Financial Econometrics, 22(1):252–296.
- Nonparametric modeling of longitudinal covariance structure in functional mapping of quantitative trait loci. Biometrics, 65(4):1068–1077.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.