The Fourier–Malliavin Volatility (FMVol) MATLAB® library

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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. Furthermore, 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.