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arXiv · 2402.00172

The Fourier-Malliavin Volatility (FMVol) MATLAB library

Simona Sanfelici·Giacomo Toscano
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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.

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Simona Sanfelici, Giacomo Toscano. 2024-01-31. The Fourier-Malliavin Volatility (FMVol) MATLAB library. https://arxiv.org/abs/2402.00172

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