The Fourier-Malliavin Volatility (FMVol) MATLAB library

TL;DR

This paper introduces the FMVol MATLAB library, implementing Fourier-Malliavin estimators for volatility and related measures, offering a robust, non-parametric approach suitable for irregular and noisy financial data.

Contribution

The paper provides a comprehensive MATLAB library for Fourier-Malliavin volatility estimation, enabling robust, non-parametric analysis of stochastic volatility from discrete, irregular, and noisy observations.

Findings

Robustness to measurement errors and noise

Applicability to irregular and asynchronous data

Provides estimates of volatility, co-volatility, quarticity, and leverage

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.