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.

翻译：本文介绍了用于MATLAB的傅里叶-马利亚文波动率（FMVol）估计工具箱。该工具箱包含一系列函数，用于实现连续随机波动率过程的波动率及其协波动率的傅里叶-马利亚文估计方法（参见Malliavin和Mancino，2002, 2009），以及二阶级量（如四次波动率（即波动率的平方）、波动率的波动率和杠杆效应（即过程变化与其波动率变化之间的协方差））。傅里叶-马利亚文方法完全非参数化，无需等间距观测，且对测量误差或噪声具有鲁棒性，无需对观测数据进行任何初步偏差校正或预处理。此外，在其多变量版本中，该方法对不规则和异步采样具有内在鲁棒性。尽管该方法最初是为金融计量经济学中的特定应用（即资产波动率估计）而提出的，但作为一种通用方法，只要研究者希望根据离散观测重建连续随机波动率过程的潜在波动率和二阶级量，即可应用该傅里叶-马利亚文方法。