Simona Sanfelici, Giacomo Toscano
arXiv 31 Jan 2024 · Statistics — Computation · publishedMathematics and Computers in Simulation (2024) · 4 citations (OpenAlex)
arXiv:2402.00172 · PDF · DOI · OpenAlex · Extracted main text
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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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Malliavin, P. and Mancino, M (2009) A fourier transform method for nonparametric estimation of volatility | 1.000 | 6 | 4 | 100% |
| 2 | Malliavin, P. and Mancino, M (2002) Fourier series method for measurement of multivariate volatilities | 1.000 | 5 | 3 | 100% |
| 3 | Mancino, M. and Sanfelici, S (2008) Robustness of fourier estimator of integrated volatility in the presence of microstructure noise self | 0.811 | 4 | 2 | 100% |
| 4 | Mancino, M., Mariotti, T., and Toscano, G (2022) Asymptotic normality for the spot volatility fourier estimator in the presence of microstructure noise contamination self | 0.811 | 4 | 2 | 100% |
| 5 | Malliavin, P (1995) Integration and probability | 0.737 | 3 | 2 | 100% |
| 6 | Mancino, M. and Sanfelici, S (2011) Estimating covariance via fourier method in the presence of asynchronous trading and microstructure noise self | 0.644 | 2 | 2 | 100% |
| 7 | Toscano, G., Livieri, G., Mancino, M., and Marmi, S (2024) Volatility of volatility estimation: central limit theorems for the fourier transform estimator and empirical study of the daily… self | 0.644 | 2 | 2 | 100% |
| 8 | Heston, S (1993) A closed-form solution for options with stochastic volatility with applications to bond and currency options | 0.511 | 2 | 2 | 50% |
| 9 | Curato, I (2019) Estimation of the stochastic leverage effect using the fourier transform method | 0.511 | 2 | 1 | 100% |
| 10 | Livieri, G., Mancino, M., and Marmi, S (2019) Asymptotic results for the fourier estimator of the integrated quarticity | 0.511 | 2 | 1 | 100% |
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