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Estimation of the stochastic leverage effect using the Fourier transform method

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  • Curato, Imma Valentina

Abstract

We define a non-parametric estimator of the integrated leverage effect as the integrated covariation between the logarithmic asset price and its volatility. In Curato and Sanfelici (2015), a consistent estimator of the leverage effect has been introduced through a pre-estimate of the Fourier coefficients of the volatility. This is a novel approach compared to the ones present in the literature which use a pre-estimate of the spot volatility path. In this paper, we show the asymptotic normality of the Fourier estimator for non-equidistant observations. Moreover, its finite sample properties are analyzed in a simulation study also in the presence of microstructure noise.

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  • Curato, Imma Valentina, 2019. "Estimation of the stochastic leverage effect using the Fourier transform method," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3207-3238.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:9:p:3207-3238
    DOI: 10.1016/j.spa.2018.09.001
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    Cited by:

    1. Todorov, Viktor, 2021. "Higher-order small time asymptotic expansion of Itô semimartingale characteristic function with application to estimation of leverage from options," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 671-705.
    2. Huiling Yuan & Yulei Sun & Lu Xu & Yong Zhou & Xiangyu Cui, 2022. "A new volatility model: GQARCH‐ItÔ model," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(3), pages 345-370, May.
    3. Allaj, Erindi & Sanfelici, Simona, 2023. "Early Warning Systems for identifying financial instability," International Journal of Forecasting, Elsevier, vol. 39(4), pages 1777-1803.
    4. Imma Valentina Curato & Simona Sanfelici, 2019. "Stochastic leverage effect in high-frequency data: a Fourier based analysis," Papers 1910.06660, arXiv.org, revised Mar 2021.
    5. Sanfelici, Simona & Toscano, Giacomo, 2024. "The Fourier–Malliavin Volatility (FMVol) MATLAB® library," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 226(C), pages 338-353.
    6. Yuan, Huiling & Zhou, Yong & Xu, Lu & Sun, Yulei & Cui, Xiangyu, 2020. "A New Volatility Model: GQARCH-Ito Model," SocArXiv hkzdr, Center for Open Science.
    7. Curato, Imma Valentina & Sanfelici, Simona, 2022. "Stochastic leverage effect in high-frequency data: a Fourier based analysis," Econometrics and Statistics, Elsevier, vol. 23(C), pages 53-82.

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