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Spot volatility estimation using the Laplace transform

Author

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  • Curato, Imma Valentina
  • Mancino, Maria Elvira
  • Recchioni, Maria Cristina

Abstract

A new non-parametric estimator of the instantaneous volatility is defined relying on the link between the Laplace transform of the price process and that of the volatility process for Brownian semimartingale models. The proposed estimation method is a global one, in the spirit of methods based on Fourier series decomposition, with a plus for improving the precision of the volatility estimates near the boundary of the time interval. Consistency and asymptotic normality of the proposed estimator are proved. A simulation study confirms the theoretical results and Monte Carlo evidence of the favorable performance of the proposed estimator in the presence of microstructure noise effects is presented.

Suggested Citation

  • Curato, Imma Valentina & Mancino, Maria Elvira & Recchioni, Maria Cristina, 2018. "Spot volatility estimation using the Laplace transform," Econometrics and Statistics, Elsevier, vol. 6(C), pages 22-43.
    • Handle: RePEc:eee:ecosta:v:6:y:2018:i:c:p:22-43
    DOI: 10.1016/j.ecosta.2016.07.002
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    Cited by:

    1. 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.
    2. Madan, Dilip B. & Wang, King, 2018. "Strike asymptotics for Laplace implied volatilities," Finance Research Letters, Elsevier, vol. 25(C), pages 183-189.
    3. Maria Elvira Mancino & Maria Cristina Recchioni, 2015. "Fourier Spot Volatility Estimator: Asymptotic Normality and Efficiency with Liquid and Illiquid High-Frequency Data," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-33, September.

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    More about this item

    Keywords

    Laplace transform; Convolution; Spot volatility; Non-parametric estimation; High frequency data; Microstructure noise;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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