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Nonparametric Stochastic Volatility

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  • Bandi, Federico M.
  • Renò, Roberto

Abstract

We provide nonparametric methods for stochastic volatility modeling. Our methods allow for the joint evaluation of return and volatility dynamics with nonlinear drift and diffusion functions, nonlinear leverage effects, and jumps in returns and volatility with possibly state-dependent jump intensities, among other features. In the first stage, we identify spot volatility by virtue of jump-robust nonparametric estimates. Using observed prices and estimated spot volatilities, the second stage extracts the functions and parameters driving price and volatility dynamics from nonparametric estimates of the bivariate process’ infinitesimal moments. For these infinitesimal moment estimates, we report an asymptotic theory relying on joint in-fill and long-span arguments which yields consistency and weak convergence under mild assumptions.

Suggested Citation

  • Bandi, Federico M. & Renò, Roberto, 2018. "Nonparametric Stochastic Volatility," Econometric Theory, Cambridge University Press, vol. 34(6), pages 1207-1255, December.
    • Handle: RePEc:cup:etheor:v:34:y:2018:i:06:p:1207-1255_00
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    Cited by:

    1. Bandi, Federico M. & Renò, Roberto, 2022. "β in the tails," Journal of Econometrics, Elsevier, vol. 227(1), pages 134-150.
    2. M.E. Mancino & S. Scotti & G. Toscano, 2020. "Is the Variance Swap Rate Affine in the Spot Variance? Evidence from S&P500 Data," Applied Mathematical Finance, Taylor & Francis Journals, vol. 27(4), pages 288-316, July.
    3. Arthur T. Rego & Thiago R. dos Santos, 2018. "Non-Gaussian Stochastic Volatility Model with Jumps via Gibbs Sampler," Papers 1809.01501, arXiv.org, revised Oct 2018.
    4. Patrick Chang, 2020. "Fourier instantaneous estimators and the Epps effect," Papers 2007.03453, arXiv.org, revised Sep 2020.
    5. Bu, Ruijun & Kim, Jihyun & Wang, Bin, 2023. "Uniform and Lp convergences for nonparametric continuous time regressions with semiparametric applications," Journal of Econometrics, Elsevier, vol. 235(2), pages 1934-1954.

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