Nonparametric Stochastic Volatility

43 Pages Posted: 12 Jul 2008 Last revised: 19 Jul 2018

See all articles by Federico M. Bandi

Federico M. Bandi

Johns Hopkins University - Carey Business School

Roberto Renò

University of Verona - Department of Economics

Date Written: May 30, 2018


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.

Keywords: Spot variance, stochastic volatility, jump, microstructure

JEL Classification: C13, C14, C51, G1

Suggested Citation

Bandi, Federico Maria and Renò, Roberto, Nonparametric Stochastic Volatility (May 30, 2018). Available at SSRN: or

Federico Maria Bandi

Johns Hopkins University - Carey Business School ( email )

100 International Drive
Baltimore, MD 21202
United States

Roberto Renò (Contact Author)

University of Verona - Department of Economics ( email )

Via dell'Artigliere, 8
37129 Verona

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