Nonparametric Stochastic Volatility

Abstract:     
We provide nonparametric methods for stochastic volatility modelling. 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. 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. We present a complete asymptotic theory under recurrence, thereby accommodating the persistence properties of volatility in finite samples.

Number of Pages in PDF File: 44

Keywords: Spot variance, stochastic volatility, jump, microstructure

JEL Classification: C13, C14, C51, G1

working papers series