Published online by Cambridge University Press: 03 July 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.
We thank the participants at the SoFiE Inaugural conference (New York, June 4–6, 2008), the Festschrift in honor of Peter C.B. Phillips (Singapore, July 14–15, 2008), the Far Eastern and South Asian Meetings of the Econometric Society (Singapore, July 16–18, 2008), the Hitotsubashi University’s International Conference on High Frequency Data Analysis in Financial Markets (Tokyo, October 25–26, 2008), the LSE Conference on Recent Advances in High-Frequency Financial Econometrics (London, November 15, 2008), and the North American Winter Meetings of the Econometric Society (San Francisco, January 3–5, 2009) for discussions. We are grateful to three anonymous referees, the Editors Oliver Linton and Peter C.B. Phillips, Valentina Corradi, Fulvio Corsi, Cecilia Mancini, and Eric Renault for useful comments and suggestions. The usual disclaimers apply.