Post by Sapphire Capital on Aug 19, 2008 23:53:21 GMT 4
Nonparametric Stochastic Volatility
Federico M. Bandi
University of Chicago - Graduate School of Business
Roberto Renò
University of Siena - Department of Economics
July 11, 2008
Abstract:
Using recent advances in the nonparametric estimation of continuous-time processes under mild statistical assumptions as well as recent developments on nonparametric volatility estimation by virtue of market microstructure noise-contaminated high-frequency asset price data, we provide a theory of spot variance estimation and functional methods for stochastic volatility modelling. Our methods allow for the joint evaluation of return and volatility dynamics with nonlinear drift and diffusion functions, leverage effects, jumps in returns and volatility with possibly state-dependent jump intensities, as well as risk-return trade-offs. Our identification approach and symptotic results apply under weak recurrence assumptions and, hence, accommodate the persistence properties of variance in finite samples. Functional estimation of a generalized (i.e., nonlinear) version of the square-root stochastic variance model with jumps in both volatility and returns for the S&P500 index suggests the need for richer variance dynamics than in existing work. We find a linear specification for the variance's diffusive variance to be misspecified (and inferior to a more flexible CEV specification) even when allowing for jumps in the variance dynamics.
papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1158438_code327190.pdf?abstractid=1158438&mirid=3
Federico M. Bandi
University of Chicago - Graduate School of Business
Roberto Renò
University of Siena - Department of Economics
July 11, 2008
Abstract:
Using recent advances in the nonparametric estimation of continuous-time processes under mild statistical assumptions as well as recent developments on nonparametric volatility estimation by virtue of market microstructure noise-contaminated high-frequency asset price data, we provide a theory of spot variance estimation and functional methods for stochastic volatility modelling. Our methods allow for the joint evaluation of return and volatility dynamics with nonlinear drift and diffusion functions, leverage effects, jumps in returns and volatility with possibly state-dependent jump intensities, as well as risk-return trade-offs. Our identification approach and symptotic results apply under weak recurrence assumptions and, hence, accommodate the persistence properties of variance in finite samples. Functional estimation of a generalized (i.e., nonlinear) version of the square-root stochastic variance model with jumps in both volatility and returns for the S&P500 index suggests the need for richer variance dynamics than in existing work. We find a linear specification for the variance's diffusive variance to be misspecified (and inferior to a more flexible CEV specification) even when allowing for jumps in the variance dynamics.
papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1158438_code327190.pdf?abstractid=1158438&mirid=3