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Nonparametric Stochastic Volatility

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  • Federico M. Bandi
  • Roberto Reno

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 (i) a theory of spot variance estimation and (ii) functional 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, jumps in returns and volatility with possibly state-dependent jump intensities, as well as nonlinear risk-return trade-offs. Our identification approach and asymptotic 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.

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Bibliographic Info

Paper provided by Institute of Economic Research, Hitotsubashi University in its series Global COE Hi-Stat Discussion Paper Series with number gd08-035.

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Date of creation: Mar 2009
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Handle: RePEc:hst:ghsdps:gd08-035

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Keywords: Spot variance; stochastic volatility; jumps in returns; jumps in volatility; leverage effects; risk-return trade-offs; kernel methods; recurrence; market microstructure noise.;

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References

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Cited by:
  1. Valentina Corradi & Norman R. Swanson, 2011. "Predictive density construction and accuracy testing with multiple possibly misspecified diffusion models," Post-Print hal-00796745, HAL.
  2. Jun Yu, 2008. "A Semiparametric Stochastic Volatility Model," Working Papers CoFie-04-2008, Sim Kee Boon Institute for Financial Economics.
  3. Aleksandar Mijatovic & Paul Schneider, 2009. "Empirical Asset Pricing with Nonlinear Risk Premia," Working Papers wp09-03, Warwick Business School, Finance Group.
  4. Cecilia Mancini & Vanessa Mattiussi & Roberto Reno', 2012. "Spot Volatility Estimation Using Delta Sequences," Working Papers - Mathematical Economics 2012-10, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.

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