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Nonparametric Stochastic Volatility

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Author Info
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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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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  1. Jacquier, Eric & Polson, Nicholas G. & Rossi, P.E.Peter E., 2004. "Bayesian analysis of stochastic volatility models with fat-tails and correlated errors," Journal of Econometrics, Elsevier, vol. 122(1), pages 185-212, September. [Downloadable!] (restricted)
  2. Bandi, Federico M. & Perron, Benoît, 2008. "Long-run risk-return trade-offs," Journal of Econometrics, Elsevier, vol. 143(2), pages 349-374, April. [Downloadable!] (restricted)
  3. Chernov, Mikhail & Ronald Gallant, A. & Ghysels, Eric & Tauchen, George, 2003. "Alternative models for stock price dynamics," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 225-257. [Downloadable!] (restricted)
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  4. Federico M. Bandi & Peter C. B. Phillips, 2003. "Fully Nonparametric Estimation of Scalar Diffusion Models," Econometrica, Econometric Society, vol. 71(1), pages 241-283, January. [Downloadable!] (restricted)
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  5. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, 06. [Downloadable!] (restricted)
  6. Bandi & Russell, 2008. "Microstructure Noise, Realized Variance, and Optimal Sampling," Review of Economic Studies, Blackwell Publishing, vol. 75(2), pages 339-369, 04. [Downloadable!] (restricted)
  7. Michael McAleer & Marcelo Cunha Medeiros, 2006. "Realized volatility: a review," Textos para discussão 531 Publication status: F, Department of Economics PUC-Rio (Brazil). [Downloadable!]
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  8. Ren?, Roberto, 2008. "Nonparametric Estimation Of The Diffusion Coefficient Of Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 24(05), pages 1174-1206, October. [Downloadable!]
  9. Peter Reinhard Hansen & Asger Lunde, 2005. "A Realized Variance for the Whole Day Based on Intermittent High-Frequency Data," Journal of Financial Econometrics, Oxford University Press, vol. 3(4), pages 525-554. [Downloadable!] (restricted)
  10. Ole E. Barndorff-Nielsen & Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal Of The Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280. [Downloadable!] (restricted)
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  11. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March. [Downloadable!] (restricted)
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  12. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
  13. Ole E. Barndorff-Nielsen, 2004. "Power and Bipower Variation with Stochastic Volatility and Jumps," Journal of Financial Econometrics, Oxford University Press, vol. 2(1), pages 1-37. [Downloadable!] (restricted)
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  14. Pan, Jun, 2002. "The jump-risk premia implicit in options: evidence from an integrated time-series study," Journal of Financial Economics, Elsevier, vol. 63(1), pages 3-50, January. [Downloadable!] (restricted)
  15. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. " Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-49, December. [Downloadable!] (restricted)
  16. Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers ysm54, Yale School of Management. [Downloadable!]
  17. Harvey, Andrew C & Shephard, Neil, 1996. "Estimation of an Asymmetric Stochastic Volatility Model for Asset Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 429-34, October.
  18. Jones, Christopher S., 2003. "The dynamics of stochastic volatility: evidence from underlying and options markets," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 181-224. [Downloadable!] (restricted)
  19. Lin Peng & Turan G. Bali, 2006. "Is there a risk-return trade-off? Evidence from high-frequency data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(8), pages 1169-1198. [Downloadable!]
  20. van Zanten, Harry, 2000. "A multivariate central limit theorem for continuous local martingales," Statistics & Probability Letters, Elsevier, vol. 50(3), pages 229-235, November. [Downloadable!] (restricted)
  21. Yu, Jun, 2005. "On leverage in a stochastic volatility model," Journal of Econometrics, Elsevier, vol. 127(2), pages 165-178, August. [Downloadable!] (restricted)
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  22. Reno, Roberto, 2006. "Nonparametric estimation of stochastic volatility models," Economics Letters, Elsevier, vol. 90(3), pages 390-395, March. [Downloadable!] (restricted)
  23. Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers ysm65, Yale School of Management. [Downloadable!]
  24. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 371-89, October.
    Other versions:
  25. Bandi, Federico M. & Nguyen, Thong H., 2003. "On the functional estimation of jump-diffusion models," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 293-328. [Downloadable!] (restricted)
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