968 Continuous-Time Stochastic Volatility Models
of realized volatility takes into account market microstructure noise using a technique
proposed by Zhang, Mykland and Aït-Sahalia (2005).- At-the-money implied volatility is sometimes used as a proxy for instantaneous volatility.
However, the two are only identical when volatility is uncorrelated with the asset price,
the market price of volatility risk is zero, and the time to maturity of the option is short.
References
Aït-Sahalia, Y. (1999) Transition densities for interest rate and other nonlinear diffusions.
Journal of Finance 54 , 1361–95.
Aït-Sahalia, Y. (2002) Transition densities for interest rate and other nonlinear diffusions:
a closed-form approximation approach.Econometrica 70 , 223–62.
Aït-Sahalia, Y. (2007) Estimating continuous-time models using discretely sampled data.
In R. Blundell, P. Torsten and W.K. Newey (eds.),Advances in Economics and Econometrics,
Theory and Applications, Ninth World Congress. Cambridge: Cambridge University Press.
Aït-Sahalia, Y. (2008) Closed-form likelihood expansions for multivariate diffusions.Annals
of Statistics 36 , 906–37.
Aït-Sahalia, Y. and R. Kimmel (2007) Maximum likelihood estimation of stochastic
volatility models.Journal of Financial Economics 83 , 413–52.
Aït-Sahalia, Y., P.A. Mykland and L. Zhang (2005) How often to sample a continuous-time
process in the presence of market microstructure noise.Review of Financial Studies 18 ,
351–416.
Alizadeh, S., M.W. Brandt and F.X. Diebold (2002) Range-based estimation of stochastic
volatility models.Journal of Finance 57 , 1047–91.
Andersen, T.G., L. Benzoni and J. Lund (2002) An empirical investigation of continuous-
time equity return models.Journal of Finance 57 , 1239–84.
Andersen, T.G., T. Bollerslev, F.X. Diebold and P. Labys (2001) The distribution of exchange
rate volatility.Journal of the American Statistical Association 96 , 42–55.
Andersen, T.G., H. Chung and B.E. Sørensen (1999) Efficient method of moments estima-
tion of a stochastic volatility model: a Monte Carlo study.Journal of Econometrics 91 ,
61–87.
Andersen, T.G. and J. Lund (1997) Estimating continuous-time stochastic volatility models
of the short-term interest rate.Journal of Econometrics 77 , 343–77.
Baillie, R.T. (2006) Modelling volatility. In T.C. Mills and K.D. Patterson (eds.),Pal-
grave Handbook of Econometrics. Volume 1: Econometric Theory, pp. 737–64. Basingstoke:
Palgrave Macmillan.
Bakshi, G., C. Cao and Z. Chen (1997) Empirical performance of alternative option pricing
models.Journal of Finance 52 , 2003–49.
Bakshi, G., N. Ju and H. Ou-Yang (2006) Estimation of continuous-time models with an
application to equity volatility dynamics.Journal of Financial Economics 82 , 227–49.
Bansal, R., A.R. Gallant, R. Hussey and G.E. Tauchen (1993) Computational aspects of
nonparametric simulation estimation. In D.A. Belsley (ed.),Computational Techniques for
Econometrics and Economic Analysis, pp. 3–22. Boston: Kluwer Academic Publishers.
Bansal, R., A.R. Gallant, R. Hussey and G.E. Tauchen (1995) Nonparametric estimation of
structural models for high-frequency currency market data.Journal of Econometrics 66 ,
251–87.
Barndorff-Nielsen, O.E. and N. Shephard (2002) Econometric analysis of realised volatility
and its use in estimating stochastic volatility models.Journal of the Royal Statistical Society,
Series B 64 , 253–80.
Barndorff-Nielsen, O.E. and N. Shephard (2006) Econometrics of testing for jumps in
financial economics using bipower variation.Journal of Financial Econometrics 4 , 1–30.