Simulation Monte Carlo methods in extended stochastic volatility models

A new technique for nonlinear state and parameter estimation of discrete time stochastic volatility models is developed. Algorithms of Gibbs sampler and simulation filters are used to construct a simulation tool that reflects both inherent model variability and parameter uncertainty. The proposed chain converges to equilibrium enabling the estimation of unobserved volatilities and unknown model parameter distributions. The estimation algorithm is illustrated using numerical examples. Copyright © 2002 John Wiley & Sons, Ltd.

[1]  Bent E. Sørensen,et al.  GMM Estimation of a Stochastic Volatility Model: A Monte Carlo Study , 1996 .

[2]  Petros G. Voulgaris,et al.  On optimal ℓ∞ to ℓ∞ filtering , 1995, Autom..

[3]  M. Tanner.  Tools for statistical inference: methods for the exploration of posterior distributions and likeliho , 1994 .

[4]  B. Anderson,et al.  Optimal Filtering , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[5]  Toshiaki Watanabe,et al.  A Non-linear Filtering Approach to Stochastic Volatility Models with an Application to Daily Stock Returns , 1999 .

[6]  E. Ruiz.  Quasi-maximum likelihood estimation of stochastic volatility models , 1994 .

[7]  M. Simandl,et al.  CRAMÉR-RAO BOUND FOR STOCHASTIC VOLATILITY MODEL , 2002 .

[8]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[9]  Harold W. Sorenson,et al.  Recursive Bayesian estimation using piece-wise constant approximations , 1988, Autom..

[10]  Petr Tichavský,et al.  Filtering, predictive, and smoothing Cramér-Rao bounds for discrete-time nonlinear dynamic systems , 2001, Autom..

[11]  Jun S. Liu,et al.  Sequential Monte Carlo methods for dynamic systems , 1997 .

[12]  M. Simandl,et al.  Gibbs sampler to stochastic volatility models , 2001, 2001 European Control Conference (ECC).

[13]  Peter E. Rossi,et al.  Bayesian Analysis of Stochastic Volatility Models , 1994 .

[14]  Harold W. Sorenson,et al.  On the development of practical nonlinear filters , 1974, Inf. Sci..

[15]  M. A. Tanner,et al.  Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions, 3rd Edition , 1998 .

[16]  Jón Dańıelsson.  Stochastic volatility in asset prices estimation with simulated maximum likelihood , 1994 .

[17]  Miroslav Šimandl.  State Estimation for Non-Gaussian Models , 1996 .

[18]  Jussi Tolvi,et al.  Modeling Financial Time Series with S‐Plus , 2003 .