Kleppe, Tore Selland and Skaug, Hans J. (2008): Simulated maximum likelihood for general stochastic volatility models: a change of variable approach.
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Maximum likelihood has proved to be a valuable tool for fitting the log-normal stochastic volatility model to financial returns time series. Using a sequential change of variable framework, we are able to cast more general stochastic volatility models into a form appropriate for importance samplers based on the Laplace approximation. We apply the methodology to two example models, showing that efficient importance samplers can be constructed even for highly non-Gaussian latent processes such as square-root diffusions.
|Item Type:||MPRA Paper|
|Original Title:||Simulated maximum likelihood for general stochastic volatility models: a change of variable approach|
|Keywords:||Change of Variable; Heston Model; Laplace Importance Sampler; Simulated Maximum Likelihood; Stochastic Volatility|
|Subjects:||C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General
C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes
|Depositing User:||Tore Selland Kleppe|
|Date Deposited:||09. Dec 2008 00:35|
|Last Modified:||16. Feb 2013 05:05|
Aït-Sahalia, Y. and R. Kimmel (2007). Maximum likelihood estimation of stochastic volatility models. Journal of Financial Economics 134, 507–551.
Barndorff-Nielsen, O. E. and D. R. Cox (1989). Asymptotic techniques for use in statistics. Chapman & Hall.
Barndorff-Nielsen, O. E. and N. Shephard (2001). Non-gaussian ornsteinuhlenbeck-based models and some of their uses in financial economics. Journal of the Royal Statistical Society. Series B (Statistical Methodology) 63, 167–241.
Butler, R. (2007). Saddlepoint Approximations with Applications. Cambridge University Press.
Carlin, B. P. and T. A. Louis (1996). Bayes and Empirical Bayes Methods for Data Analysis. Chapman & Hall.
Cox, J. C., J. E. Ingersoll, and S. A. Ross (1985). A theory of the term structure of interest rates. Econometrica 53(2), 385–407.
Danielsson, J. (1994). Stochastic volatility in asset prices: Estimation with simulated maximum likelihood. Journal of Econometrics 64, 375–400.
Danielsson, J. and J. F. Richard (1993). Accelerated gaussian importance sampler with application to dynamic latent variable models. Journal of Applied Econometrics 8, 153–173.
Durbin, J. and S. Koopman (2001). Time Series Analysis by State Space Methods. Oxford University Press.
Durham, G. B. (2006). Monte carlo methods for estimating, smoothing, and filtering one and two-factor stochastic volatility models. Journal of Econometrics 133, 273–305.
Durham, G. B. (2007). Sv mixture models with application to s&p 500 index returns. Journal of Financial Economics 85, 822–856.
Griewank, A. (2000). Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation. SIAM, Philadelphia.
Harvey, A., E. Ruiz, and N. Shephard (1994). Multivariate stochastic variance models. The Review of Economic Studies 61, 247–264.
Hascoët, L. and V. Pascual (2004). Tapenade 2.1 user’s guide. Technical Report 0300, INRIA.
Heston, S. L. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. The Review of Financial Studies 6, 327–343.
Jones, C. S. (2003). The dynamics of stochastic volatility: evidence from underlying and options markets. Journal of Econometrics 116(1-2), 181–224.
Kuk, A. Y. C. (1999). Laplace importance sampling for generalized linear mixed models. Journal of Statistical Computation and Simulation 63, 143–158.
Liesenfeld, R. and J. Richard (2003). Univariate and multivariate stochastic volatility models: Estimation and diagnostics. Journal of Empirical Finance 10, 505–531.
Liesenfeld, R. and J. Richard (2006). Classical and bayesian analysis of univariate and multivariate stochastic volatility models. Econometric Reviews 25, 335–360.
Mackay, D. (1998). Choice of basis for Laplace approximation. Machine learning 33, 77–86.
Nelson, D. B. (1990). Arch models as diffusion approximations. Journal of Econometrics 45(1-2), 7–38.
Nielsen, B. and N. Shephard (2003). Likelihood analysis of a first-order autoregressive model with exponential innovations. Journal of Time Series Analysis 24, 337–344.
Nocedal, J. and S. J. Wright (1999). Numerical Optimization. Springer.
Omori, Y., S. Chib, N. Shephard, and J. Nakajima (2007). Stochastic volatility with leverage: Fast and efficient likelihood inference. Journal of Econometrics 127 (2), 425–449.
Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery (1992). Numerical recipes in fortran (second ed.). Cambridge university press.
Richard, J.-F. and W. Zhang (2007). Efficient high-dimensional importance sampling. Journal of Econometrics 127 (2), 1385–1411.
Sandmann, G. and S. Koopman (1998). Maximum likelihood estimation of stochastic volatility models. Journal of Econometrics 63, 289–306.
Shepard, N. and M. K. Pitt (1997). Likelihood analysis of non-gaussian measurement time series. Biometrika 84, 653–667.
Skaug, H. and D. Fournier (2006). Automatic approximation of the marginal likelihood in non-gaussian hierarchical models. Computational Statistics & Data Analysis 56, 699–709.
Skaug, H. J. (2002). Automatic differentiation to facilitate maximum likelihood estimation innonlinear random effects models. Journal of Computational and Graphical Statistics 11, 458–470.
Sydsæter, K., A. Strøm, and P. Berck (1999). Economists’ Mathmatical Manual (3 ed.). Springer.
Taylor, S. J. (1982). Financial returns modelled by the product of two stochastic processes - a study of the daily sugar prices 1961-75. In O. D. Anderson (Ed.), Time Series Analysis: Theory and Practice, Number 1. North-Holland, Amsterdam.