2014 |
Rombouts, Jeroen V. K.; Stentoft, Lars Bayesian Option Pricing Using Mixed Normal Heteroskedasticity Models Journal Article In: Computational Statistics & Data Analysis, vol. Volume 76, pp. 588–605, 2014. Abstract | Links | BibTeX | Tags: Bayesian @article{JR-Journal5q,Option pricing using mixed normal heteroscedasticity models is considered. It is explained how to perform inference and price options in a Bayesian framework. The approach allows to easily compute risk neutral predictive price densities which take into account parameter uncertainty. In an application to the S&P 500 index, classical and Bayesian inference is performed on the mixture model using the available return data. Comparing the ML estimates and posterior moments small differences are found. When pricing a rich sample of options on the index, both methods yield similar pricing errors measured in dollar and implied standard deviation losses, and it turns out that the impact of parameter uncertainty is minor. Therefore, when it comes to option pricing where large amounts of data are available, the choice of the inference method is unimportant. The results are robust to different specifications of the variance dynamics but show however that there might be scope for using Bayesian methods when considerably less data is available for inference. |
2007 |
Bauwens, Luc; Rombouts, Jeroen V. K. Bayesian Inference for the Mixed Conditional Heteroskedasticity Model Journal Article In: The Econometrics Journal , vol. Volume 10, Issue 2, pp. Pages 408–425, 2007. Abstract | Links | BibTeX | Tags: Bayesian @article{JR-Journal5c,We estimate by Bayesian inference the mixed conditional heteroskedasticity model of Haas et al. (2004a Journal of Financial Econometrics 2, 211–50). We construct a Gibbs sampler algorithm to compute posterior and predictive densities. The number of mixture components is selected by the marginal likelihood criterion. We apply the model to the SP500 daily returns. |
Bauwens, Luc; Rombouts, Jeroen V. K. Bayesian Clustering of Many Garch Models Journal Article In: Econometric Reviews , vol. Volume 26, Issue 2-4, 2007. Abstract | Links | BibTeX | Tags: Bayesian @article{JR-Journal5,We consider the estimation of a large number of GARCH models, of the order of several hundreds. Our interest lies in the identification of common structures in the volatility dynamics of the univariate time series. To do so, we classify the series in an unknown number of clusters. Within a cluster, the series share the same model and the same parameters. Each cluster contains therefore similar series. We do not know a priori which series belongs to which cluster. The model is a finite mixture of distributions, where the component weights are unknown parameters and each component distribution has its own conditional mean and variance. Inference is done by the Bayesian approach, using data augmentation techniques. Simulations and an illustration using data on U.S. stocks are provided. |