Journal of Mathematical Finance, 2014, 4, 95-103 Published Online February 2014 (http://www.scirp.org/journal/jmf ) http://dx.doi.org/10.4236/jmf.2014.42009 Bayesian Estimation of Non-Gaussian Stochastic Volatility Models Asma Graja Elabed, Afif Masmoudi Sfax University, Sfax, Tunisia Email: asmagraja2002@yahoo.fr Received October 7, 2013; revised November 18, 2013; accepted December 9, 2013 Copyright © 2014 Asma Graja Elabed, Afif Masmoudi. This is an open access article distributed under the Creative Commons At- tribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is prop- erly cited. In accordance of the Creative Commons Attribution License all Copyrights © 2014 are reserved for SCIRP and the owner of the intellectual property Asma Graja Elabed, Afif Masmoudi. All Copyright © 2014 are guarded by law and by SCIRP as a guar- dian. ABSTRACT In this paper, a general Non-Gaussian Stochastic Volatility model is proposed instead of the usual Gaussian model largely studied. We consider a new specification of SV model where the innovations of the return process have centered non-Gaussian error distribution rather than the standard Gaussian distribution usually employed. The model describes the behaviour of random time fluctuations in stock prices observed in the financial markets. It offers a response to better model the heavy tails and the abrupt changes observed in financial time series. We consider the Laplace density as a special case of non-Gaussian SV models to be applied to our data base. Markov Chain Monte Carlo technique, based on the bayesian analysis, has been employed to estimate the model’s para- meters. KEYWORDS Non-Gaussian Distribution; Stochastic Volatility; Laplace Density; Fat Tails; Kullback Leiber Divengence; Bayesian Analysis; MCMC Algorithm 1. Introduction The Stochastic Volatility models have been widely used to model a changing variance of time series Financial data [1,2]. These models usually assume Gaussian distribution for asset returns conditional on the latent volatility. However, it has been pointed out in many empirical studies that daily asset returns have heavier tails than those of normal distribution. To account for heavy tails observed in returns series, [3] proposes a SV model with student-t-errors. This density, although considered as the most popular basic model to account for heavier tailed returns, has been found insufficient to express the tail fatness of returns. [4] fitted a student-t-distribution and a Generalized Error Distribution (GED) as well as a normal distribution to the error distribution in the SV model by using the simulated maximum likelihood method developed by [5,6]. [7] considered a mixture of normal distribution as the error distribution in the SV model. He used a bayesian method via MCMC technique to estimate the model’s parameters. According to Bayes factors, he found that the t-distribution fits the Tokyo Index Return better than the normal, the GED and the normal mixture. However the mixture of normal distributions gives a better fit to the Yen/Dollar exchange rate than other models. This survey of literature proves that we can’t affirm absolutely that one distribution is better than another one. The selection of a density should be based on other parameters. In our work, we consider a general model of non- Gaussian centered error distribution. We prove that the efficiency of a specification of SV model depends on the dispersion of the data base. In fact, we find that when the data base is very dispersed, the Gaussian specification behaves better than the non-Gaussian one. On the contrary, if the data base presents a little dispersion measure, the non-Gaussian centered error specification will behave better than the Gaussian one. For this reason, we propose a general SV model where the diffusion of the stock return follows a non-Gaussian distribution. OPEN ACCESS JMF