Abstract:
In this paper we propose a Bayesian method for estimating hyperbolic diffusion models. The approach is based on the Markov Chain
Monte Carlo (MCMC) method after discretization via the Milstein scheme. Our simulation study shows that the hyperbolic diffusion
exhibits many of the stylized facts about asset returns documented in the financial econometrics literature, such as a slowly declining
autocorrelation function of absolute returns. We demonstrate that the MCMC method provides a useful tool to analyze hyperbolic
diffusions. In particular, quantities of posterior distributions obtained from MCMC outputs can be used for statistical inferences.
