Modeling Stock Market Dynamics with Stochastic Differential Equation Driven by Fractional Brownian Motion: A Bayesian Method

N. Harnpornchai, K. Autchariyapanitkul

Abstract

A Bayesian method is proposed for the parameter identification ofa stock market dynamics which is modeled by a Stochastic Differential Equation(SDE) driven by fractional Brownian motion (fBm).  The formulation for theidentification is based on the Wick-product solution of the SDE driven by an fBm. The determination of the solution is carried out using an independence MetropolisHastings algorithm. The historical record of SET index is employed for the purposeof method demonstration. For the SET index example, the estimate of the Hurstexponent is approximately 0.5. Consequently, the market is considered efficient.