Modeling stock market dynamics with stochastic differential equation driven by fractional brownian motion: A Bayesian method

Abstract

© 2016 by the Mathematical Association of Thailand. All rights reserved. A Bayesian method is proposed for the parameter identification of a stock market dynamics which is modeled by a Stochastic Differential Equation (SDE) driven by fractional Brownian motion (fBm). The formulation for the identification 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 Metropolis Hastings algorithm. The historical record of SET index is employed for the purpose of method demonstration. For the SET index example, the estimate of the Hurst exponent is approximately 0.5. Consequently, the market is considered efficient.