Maximum likelihood estimators from discrete data modeled by mixed fractional Brownian motion with application to the Nordic stock markets

Abstract

Mixed fractional Brownian motion is a linear combination of Brownian motion and independent Fractional Brownian motion that is extensively used for option pricing. The consideration of the mixed process is able to capture the long–range dependence property that financial time series exhibit. This paper examines the problem of deriving simultaneously the estimators of all the unknown parameters for a model driven by the mixed fractional Brownian motion using the maximum likelihood estimation method. The consistency and asymptotic normality properties of these estimators are provided. The performance of the methodology is tested on simulated data sets, and the outcomes illustrate that the maximum likelihood technique is efficient and reliable. An empirical application of the proposed method is also made to the real financial data from four Nordic stock market indices.