Parameter identification for the discretely observed geometric fractional Brownian motion

AbstractThis paper deals with the problem of estimating all the unknown parameters of geometric fractional Brownian processes from discrete observations. The estimation procedure is built upon the marriage of the quadratic variation and the maximum likelihood approach. The asymptotic properties of the estimators are provided. Moveover, we compare our derived method with the approach proposed by Misiran et al. [Fractional Black-Scholes models: complete MLE with application to fractional option pricing. In International conference on optimization and control; Guiyang, China; 2010. p. 573–586.], namely the complete maximum likelihood estimation. Simulation studies confirm theoretical findings and illustrate that our methodology is efficient and reliable. To show how to apply our approach in realistic contexts, an empirical study of Chinese financial market is also presented.Keywords: geometric fractional Brownian motionmaximum likelihood estimationquadratic variationasymptotic behaviourdiscrete observationsAMS Subject Classifications: 62M0960G1860H0760H10 AcknowledgementsThis research was supported by the National Natural Science Foundation of China (Nos. 71101056; 71171086), the major program of National Social Science Foundation of China (11&ZD156), Natural Science Foundation of Guangdong Province, China (No. S2011040005723), Distinguished Young Talents in Higher Education of Guangdong, China (No. WYM11010), the Fundamental Research Funds for the Central Universities, SCUT (No. 2012ZM0029). Humanity and Social Science Youth foundation of Ministry of Education of China (No. 13YJC630227), Zhejiang Provincial Natural Science Foundation of China (No. LQ13G010001) and the Fundamental Research Funds for the Central Universities.