Fractional Liu process with application to finance

Authors:
Zhongfeng Qin;Xin Gao
Affiliations:
Department of Insurance and Risk Management, School of Economics and Management, Beihang University, Beijing 100191, China;School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2009

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Abstract

As a fuzzy counterpart of Brownian motion, Liu process has attracted more and more attention in the recent literature. In this paper, the concept of fractional Liu process is proposed as an extension of Liu process. Furthermore, we obtain the expressions of the membership functions, expected values and variances of arithmetic and geometric fractional Liu processes for each fixed time. As an application, geometric fractional Liu process is assumed to characterize the stock price, which formulates a new fuzzy stock model. Based on this proposed model, European option pricing formulas are gained and two numerical examples are given with different parameters.