Evaluation of Geometric Asian Power Options under Fractional Brownian Motion

Zhijuan Mao, Zhian Liang

Department of Applied Mathematics, Shanghai University of Finance and Economics, Shanghai, China.
School of Finance, Shanghai University of Finance and Economics, Shanghai, China.

DOI: 10.4236/jmf.2014.41001                

Abstract

Modern option pricing techniques are often considered among the most mathematical complex of all applied areas of financial mathematics. In particular, the fractional Brownian motion is proper to model the stock dynamics for its long-range dependence. In this paper, we evaluate the price of geometric Asian options under fractional Brownian motion framework. Furthermore, the options are generalized to those with the added feature whose payoff is a power function. Based on the equivalent martingale theory, a closed form solution has been derived under the risk neutral probability.

Keywords

Fractional Brownian Motion; Geometric Asian Options; Closed-Form Solution; Risk-Free Rate

Conflicts of Interest

The authors declare no conflicts of interest.

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