TITLE:
Evaluation of Geometric Asian Power Options under Fractional Brownian Motion
AUTHORS:
Zhijuan Mao, Zhian Liang
KEYWORDS:
Fractional Brownian Motion; Geometric Asian Options; Closed-Form Solution; Risk-Free Rate
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.4 No.1,
December
25,
2013
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.