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N. Wiener, “The Average of an Analytical Functional,” Proceedings of the National Academy of Sciences, Vol. 7, No. 9, 1921, pp. 253-260. http://dx.doi.org/10.1073/pnas.7.9.253

has been cited by the following article:

• 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.