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Evaluation of Geometric Asian Power Options under Fractional Brownian Motion
School of Finance, Shanghai University of Finance and Economics, Shanghai, China
Department of Applied Mathematics, Shanghai University of Finance and Economics, Shanghai, China
- 1 School of Finance, Shanghai University of Finance and Economics, Shanghai, China
- 2 Department of Applied Mathematics, Shanghai University of Finance and Economics, Shanghai, China
Journal of Mathematical Finance·Volume 04 (2013)·Pages 1–9·Published 20 December 2013·DOI10.4236/jmf.2014.41001
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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 dy namics 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.
KeywordsFractional Brownian MotionGeometric Asian OptionsClosed-Form SolutionRisk-Free Rate
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