eng Science and Education Publishing International Journal of Partial Differential Equations and Applications 2376-9556 2016-08-18 4 2 20 24 10.12691/ijpdea-4-2-1 IJPDEA2016421 article Bright O. Osu megaobrai@hotmail.com 1 Chukwunezu A. Ifeoma 2 Department of Mathematics, Michael Okpara University of Agriculture, Umudike Department of Mathematics/Statistics, Federal Polytechnic, Nekede, Owerri Option price and random arbitrage returns change on different time scales allow the development of an asymptotic pricing theory involving the options rather than exact prices. The role that random arbitrage opportunities play in pricing financial derivatives can be determined. In this paper, we construct Green's functions for terminal boundary value problems of the fractional Black-Scholes equation. We follow further an approach suggested in literature and focus on the pricing bands for options that account for random arbitrage opportunities and got similar result for the fractional Black- Scholes option pricing. http://pubs.sciepub.com/ijpdea/4/2/1/ijpdea-4-2-1.pdf arbitrage returns option pricing green function FBS equation