Fractional Black Scholes Option Pricing with Stochastic Arbitrage Return

Abstract

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.