Critical value-based Asian option pricing model for uncertain financial markets

Asian option has become one of the most popular financial derivatives in the OTC (Over the -Counter) market due to its low risk and cost. The option pricing problem which regards the price of the underlying asset as a random variable has been extensively studied based on the sufficient historical data. It may be modeled as an uncertain variable when the historical data is lack. This paper investigates the Asian option pricing problem based on uncertainty theory, in which the price of the underlying asset follows the mean-reverting process involving an uncertain fractional differential equation. The pricing formulas of the Asian options are derived based on the expected value and optimistic value. Some numerical experiments are performed to illustrate the results. (C) 2019 Published by Elsevier B.V.