Pricing of shout option in uncertain financial market

Abstract

The shout option allows the investors to make "shouts" to the seller throughout the option’s duration. The investors’ payoff is higher between the intrinsic value at shout time and the intrinsic value at the maturity time. Previous shout option pricing is in the framework of probability theory. However, some unexpected events in real life can make the frequency deviate from the estimated distribution function, in which case we should use the uncertainty theory. This study investigates shout option pricing problems under uncertainty theory. It also derives pricing formulas for shout-call and shout-put options. Additionally, we design a numerical algorithm to compute the price of the shout options. Finally, this study applies the concept of the shout option to Microsoft’s stock data and examines the relationship between the option price and crucial parameters.