The option pricing problem based on the uncertain fractional volatility stock model

Abstract

Uncertain fractional differential equations fit more with the actual financial market since they have the non-locality features to mirror the memory and hereditary characteristics of the underlying asset price. In this paper, we investigate the option price in the asset price and volatility following the uncertain fractional differential equations in the sense of Caputo. Firstly, we propose the stock model with an uncertain fractional volatility and present the \(\alpha \)-path of the uncertain fractional volatility model. Secondly, the pricing formulas of European and American options are obtained for the proposed model. Lastly, numerical experiments on market data are presented. Numerical calculations and data examples show the accuracy and efficiency of the proposed model.