Vulnerable European Call Option Pricing Based on Uncertain Fractional Differential Equation

This paper presents two new versions of uncertain market models for valuing vulnerable European call option. The dynamics of underlying asset, counterparty asset, and corporate liability are formulated on the basis of uncertain differential equations and uncertain fractional differential equations of Caputo type, respectively, and the solution to an uncertain fractional differential equation of Caputo type is presented by employing the Mittag-Leffler function and α-path. Then, the pricing formulas of vulnerable European call option based on the proposed models are investigated as well as some algorithms. Some numerical experiments are performed to verify the effectiveness of the results.