Exponential integral method for European option pricing - Lu, Xun; Shi, Wei; Yang, Changhao; Yang, Fan (AIMS mathematics, 2025)
Since the official launch of domestic exchange-traded options in 2015, options have gradually become an important component of the financial market. With the diversification of option types and the expansion of market size, option pricing research has received widespread attention. In this paper, we propose a finite difference method based on exponential integrals for the pricing of European call options, based on the Black-Scholes differential equation. Through numerical analysis, this method discretizes only the price region and uses the exponential Euler method to solve the nonhomogeneous system of linear differential equations in the time direction. Numerical experiments have verified the effectiveness of this method, showing that it can stably solve option pricing problems, especially when the price is close to the exercise price, demonstrating superior numerical performance.