Exponential integral method for European option pricing

Xun Lu; Wei Shi; Changhao Yang; Fan Yang; Xun Lu; Wei Shi; Changhao Yang; Fan Yang

doi:10.3934/math.2025580

AIMS Mathematics

2025, Volume 10, Issue 6: 12900-12918. doi: 10.3934/math.2025580

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Research article

Exponential integral method for European option pricing

Department of Mathematics and Science, Nanjing Tech University, Nanjing, 211816, Jiangsu, China

Received: 09 February 2025 Revised: 22 April 2025 Accepted: 07 May 2025 Published: 04 June 2025
MSC : 65L05, 65L07, 65L10, 65J15, 91G60

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.
- option pricing,
- European options,
- exponential integral method,
- finite difference
Citation: Xun Lu, Wei Shi, Changhao Yang, Fan Yang. Exponential integral method for European option pricing[J]. AIMS Mathematics, 2025, 10(6): 12900-12918. doi: 10.3934/math.2025580

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Abstract

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.

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