New IMEX Scheme Shows Second-Order Convergence for Option Pricing Equations

Researchers have proposed and analyzed an implicit-explicit (IMEX) difference scheme for solving a two-dimensional variable-coefficient partial integro-differential equation (PIDE) that arises in option pricing. The work, published in Advances in Continuous and Discrete Models, is authored by Leixiao Huang, Shuang Zhao and Zhengguang Shi, and appeared as an open access research article on 4 September 2026.

The equation under study comes from option pricing under a stochastic intensity jump model driven by mixed fractional Brownian motion, a setting that combines jump dynamics with fractional stochastic behavior. Because the pricing problem involves a two-dimensional main PIDE together with an associated boundary condition governed by a one-dimensional PIDE, the authors first developed an IMEX scheme capable of solving both the main equation and its boundary equation.

A central contribution of the paper is a rigorous convergence analysis. The authors established second-order convergence rates for the scheme: for the boundary PIDE, the rate was proven in the discrete H1-norm, while for the main two-dimensional PIDE it was proven in the discrete L2-norm. These theoretical guarantees indicate how quickly the numerical approximation approaches the true solution as the computational grid is refined.

To complement the analysis, the researchers conducted numerical experiments designed to validate the theoretical convergence results.

The article is classified as Research and is available under open access, with the published record noting full access to the article.

Subject of Research: Convergence analysis of an implicit-explicit difference scheme for a two-dimensional PIDE in option pricing under a stochastic intensity jump model with mixed fractional Brownian motion

Article Title: Convergence analysis of an IMEX scheme for option pricing under stochastic intensity jump model with mixed fractional Brownian motion

Article References: Huang, L., Zhao, S., & Shi, Z. (2026). Convergence analysis of an IMEX scheme for option pricing under stochastic intensity jump model with mixed fractional Brownian motion. Advances in Continuous and Discrete Models. https://doi.org/10.1186/s13662-026-04125-9

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DOI: 10.1186/s13662-026-04125-9

Keywords: IMEX scheme, option pricing, partial integro-differential equation, mixed fractional Brownian motion, stochastic intensity, jump model, convergence analysis, numerical methods, computational finance, second-order convergence, Convergence, analysis