Adaptive isogeometric analysis with truncated hierarchical B-splines for nonlinear option pricing problems
Year: 2026
Type: article
Abstract: This work develops an adaptive isogeometric analysis (IGA) framework based on truncated hierarchical B-spline (THB-spline) for pricing nonlinear multi-asset European options. The framework effectively handles both Black-Scholes and Heston stochastic volatility models by employing Newton linearization method for the nonlinear PDEs and the Crank-Nicolson scheme for temporal discretization. The discrete governing equation is derived via the Galerkin weighted residual method. A least-squares technique is utilized to accurately enforce initial and boundary conditions, while a smoothing-based error estimator drives the adaptive process. The precision and computational efficiency of the proposed framework are validated through comprehensive numerical analysis, establishing it as a robust tool for pricing multi-asset options with nonlinear features.
Author: Ruo-Xi Yu
Institution: Jiangsu Normal University
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,170
OpenAlex ID: W7128923926