Adaptive isogeometric analysis with truncated hierarchical B-splines for nonlinear option pricing problems

• An adaptive IGA framework for pricing nonlinear multi-asset options is proposed. • A smoothing-based error estimator is developed for the adaptive scheme. • Initial and boundary conditions are imposed via least-squares technique. • The proposed framework is applied to Black-Scholes and Heston models. 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.