An efficient and provable sequential quadratic programming method for American and swing option pricing

• Published in: European journal of operational research Vol. 316; no. 1; pp. 19 - 35
• Main Authors: Shen, Jinye, Huang, Weizhang, Ma, Jingtang
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.07.2024
• Subjects: American option; Heston model; Jump diffusion; Quadratic programming; Swing option; American option; Quadratic programming; Heston model; Jump diffusion; Swing option
• ISSN: 0377-2217
• DOI: 10.1016/j.ejor.2023.11.012

A sequential quadratic programming numerical method is proposed for American option pricing based on the variational inequality formulation. The variational inequality is discretized using the θ-method in time and the finite element method in space. The resulting system of algebraic inequalities at each time step is solved through a sequence of box-constrained quadratic programming problems, with the latter being solved by a globally and quadratically convergent, large-scale suitable reflective Newton method. It is proved that the sequence of quadratic programming problems converges with a constant rate under a mild condition on the time step size. The method is general in solving the variational inequalities for the option pricing with many styles of optimal stopping and complex underlying asset models. In particular, swing options and stochastic volatility and jump diffusion models are studied. Numerical examples are presented to confirm the effectiveness of the method. •A fast sequential quadratic programming method (SQPM) is developed.•The convergence of the SQPM is proved.•The SQPM can solve non-symmetric variational inequalities.•The SQPM is efficient for solving general classes of American and swing options.