High-order time stepping scheme for pricing American option under Bates model

Pricing of European and American options under Bates model give rise to a partial integro-differential equation. In this paper a strongly stable fourth-order implicit predictor–corrector time stepping method based on exponential time differencing) is proposed for solving such problems. We provide stability, and convergence of the proposed method, and study the impact of the jump intensity, penalty and other parameters on convergence and solution accuracy. The American option constraint is enforced by using a penalty method. Spatial derivatives are approximated using second-order finite central differences which leads to block tridiagonal systems. The integral term is evaluated using simple quadrature where the non-locality of the jump term in such models leads to dense matrix. We treat the approximated integral term and nonlinear penalty term explicitly in time. Numerical experiments are demonstrated by discussing the efficiency, accuracy and reliability of the proposed method.