Solving complex PIDE systems for pricing American option under multi-state regime switching jump-diffusion model

Based on exponential time differencing approach, an efficient second order method is developed for solving systems of partial integral differential equations. The method is implemented to solve American options under multi-state regime switching with jumps. The method is seen to be strongly stable (L-stable) and avoids any spurious oscillations caused by non-smooth initial data. The predictor-corrector nature of the method makes it highly efficient in solving nonlinear PIDEs in each regime with different volatilities and interest rates. Penalty method approach is applied to handle the free boundary constraint of American options. Numerical results are presented to illustrate the performance of the method for American options under Merton's jump-diffusion models. Padé approximation of matrix exponential functions and partial fraction splitting technique are applied to construct computationally efficient version of the method. Efficiency, accuracy and reliability of the method are compared with those of the existing methods available in the literature.