Partial differential integral equation model for pricing American option under multi state regime switching with jumps

In this paper, we consider a two dimensional partial differential integral equation (PDIE) model for pricing American option. A nonlinear rationality parameter function for two asset problems is introduced to deal with the free boundary. The rationality parameter function is added in the PDIEs used for pricing American option problems under multi-state regime switching with jumps. The resulting two dimensional nonlinear system of PDIE is then numerically solved. Based on real poles rational approximation, a strongly stable highly efficient and reliable method is developed to solve such complicated systems of PIDEs. The method is build in a predictor corrector style which makes it linearly implicit, therefore, avoids solving nonlinear systems of equations at each time step in all regimes. The method is seen to maintain the stability and convergence for large jump sizes and high volatility in each regime. The impact of regime switching on option prices corresponding to different values interest rate, volatility, and rationality parameter is computed, illustrated by graphs and given in the tables. Convergence results in each regime are presented and time evolution graphs are given to show the effectiveness and reliability of the method.