Valuation of American Options under Multistate Regime-Switching with Jumps

Pricing and hedging American type derivative securities under regime-switching with jumps is a challenging problem. It is seen that the American derivative securities lead to an extremely difficult free boundary value problem. The purpose of this project is to solve such difficult problems by applying and extending recent breakthroughs in the numerical solution of PDEs. We have recently been successful in developing linearly implicit penalty methods, and exponential time differencing methods for single-asset American option prices with Markovian regime-switching without jumps. We have successfully treated the nonlinearities with computational efficiency. The main focus of this project is on developing efficient numerical schemes for two and three dimensional nonlinear partial differential integral equations (PDIEs) with free boundary conditions that will have significant applications on financial engineering practice, in particular the evaluation of American type derivative securities under regime switching with jumps. The methods will be tested on various type of jumps. These tasks will be accomplished through discovery and experimentation based on fundamental principles in numerical analysis of new highly accurate and efficient computational algorithms for systems of PDIEs. Performance tests will demonstrate the efficacy of the results of this project. The outcome of this project will be published in internationally renowned refereed journals and will be presented at international conference.