Abstract
An efficient second-order method based on exponential time differencing approach for solving American options under multi-state regime switching is developed and analysed for stability and convergence. The method is seen to be strongly stable (L-stable) in each regime. The implicit predictor–corrector nature of the method makes it highly efficient in solving nonlinear systems of partial differential equations arising from multi-state regime switching model. Stability and convergence of the method are examined. The impact of regime switching on option prices for different jump rates and volatility is illustrated. A general framework for multi-state regime switching in multi-asset American option has been provided. Numerical experiments are performed on one and two assets to demonstrate the performance of the method with convex as well as non-convex payoffs. The method is compared with some of the existing methods available in the literature and is found to be reliable, accurate and efficient.
Disclosure statement
No potential conflict of interest was reported by the authors.
Funding
This work is supported by the Fast Track Project # FT111008, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia.
ORCID
M. Yousuf http://orcid.org/0000-0003-3893-4776