Pricing American options under multi-state regime switching with an efficient L- stable method

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.

Keywords:

• American options
• non-smooth payoffs
• regime switching
• exponential time differencing
• strongly stable

2015 AMS Subject Classifications:

• 65M12
• 65M15
• 65Y05
• 65Y20

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