An IMEX predictor–corrector method for pricing options under regime-switching jump-diffusion models

ABSTRACT

An efficient second-order method for pricing European and American options under regime-switching jump-diffusion models is presented and analysed for stability and convergence. The implicit–explicit (IMEX) nature of the proposed method avoids the need to invert a full matrix and leads to tridiagonal systems that can be efficiently solved by direct methods. The IMEX predictor–corrector method is coupled with the operator splitting method to solve the linear complementarity problem of the American options. Numerical experiments are performed to demonstrate the stability and second-order convergence of the method.

KEYWORDS:

• Regime-switching jump-diffusion model
• option pricing
• American options
• predictor–corrector method
• L-stable

2010 AMS CLASSIFICATIONS:

• 65M06
• 65M12
• 47G20
• 91G60
• 91G20

Acknowledgments

The author would like to thank the anonymous referees for their valuable comments and suggestions which helped to improve the exposition of this paper.

Disclosure statement

No potential conflict of interest was reported by the author.