Convergence rates of the numerical methods for the delayed PDEs from option pricing under regime switching hard-to-borrow models

Abstract

The aim of this paper is to study the convergence rates of the finite difference methods (FDMs) for solving the PDEs with spatial delays which arise in the option pricing under regime switching hard-to-borrow models. The PDEs are coupled for different regime states and involve delays in two spatial directions. One of the boundary conditions is implicitly given by an initial-boundary value problem of coupled PDEs which needs to be solved before solving the main equations. This paper proves convergence rates of the FDM based on mesh-dependent expansions for solving the problems. Numerical examples confirm the theory.

Keywords:

• PDEs with delays
• option pricing
• hard-to-borrow stock models
• regime switching models
• finite difference methods
• convergence rates

2010 Mathematics subject classifications:

• 65C20
• 65C40
• 65M06
• 91G20
• 91G60

Acknowledgments

The authors are grateful to the anonymous referees for their valuable comments that have led to a greatly improved paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work was supported by National Natural Science Foundation of China (Grant No. 11671323), Program for New Century Excellent Talents in University, P.R. China (Grant No. NCET-12-0922) and the Fundamental Research Funds for the Central Universities, P.R. China (JBK1805001).