High-order compact scheme for solving nonlinear Black–Scholes equation with transaction cost

Abstract

In this paper, an unconditionally stable high-order compact finite difference scheme is proposed. The compact scheme is fourth-order accurate in both the temporal and spatial dimensions. The new method computes both the option price and the hedging delta ∂ V/∂ S simultaneously. Two numerical examples are presented to demonstrate the accuracy and efficiency of the proposed scheme.

Keywords:

• high-order compact
• Black–Scholes
• option pricing
• transaction cost

2000 AMS Subject Classifications :

• 65M06
• 65M12
• 65N06

Acknowledgements

The research of the first author was supported by the Start-up Funds (RT754015) from the Faculty of Science, University of Calgary and NSERC. The second author is thankful for the FRCA grant from Middle Tennessee State University. The authors would like to thank the anonymous referees for their time, effort and extensive comments on the revision of the manuscript.