Radial-basis-function-based finite difference operator splitting method for pricing American options

ABSTRACT

We present a new radial-basis-function (RBF)-based numerical method for pricing European and American option problems. The governing equation is time semi-discretized by a linear-implicit backward difference method. The spatial discretization is done by using the RBF-based finite difference method. The numerical scheme first derived for an European option is extended for American options by using an operator splitting method. Numerical experiments with multiquadric RBF for one- and two-asset option problems are carried out, and the results obtained are compared with the existing ones.

KEYWORDS:

• Radial basis function
• finite difference
• American option
• option pricing
• operator splitting method

2010 AMS SUBJECT CLASSIFICATIONS:

• 65M06
• 65M20
• 65N06

Acknowledgments

The authors acknowledge the anonymous referees for their valuable comments and suggestion which helped to improve the presentation of the work.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work of Alpesh Kumar is supported by National Board of Higher Mathematics India with grant no. 2/40(43)/2015/R&D-II/4175.