Application of the local radial basis function-based finite difference method for pricing American options

Abstract

In this paper we discuss a local radial basis function-based finite difference (RBF-FD) scheme for numerical solution of multi-asset American option problems. The governing equation is discretized by the θ-method and the option price is approximated by the RBF-FD method. Numerical experiments are performed with the multiquadratic radial basis function for single and double asset problem and results obtained are compared with existing ones. We show numerically that the scheme is second-order accurate. Stability of the scheme is also discussed.

Keywords:

• radial basis function
• finite difference
• Black–Scholes equation
• American option

2010 AMS Subject Classifications:

• 65L10
• 65L20

Acknowledgements

The authors are grateful to the anonymous referees and the editorial board for their valuable comments and suggestions that have led to an improved version of the article. The work of authors (Alpesh Kumar, Lok Pati Tripathi) is supported by Council of Scientific and Industrial Research, India.