A Radial Basis Function-Generated Finite Difference Method to Evaluate Real Estate Index Options

Abstract

The local radial basis functions (RBF) method is becoming increasingly popular as an alternative to the global version that suffers from ill-conditioning. The purpose of this paper is to design and describe the valuation of the real estate index options by a local RBF scheme based multiquadric radial basis function-generated finite difference (RBF-FD) method. As a generalized finite differencing scheme, the RBF-FD method functions without the need for underlying meshes to structure nodes. It offers high-order accuracy approximation and removes the difficulty of the ill-conditioned conventional global collocation methods. This paper employs an optimal variable shape parameter for the multiquadric basis functions at each grid point of the domain. Meanwhile, a local mesh refinement technique is adopted to deal with non-smooth payoffs of option. These techniques are effective and stable in improving the computational accuracy of the RBF-FD method. Several numerical experiments are presented and compared with the FD and compactly supported RBF methods to demonstrate the good performances of the proposed method. Lastly, the RBF-FD method is extended to price the American option of the real estate index.