Pricing real estate index options by compactly supported radial-polynomial basis point interpolation

This paper presents a novel method to price the real estate index options, which are modeled based on the framework proposed by Fabozzi et al. (2012). The CS-PBF method combines compactly supported radial basis functions (CSRBF) and polynomial basis functions (PBF) to yield the interpolation functions, which can guarantee interpolation shape functions with Kronecker property and overcome possible singularity associated with the PBF method. Compared with the CSRBF method and the finite difference (FD) method, the CS-PBF method is more accurate and efficient for the real estate index option. Meanwhile, a local mesh refinement technique is employed for dealing with the non-smooth options' payoffs, which is very effective and stable to improve the computational accuracy for the CS-PBF method. Finally, the CS-PBF method is extended to price American option of the real estate index.