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

Xubiao He () and Pu Gong
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Xubiao He: Huazhong University of Science and Technology
Pu Gong: Huazhong University of Science and Technology

Computational Economics, 2020, vol. 55, issue 3, No 11, 999-1019

Abstract: 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.

Keywords: Local meshless method; RBF-FD method; Multiquadric; Real estate index option (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10614-019-09924-9

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