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

Author

Listed:
  • Xubiao He

    (Huazhong University of Science and Technology)

  • Pu Gong

    (Huazhong University of Science and Technology)

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.

Suggested Citation

  • Xubiao He & Pu Gong, 2020. "A Radial Basis Function-Generated Finite Difference Method to Evaluate Real Estate Index Options," Computational Economics, Springer;Society for Computational Economics, vol. 55(3), pages 999-1019, March.
    • Handle: RePEc:kap:compec:v:55:y:2020:i:3:d:10.1007_s10614-019-09924-9
    DOI: 10.1007/s10614-019-09924-9
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    References listed on IDEAS

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