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Pricing European and American options with two stochastic factors: A highly efficient radial basis function approach

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  • Ballestra, Luca Vincenzo
  • Pacelli, Graziella

Abstract

An increasingly popular and promising approach to solve option pricing models is the use of numerical methods based on radial basis functions (RBF). These techniques yield high levels of accuracy, but have the drawback of requiring the inversion of large full system matrices. In the present paper, by combining Gaussian radial basis functions with a suitable operator splitting scheme, a new RBF method is developed in which the inversion of large system matrices is avoided. The method proposed is applied to five different problems which concern the pricing of European and American options under both the Black–Scholes and the Heston models. The results obtained reveal that the novel RBF scheme is accurate and fast, and performs fairly better than the finite difference approach. Finally, the RBF method proposed is very versatile, and, just like finite difference schemes, can be used to solve an infinite variety of models and problems, not only in the finance area but also in other fields of science and engineering.

Suggested Citation

  • Ballestra, Luca Vincenzo & Pacelli, Graziella, 2013. "Pricing European and American options with two stochastic factors: A highly efficient radial basis function approach," Journal of Economic Dynamics and Control, Elsevier, vol. 37(6), pages 1142-1167.
    • Handle: RePEc:eee:dyncon:v:37:y:2013:i:6:p:1142-1167
    DOI: 10.1016/j.jedc.2013.01.013
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    References listed on IDEAS

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    1. Gong, Pu & Zou, Dong & Wang, Jiayue, 2018. "Pricing and simulation for real estate index options: Radial basis point interpolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 500(C), pages 177-188.
    2. Kaennakham, S. & Chuathong, N., 2019. "An automatic node-adaptive scheme applied with a RBF-collocation meshless method," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 102-125.
    3. Kirkby, J. Lars & Nguyen, Duy & Cui, Zhenyu, 2017. "A unified approach to Bermudan and barrier options under stochastic volatility models with jumps," Journal of Economic Dynamics and Control, Elsevier, vol. 80(C), pages 75-100.
    4. Kentaro Hoshisashi & Yuji Yamada, 2023. "Pricing Multi-Asset Bermudan Commodity Options with Stochastic Volatility Using Neural Networks," JRFM, MDPI, vol. 16(3), pages 1-23, March.
    5. Shirzadi, Mohammad & Rostami, Mohammadreza & Dehghan, Mehdi & Li, Xiaolin, 2023. "American options pricing under regime-switching jump-diffusion models with meshfree finite point method," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    6. Reza Mollapourasl & Ali Fereshtian & Michèle Vanmaele, 2019. "Radial Basis Functions with Partition of Unity Method for American Options with Stochastic Volatility," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 259-287, January.
    7. Guarin, Alexander & Liu, Xiaoquan & Ng, Wing Lon, 2014. "Recovering default risk from CDS spreads with a nonlinear filter," Journal of Economic Dynamics and Control, Elsevier, vol. 38(C), pages 87-104.
    8. Jamal Amani Rad & Kourosh Parand & Saeid Abbasbandy, 2014. "Local weak form meshless techniques based on the radial point interpolation (RPI) method and local boundary integral equation (LBIE) method to evaluate European and American options," Papers 1412.6063, arXiv.org.
    9. A. Golbabai & E. Mohebianfar, 2017. "A New Stable Local Radial Basis Function Approach for Option Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 49(2), pages 271-288, February.
    10. Sinem Kozp{i}nar & Murat Uzunca & Bulent Karasozen, 2016. "Pricing European and American Options under Heston Model using Discontinuous Galerkin Finite Elements," Papers 1606.08381, arXiv.org, revised Mar 2020.
    11. Kozpınar, Sinem & Uzunca, Murat & Karasözen, Bülent, 2020. "Pricing European and American options under Heston model using discontinuous Galerkin finite elements," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 568-587.
    12. Yusho Kagraoka, 2020. "The Fractional Step Method versus the Radial Basis Functions for Option Pricing with Correlated Stochastic Processes," IJFS, MDPI, vol. 8(4), pages 1-13, December.
    13. Alessandro Andreoli & Luca Vincenzo Ballestra & Graziella Pacelli, 2018. "Pricing Credit Default Swaps Under Multifactor Reduced-Form Models: A Differential Quadrature Approach," Computational Economics, Springer;Society for Computational Economics, vol. 51(3), pages 379-406, March.
    14. Golbabai, Ahmad & Mohebianfar, Ehsan, 2017. "A new method for evaluating options based on multiquadric RBF-FD method," Applied Mathematics and Computation, Elsevier, vol. 308(C), pages 130-141.
    15. Weiwei Liu & Zhile Yang & Kexin Bi, 2017. "Forecasting the Acquisition of University Spin-Outs: An RBF Neural Network Approach," Complexity, Hindawi, vol. 2017, pages 1-8, October.
    16. Zaheer-ud-Din & Muhammad Ahsan & Masood Ahmad & Wajid Khan & Emad E. Mahmoud & Abdel-Haleem Abdel-Aty, 2020. "Meshless Analysis of Nonlocal Boundary Value Problems in Anisotropic and Inhomogeneous Media," Mathematics, MDPI, vol. 8(11), pages 1-19, November.
    17. Jamal Amani Rad & Kourosh Parand, 2014. "Numerical pricing of American options under two stochastic factor models with jumps using a meshless local Petrov-Galerkin method," Papers 1412.6064, arXiv.org.
    18. Rad, Jamal Amani & Parand, Kourosh & Ballestra, Luca Vincenzo, 2015. "Pricing European and American options by radial basis point interpolation," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 363-377.

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