Radial Basis Function Approximation Method for Pricing of Basket Options Under Jump Diffusion Model

  • Ali Safdari-VaighaniEmail author
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 126)


Option contracts under actual market conditions which are more complex than a simple Black-Scholes model are important hedging strategies in the modern financial market. Basket options are attractive products which required the reliable pricing method to take all the beneficial characteristics of a basket option such as correlation effect of underlying assets. The focus of this paper is to present the radial basis function partition of unity method (RBF–PUM) for evaluation of basket options in which underlying assets price follow the Merton jump diffusion model. Numerical experiments are performed for the resulting partial integro-differential equation (PIDE). The resulting valuation method allow for an adaptive space discretization in region near the exercise price to reduce computational cost. The domain truncation effects on the computational error is investigated for the proposed numerical approach. Our numerical examples with two and three underlying assets show that the proposed scheme is accurate, capability of local adaptivity, and efficient in comparison of alternative methods for accurate option prices.



The author would like to thank Elisabeth Larsson, Uppsala University for a valuable discussion on the issues regarding RBF–PUM.


  1. 1.
    F. Black, M. Scholes, The pricing of options and corporate liabilities. J. Polit. Econ. 81(3), 637–654 (1973)MathSciNetCrossRefGoogle Scholar
  2. 2.
    S.S. Clift, P.A. Forsyth, Numerical solution of two asset jump diffusion models for option valuation. Appl. Numer. Math. 58(6), 743–782 (2008)MathSciNetCrossRefGoogle Scholar
  3. 3.
    G. Fasshauer, A.Q.M. Khaliq, D.A. Voss, Using mesh free approximation for multi asset American options in Mesh Free Methods, ed. by C.S. Chen. J. Chin. Inst. Eng. 27, 563–571 (2004)Google Scholar
  4. 4.
    E. Hairer, S. Nørsett, G. Wanner, Solving Ordinary Differential Equations I. Nonstiff Problems, 2nd edn. (Springer, Berlin, 2000)Google Scholar
  5. 5.
    K.J. In’t Hout, S. Foulon, ADI finite difference schemes for option pricing in the Heston model with correlation. Int. J. Numer. Anal. Model. 7(2), 303–320 (2010)MathSciNetGoogle Scholar
  6. 6.
    E. Larsson, V. Shcherbakov, A. Heryudono, A least squares radial basis function partition of unity method for solving PDEs. SIAM J. Sci. Comput. 39(6), 2538–2563 (2017)MathSciNetCrossRefGoogle Scholar
  7. 7.
    R.C. Merton, Option pricing when underlying stock returns are discontinuous. J. Financ. Econ. 3(1–2), 125–144 (1976)CrossRefGoogle Scholar
  8. 8.
    R. Mollapourasl, A. Fereshtian, H. Li, X. Lu, RBF-PU method for pricing options under the jump diffusion model with local volatility. J. Comput. Appl. Math. (2018).
  9. 9.
    U. Pettersson, E. Larsson, G. Marcusson, J. Persson, Improved radial basis function methods for multi-dimensional option pricing. J. Comput. Appl. Math. 222(1), 82–93 (2008)MathSciNetCrossRefGoogle Scholar
  10. 10.
    A. Safdari-Vaighani, A. Heryudono, E. Larsson, A radial basis function partition of unity collocation method for convection-diffusion equations arising in financial applications. J. Sci. Comput. 64(2), 341–367 (2015)MathSciNetCrossRefGoogle Scholar
  11. 11.
    V. Shcherbakov, Radial basis function partition of unity operator splitting method for pricing multi-asset American options. BIT Numer. Math. 56(4), 1401–1423 (2016)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Mathematical and Computer SciencesAllameh Tabataba’i UniversityTehranIran

Personalised recommendations