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A Radial Point Interpolation Method for Pricing Options on a Dividend Paying Asset

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Year of Publication: 2017
Abdelmgid O. M. Sidahmed

Abdelmgid O M Sidahmed. A Radial Point Interpolation Method for Pricing Options on a Dividend Paying Asset. International Journal of Computer Applications 172(7):1-6, August 2017. BibTeX

	author = {Abdelmgid O. M. Sidahmed},
	title = {A Radial Point Interpolation Method for Pricing Options on a Dividend Paying Asset},
	journal = {International Journal of Computer Applications},
	issue_date = {August 2017},
	volume = {172},
	number = {7},
	month = {Aug},
	year = {2017},
	issn = {0975-8887},
	pages = {1-6},
	numpages = {6},
	url = {},
	doi = {10.5120/ijca2017915180},
	publisher = {Foundation of Computer Science (FCS), NY, USA},
	address = {New York, USA}


We present the radial point interpolation method (RPIM) to solve problems for pricing American and European put options on a dividend paying asset. Using RPIM, we get a system of ordinary differential equations which is then solved by a time integration methods . To resolve the difficulties associated with solving the free boundary problem associated with American options, we use a penalty approach. Numerical experiments are presented which prove the computational efficiency of the RPIM.


  1. Barone-Adesi G. and Whaley E. 1987. Efficient analytic approximation of American option values. The Journal of Finance, XLII (2).
  2. Battauz A. and Pratelli M. 2004. Optimal stopping and American options with discrete dividends and exogenous risk, Insurance: Mathematics and Economics, 35, 255-265.
  3. Company R., Gonzalez A.L. and Jodar L. 2006. Numerical solution of modified Black-Scholes equation pricing stock options with discrete dividend, Mathematical and Computer Modelling, 44, 1058-1068.
  4. Han H. and Wu X. 2003. A fast numerical method for the Black-Scholes equation of American options, SIAM Journal of Numerical Analysis, 41(6), 2081-2095.
  5. Kallast S. and Kivinukk A. 2003. Pricing and Hedging American Options Using Approximations by Kim Integral Equations, European Finance Review, 7 , 361-383.
  6. Khaliq A.Q.M., Voss D.A. and Kazmi S.H.K. 2006. A linearly implicit predictor-corrector scheme for pricing American options using a penalty method approach, Journal of Banking & Finance, 30, 489-502.
  7. Khaliq A.Q.M., Voss D.A. and Kazmi S.H.K. 2008. Adaptive θ-methods for pricing American options, Journal of Computational and Applied Mathematics, 222, 210-227.
  8. Kim I.K. 1990. The analytical valuation of American options, Review of Financial Studies, 3, 547-572.
  9. Liu G.R. and Gu Y. T. 2005. An Introduction to Meshfree Methods and Their Programming, Springer.
  10. Liu Q., Liu F., Gu Y.T., Zhuang P., Chen J. and Turner I. 2015. A meshless method based on Point Interpolation Method (PIM) for the space fractional diffusion equation, Applied Mathematics and Computation, 256, 930-938.
  11. Mallier R. and Alobaidi G. 2000. Laplace transforms and American options, Applied Mathematical Finance, 7, 241- 256.
  12. Meyer G.H. 2002. Numerical investigation of early exercise in American puts with discrete dividends, Journal of Computational Finance, 5(2), 37-53.
  13. Rad J.A., Parand K. and Ballestra L.V. 2015. Pricing European and American options by radial basis point interpolation, Applied Mathematics and Computation, 251, 363-377.
  14. Tangman D.Y., Gopaul A. and Bhuruth M. 2008. A fast highorder finite difference algorithm for pricing American options, Journal of Computational and Applied Mathematics, 222(1), 17-29.
  15. Vellekoop M.H. and Nieuwenhuis J.W. 2006. Efficient pricing of derivatives on assets with discrete dividends, Applied Mathematical Finance, 13(3), 265-284.
  16. Wilmott P., Howison S. and Dewynne J. 1995. The Mathematics of Financial Derivatives: A Student Introduction, Cambridge University Press, Oxford, UK.
  17. Zhao J. , Davison M. and Corless R.M. 2007. Compact finite difference method for American option pricing, Journal of Computational and Applied Mathematics, 206, 306 - 321.


European put options, American put options, dividend paying, radial point interpolation method