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The Pushpa Publishing House proposes to organize a five day "International Conference on Mathematics of Date" from December 31, 2010 to January 04, 2011 scheduled to be held at Allahabad, India.

 
  Far East Journal of Applied Mathematics  
 ISSN: 0972-0960
 
 
 

     Far East Journal of Applied Mathematics
    Volume 30, Issue 1, Pages 1 - 41 (January 2008)


DISCRETIZATION OF THE BLACK-SCHOLES OPERATOR WITH A NATURAL LEFT-HAND SIDE BOUNDARY CONDITION

Lutz Angermann (Germany)

Received September 11, 2007

References:



[1] L. Angermann, Error estimates for the finite element solution of an elliptic singularly perturbed problem, IMA J. Numer. Anal. 15 (1995), 161-196.

[2] L. Angermann and S. Wang, Three-dimensional exponentially fitted conforming tetrahedral finite elements for the semiconductor continuity equations, Appl. Numer. Math. 46(1) (2003), 19-43.

[3] L. Angermann and S. Wang, Convergence of a fitted finite volume method for the penalized Black-Scholes equation governing European and American option pricing, Numer. Math. 106(1) (2007), 1-40.

[4] O. Axelsson, Iterative Solution Methods, Cambridge University Press, Cambridge, 1994.

[5] G. Barles, Convergence of Numerical Schemes for Degenerate Parabolic Equations Arising in Finance Theory, In L. C. G. Rogers and D. Taley, editors, Numerical Methods in Finance, Cambridge University Press, Cambridge, 1997, pp. 1-21.

[6] G. Barles, Ch. Daher and M. Romano, Convergence of numerical schemes for problems arising in finance theory, Math. Models Methods Appl. Sci. 5 (1995), 125-143.

[7] F. Black and M. Scholes, The pricing of options and corporate liabilities, J. Political Economy 81 (1973), 637-659.

[8] M. Holtz and A. Kunoth, B-spline-based Monotone Multigrid Methods, Preprint 252, SFB 611, Universtät Bonn, 2005.

[9] A. Kufner, Weighted Sobolev Spaces, John Wiley & Sons Inc., New York, 1985, Translated from the Czech.

[10] J. J. H. Miller and S. Wang, An exponentially fitted finite volume method for the numerical solution of 2D unsteady incompressible flow problems, J. Comput. Phys. 115(1) (1994), 56-64.

[11] J. J. H. Miller and S. Wang, A tetrahedral mixed finite element for the stationary semiconductor continuity equations, SIAM J. Numer. Anal. 31(1) (1994), 196-216.

[12] C. Vázquez, An upwind numerical approach for an American and European option pricing model, Appl. Math. Comput. 97(2-3) (1998), 273-286.

[13] S. Wang, A novel fitted finite volume method for the Black-Scholes equation governing option pricing, IMA J. Numer. Anal. 24 (2004), 699-720.

[14] S. Wang, X. Q. Yang and K. L. Teo, Power penalty method for a linear complementary problem arising from American option valuation, JOTA 129(2) (2006), 227-254.

[15] P. Wilmott, J. Dewynne and S. Howison, Option Pricing: Mathematical Models and Computation, Oxford Financial Press, Oxford, 1993.

Keywords and phrases: Black-Scholes equation, option valuation, fitted finite volume method.

 


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