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Numerical solution of linear and nonlinear Black–Scholes option pricing equations

Authors
Journal
Computers & Mathematics with Applications
0898-1221
Publisher
Elsevier
Publication Date
Volume
56
Issue
3
Identifiers
DOI: 10.1016/j.camwa.2008.02.010
Keywords
  • Black-Scholes Equation
  • Numerical Solution
  • Option Pricing
  • Semidiscretization
  • Transaction Cost
Disciplines
  • Mathematics

Abstract

Abstract This paper deals with the numerical solution of Black–Scholes option pricing partial differential equations by means of semidiscretization technique. For the linear case a fourth-order discretization with respect to the underlying asset variable allows a highly accurate approximation of the solution. For the nonlinear case of interest modeling option pricing with transaction costs, semidiscretization technique provides a competitive numerical solution with respect to others recently given in [B. Düring, M. Fournier, A. Jüngel, Convergence of a high order compact finite difference scheme for a nonlinear Black–Scholes equation, Esaim–Math. Modelling Numer. Anal.–Modelisation Mathematique et Analyse Numerique 38 (2004) 359–369; B. Düring, Black–Scholes type equations: mathematical analysis, parameter identification & numerical solution, Dissertation, University Mainz, July 2005].

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