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Arenas, A.J., Gonzalez-Parra, G. and Caraballo, B.M. (2013) A Nonstandard Finite Difference Scheme for a Nonlinear Black-Scholes Equation. Mathematical and Computer Modelling, 57, 1663-1670. https://doi.org/10.1016/j.mcm.2011.11.009

has been cited by the following article:

• TITLE: Using the Power Series Method to Evaluate Non-Linear Contingent Claim Partial Differential Equations

  AUTHORS: Gerald W. Buetow Jr., James Sochacki, Bernd Hanke

  KEYWORDS: Power Series Method, Contingent Claim Valuation, Non-Linear Contingent Claim Partial Differential Equation, Contingent Claim Partial Differential Equation, Symbolic Analysis, Finite Differences, Options Pricing

  JOURNAL NAME: Journal of Mathematical Finance, Vol.12 No.4, November 29, 2022

  ABSTRACT: We use the Power Series Method (PSM) numerical framework for estimating nonlinear variations of the Black-Scholes partial differential equations (PDE). The PSM offers an alternative to using traditional finite difference methods. Traditional approaches often require complicated mathematical manipulations of the nonlinear PDE before they can be deployed; or non-linear relationships are approximated linearly usually involving an iterative solver. The PSM does not have these requirements to be implemented and avoids needing an iterative solver. The PSM allows both symbolic and numerical analysis with full choice of the order of the solver in time. This paper illustrates how the PSM offers an alternative and superior, framework to evaluate nonlinear PDE’s. Several extensions for future research are also offered.