Author(s)

Gerald W. Buetow Jr.¹, James Sochacki², Bernd Hanke³

¹BFRC Services, LLC, Irmo, SC, USA.
²James Madison University, Harrisonburg, VA, USA.
³BFRC Services, LLC, Monaco.

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.

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

Buetow Jr., G. , Sochacki, J. and Hanke, B. (2022) Using the Power Series Method to Evaluate Non-Linear Contingent Claim Partial Differential Equations. Journal of Mathematical Finance, 12, 743-762. doi: 10.4236/jmf.2022.124039.