A Unified Numerical Approach for a Large Class of Nonlinear Black-Scholes Models
In this paper, we consider a class of non-linear models in mathematical finance, where the volatility depends on the second spatial derivative of the option value. We study the convergence and realization of the constructed, on a fitted non-uniform meshes, implicit difference schemes. We implement various Picard and Newton iterative processes. Numerical experiments are discussed.
This research was supported by the Bulgarian National Fund of Science under Project “Advanced Analytical and Numerical Methods for Nonlinear Differential Equations with Applications in Finance and Environmental Pollution”-2017.
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