Abstract
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.
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Acknowledgements
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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Koleva, M.N., Vulkov, L.G. (2018). A Unified Numerical Approach for a Large Class of Nonlinear Black-Scholes Models. In: Lirkov, I., Margenov, S. (eds) Large-Scale Scientific Computing. LSSC 2017. Lecture Notes in Computer Science(), vol 10665. Springer, Cham. https://doi.org/10.1007/978-3-319-73441-5_64
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DOI: https://doi.org/10.1007/978-3-319-73441-5_64
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