Vladimir E. Fedorov     (Laboratory of Quantum Topology, Mathematical Analysis Department, Chelyabinsk State University, Chelyabinsk, Russian Federation)
Mikhail M. Dyshaev     (Mathematical Analysis Department, Chelyabinsk State University, Chelyabinsk, Russian Federation)


We consider a family of equations with two free functional parameters containing the classical Black–Scholes model, Schönbucher–Wilmott model, Sircar–Papanicolaou equation for option pricing as partial cases. A five-dimensional group of equivalence transformations is calculated for that family. That group is applied to a search for specifications' parameters specifications corresponding to additional symmetries of the equation. Seven pairs of specifications are found.



Nonlinear partial differential equation, Group analysis, Group of equivalency transformations, Group classification, Nonlinear Black–Scholes equation, Option pricing, Dynamic hedging, Feedback effects of hedging

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