Group classification for a general nonlinear model of option pricing. (English) Zbl 1398.91584

Summary: We consider a family of equations with two free functional parameters containing the classical Black-Scholes model, Schonbucher-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.


91G20 Derivative securities (option pricing, hedging, etc.)
35Q91 PDEs in connection with game theory, economics, social and behavioral sciences
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