Geodesic
Group classification for a general nonlinear model of option pricing
Ural mathematical journal, Tome 2 (2016) no. 2, pp. 37-44

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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.
Keywords: Nonlinear partial differential equation, Group analysis, Group of equivalency transformations, Nonlinear Black-Scholes equation, Pricing options, Dynamic hedging, Feedback effects of hedging.
Mots-clés : Group classiffcation 
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     author = {Vladimir E. Fedorov and Mikhail M. Dyshaev},
     title = {Group classification for a general nonlinear model of option pricing},
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Vladimir E. Fedorov; Mikhail M. Dyshaev. Group classification for a general nonlinear model of option pricing. Ural mathematical journal, Tome 2 (2016) no. 2, pp. 37-44. http://geodesic.mathdoc.fr/item/UMJ_2016_2_2_a3/