Vladimir E. Fedorov, Mikhail M. Dyshaev, “Group classification for a general nonlinear model of option pricing”, Ural Math. J., 2016, Volume 2, Issue 2,Pages <nobr>37

This article is cited in 5 papers

Group classification for a general nonlinear model of option pricing

Vladimir E. Fedorov^a, Mikhail M. Dyshaev^b

^a Laboratory of Quantum Topology, Mathematical Analysis Department, Chelyabinsk State University, Chelybinsk, Russia
^b Mathematical Analysis Department, Chelyabinsk State University, Chekybinsk, Russia

Abstract: 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, Group classiffcation, Nonlinear Black-Scholes equation, Pricing options, Dynamic hedging, Feedback effects of hedging.

Language: English

DOI: 10.15826/umj.2016.2.004