Ufa Mathematical Journal
    Volume 9, Number 1, pp. 29-40

    Symmetries and exact solutions of a nonlinear pricing options equation

    Dyshaev M.M., Fedorov V.E.


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    We study the group structure of the Schonbucher--Wilmott equation with a free parameter, which models the pricing options. We find a five-dimensional group of equivalence transformations for this equation. By means of this group we find four-dimensional Lie algebras of the admitted operators of the equation in the cases of two free element specifications and we find a three-dimensional Lie algebra for other nonequivalent specifications. For each algebra we find optimal systems of subalgebras and the corresponding invariant solutions or invariant submodels.