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Fedorov, Vladimir E.; Dyshaev, Mikhail M.

Group classification for a class of non-linear models of the RAPM type. (English) Zbl 1452.91306

Commun. Nonlinear Sci. Numer. Simul. 92, Article ID 105471, 10 p. (2021).
Summary: A class of nonlinear equations of RAPM (risk-adjusted pricing methodology) model type with a free element, depending on the second derivative with respect to the underlying asset, is studied. This class contains the Jandačka-Ševčovič model of the option pricing with taking into account transactions costs. The equivalence transformations continuous group of the equations class is found and is applied to the group classification obtaining for the model. The symmetries of the found free element specifications in the considered model are used for the deriving multi-parameter exact solutions.

Cited in 2 Documents

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
22E60 Lie algebras of Lie groups
91G80 Financial applications of other theories

Keywords:

pricing options; nonlinear Black-Scholes type equation; Lie group analysis; group classification
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\textit{V. E. Fedorov} and \textit{M. M. Dyshaev}, Commun. Nonlinear Sci. Numer. Simul. 92, Article ID 105471, 10 p. (2021; Zbl 1452.91306)
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[20] In Russian.
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