GROUP CLASSIFICATION FOR A GENERAL NONLINEAR MODEL OF OPTIONS PRICING

• Main Authors: Vladimir E. Fedorov, Mikhail M. Dyshaev
• Format: Article
• Language: English
• Published: Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin. 2016-11-01
• Series: Ural Mathematical Journal
• Subjects: Nonlinear partial differential equation, Group analysis, Group of equivalency transformations, Group classification, Nonlinear Black–Scholes equation, Option pricing, Dynamic hedging, Feedback effects of hedging
• Online Access: https://umjuran.ru/index.php/umj/article/view/47
• ISSN: 2414-3952

We consider a family of equations with two free functional parameters containing the classical Black–Scholes model, Schönbucher–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.