GROUP CLASSIFICATION FOR A GENERAL NONLINEAR MODEL OF OPTIONS PRICING

GROUP CLASSIFICATION FOR A GENERAL NONLINEAR MODEL OF OPTIONS PRICING

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...

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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
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spelling doaj-295cea7b80f84724900fde32bbe742be2020-11-24T22:18:05ZengKrasovskii 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. Ural Mathematical Journal2414-39522016-11-012210.15826/umj.2016.2.00418GROUP CLASSIFICATION FOR A GENERAL NONLINEAR MODEL OF OPTIONS PRICINGVladimir E. Fedorov0Mikhail M. Dyshaev1Laboratory of Quantum Topology, Mathematical Analysis Department, Chelyabinsk State University, ChelyabinskMathematical Analysis Department, Chelyabinsk State University, ChelyabinskWe 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.https://umjuran.ru/index.php/umj/article/view/47Nonlinear partial differential equation, Group analysis, Group of equivalency transformations, Group classification, Nonlinear Black–Scholes equation, Option pricing, Dynamic hedging, Feedback effects of hedging
collection DOAJ
language English
format Article
sources DOAJ
author Vladimir E. Fedorov
Mikhail M. Dyshaev
spellingShingle Vladimir E. Fedorov
Mikhail M. Dyshaev
GROUP CLASSIFICATION FOR A GENERAL NONLINEAR MODEL OF OPTIONS PRICING
Ural Mathematical Journal
Nonlinear partial differential equation, Group analysis, Group of equivalency transformations, Group classification, Nonlinear Black–Scholes equation, Option pricing, Dynamic hedging, Feedback effects of hedging
author_facet Vladimir E. Fedorov
Mikhail M. Dyshaev
author_sort Vladimir E. Fedorov
title GROUP CLASSIFICATION FOR A GENERAL NONLINEAR MODEL OF OPTIONS PRICING
title_short GROUP CLASSIFICATION FOR A GENERAL NONLINEAR MODEL OF OPTIONS PRICING
title_full GROUP CLASSIFICATION FOR A GENERAL NONLINEAR MODEL OF OPTIONS PRICING
title_fullStr GROUP CLASSIFICATION FOR A GENERAL NONLINEAR MODEL OF OPTIONS PRICING
title_full_unstemmed GROUP CLASSIFICATION FOR A GENERAL NONLINEAR MODEL OF OPTIONS PRICING
title_sort group classification for a general nonlinear model of options pricing
publisher 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.
series Ural Mathematical Journal
issn 2414-3952
publishDate 2016-11-01
description 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.
topic Nonlinear partial differential equation, Group analysis, Group of equivalency transformations, Group classification, Nonlinear Black–Scholes equation, Option pricing, Dynamic hedging, Feedback effects of hedging
url https://umjuran.ru/index.php/umj/article/view/47
work_keys_str_mv AT vladimirefedorov groupclassificationforageneralnonlinearmodelofoptionspricing
AT mikhailmdyshaev groupclassificationforageneralnonlinearmodelofoptionspricing
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