Symmetries and exact solutions of a nonlinear pricing options equation

We discuss the numerical solving of nonlinear options pricing models to a market with the insufficient liquidity. Also for these models the sensitivity coefficients of the option price (Greeks) were found numerically. These nonlinear models were selected by us on the basis of our group classification of a general model and were previously obtained in the works of Frey and Stremme, Sircar and Papanicolaou, and Sch¨onbucher and Wilmott. The behavior of the price and its sensitivity coefficients in the nonlinear models and in the linear Black–Scholes model is compared. The results of the comparing presents in the form of graphs, a brief comparative analysis of them was made.

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“…Remark 2. Equation (2) also reduces to equation (4), see [5,7] for details. This model corresponds to the case v(u x ) = β/u x in (4).…”

Section: Remark 1 If In Equation (mentioning

confidence: 99%

“…Using the group classification of equation ( 4), obtained in the works [7][8][9][10], authors single out several cases of the free functional parameter v, which are nonequivalent in the group structure sense. These cases correspond to the all widest symmetry groups of the equation.…”

Section: Remark 1 If In Equation (mentioning

confidence: 99%

Comparing of some sensitivities for nonlinear models Comparing of some sensitivities (Greeks) for nonlinear models of option pricing with market illiquidity

Dyshaev

Fedorov

2019

№2(102) (2019)

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“…In the last decade, in the works of Bordag [24,25], of Dyshaev and Fedorov [26][27][28][29][30][31][32] group properties of various nonlinear Black-Scholes type models were studied, and their invariant solutions and submodels were calculated. In the papers of Dyshaev and Fedorov, group classifications for various classes of nonlinear Black-Scholes type models were obtained.…”

Section: Introductionmentioning

confidence: 99%

Symmetry Analysis of a Model of Option Pricing and Hedging

2022

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The Guéant and Pu model of option pricing and hedging, which takes into account transaction costs, and the impact of operations on the market is studied by group analysis methods. The infinite-dimensional continuous group of equivalence transforms of the model is found. It is applied to get the group classification of the model under consideration. In addition to the general case, the classification contains three specifications of a free element in the equation, which correspond to models with groups of symmetries of a special kind. Optimal systems of subalgebras for some concrete models from the obtained classification are derived and used for the calculation of according invariant submodels.

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