Pricing options in illiquid markets: optimal systems, symmetry reductions and exact solutions

Details Pricing options in illiquid markets: optimal systems, symmetry reductions and exact solutions Pricing options in illiquid markets: optimal systems, symmetry reductions and exact solutions

2010-02-03

arxiv.org/abs/1002.0864v1

Lobachevskii Journal of Mathematics , 2010,vol. 31,no 2, pp.90-99; ISSN 1995-0802

Economy

Quantitative Finance

Pricing of Securities

14 pages

Scientific paper

10.1134/S1995080210020022

We study a class of nonlinear pricing models which involves the feedback effect from the dynamic hedging strategies on the price of asset introduced by Sircar and Papanicolaou. We are first to study the case of a nonlinear demand function involved in the model. Using a Lie group analysis we investigate the symmetry properties of these nonlinear diffusion equations. We provide the optimal systems of subalgebras and the complete set of non-equivalent reductions of studied PDEs to ODEs. In most cases we obtain families of exact solutions or derive particular solutions to the equations.

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