Positive numerical solution for a nonarbitrage liquidity model using nonstandard finite difference schemes

In this article, we construct a numerical method based on a nonstandard finite difference scheme to solve numerically a nonarbitrage liquidity model with observable parameters for derivatives. This nonlinear model considers that the parameters involved are observable from order book data. The propos...

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Bibliographic Details
Published in:Numerical methods for partial differential equations 2014-01, Vol.30 (1), p.210-221
Main Authors: González-Parra, Gilberto, Arenasm, Abraham J., Chen-Charpentier, Benito M.
Format: Article
Language:English
Subjects:
Approximation
Black-Scholes
Derivatives
Finite difference method
Mathematical analysis
Mathematical models
non-arbitrage liquidity model
nonstandard finite difference methods
Numerical analysis
numerical solution
Preserves
Stability
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Summary:In this article, we construct a numerical method based on a nonstandard finite difference scheme to solve numerically a nonarbitrage liquidity model with observable parameters for derivatives. This nonlinear model considers that the parameters involved are observable from order book data. The proposed numerical method use a exact difference scheme in the linear convection‐reaction term, and the spatial derivative is approximated using a nonstandard finite difference scheme. It is shown that the proposed numerical scheme preserves the positivity as well as stability and consistence. To illustrate the accuracy of the method, the numerical results are compared with those produced by other methods. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 210‐221, 2014
ISSN:0749-159X
1098-2426
DOI:10.1002/num.21804