Positive numerical solution for a nonarbitrage liquidity model using nonstandard finite difference schemes
Copyright policy )Positive numerical solution for a nonarbitrage liquidity model using nonstandard finite difference schemes
AbstractIn 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
- University of Córdoba Colombia
- The University of Texas at Arlington United States
- University of the Andes Venezuela
- Universidad del Sinú Colombia
- Chartered Institute of Management Accountants United Kingdom
numerical solution, Derivative securities (option pricing, hedging, etc.), nonstandard finite difference methods, Numerical methods (including Monte Carlo methods), Black-Scholes model, Finite difference methods for initial value and initial-boundary value problems involving PDEs, no-arbitrage liquidity model
numerical solution, Derivative securities (option pricing, hedging, etc.), nonstandard finite difference methods, Numerical methods (including Monte Carlo methods), Black-Scholes model, Finite difference methods for initial value and initial-boundary value problems involving PDEs, no-arbitrage liquidity model
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