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Adaptive wavelet precise integration method for nonlinear Black-Scholes model based on variational iteration method. (English) Zbl 1275.65072
Summary: An adaptive wavelet precise integration method based on the variational iteration method (VIM) for the Black-Scholes model is proposed. The Black-Scholes model is a very useful tool on pricing options. First, an adaptive wavelet interpolation operator is constructed which can transform the nonlinear partial differential equations into a matrix of ordinary differential equations. Next, the VIM is developed to solve the nonlinear matrix differential equation, which is a new asymptotic analytical method for the nonlinear differential equations. Third, an adaptive precise integration method (PIM) for the system of ordinary differential equations is constructed, with which the almost exact numerical solution can be obtained. At last, the famous Black-Scholes model is taken as an example to test this new method. The numerical result shows the method’s higher numerical stability and precision.
MSC:
65M99Numerical methods for IVP of PDE
35G20General theory of nonlinear higher-order PDE
65T60Wavelets (numerical methods)
91G60Numerical methods in mathematical finance
91B24Price theory and market structure