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Adaptive Wavelet Precise Integration Method for Nonlinear Black‐Scholes Model Based on Variational Iteration Method

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  • Huahong Yan

Abstract

An adaptive wavelet precise integration method (WPIM) based on the variational iteration method (VIM) for Black‐Scholes model is proposed. 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 ordinary differential equations. Next, 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.

Suggested Citation

  • Huahong Yan, 2013. "Adaptive Wavelet Precise Integration Method for Nonlinear Black‐Scholes Model Based on Variational Iteration Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:735919
    DOI: 10.1155/2013/735919
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    References listed on IDEAS

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    1. Guo-Cheng Wu, 2012. "Variational Iteration Method for q -Difference Equations of Second Order," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-5, July.
    2. Wang, Jun & Liang, Jin-Rong & Lv, Long-Jin & Qiu, Wei-Yuan & Ren, Fu-Yao, 2012. "Continuous time Black–Scholes equation with transaction costs in subdiffusive fractional Brownian motion regime," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 750-759.
    3. Jana, T.K. & Roy, P., 2012. "Pseudo Hermitian formulation of the quantum Black–Scholes Hamiltonian," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(8), pages 2636-2640.
    4. Guo-Cheng Wu, 2012. "Variational Iteration Method for q‐Difference Equations of Second Order," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
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    Cited by:

    1. Shu-Li Mei & De-Hai Zhu, 2013. "Interval Shannon Wavelet Collocation Method for Fractional Fokker‐Planck Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2013(1).
    2. Shu-Li Mei, 2014. "Faber‐Schauder Wavelet Sparse Grid Approach for Option Pricing with Transactions Cost," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. Li-wei Liu, 2013. "Interval Wavelet Numerical Method on Fokker‐Planck Equations for Nonlinear Random System," Advances in Mathematical Physics, John Wiley & Sons, vol. 2013(1).
    4. Shu-Li Mei, 2013. "HAM‐Based Adaptive Multiscale Meshless Method for Burgers Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).

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