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High-accuracy PDE Method for Financial Derivative Pricing Shan Zhao and G. W. Wei Department of Computational Science

High-accuracy PDE Method for Financial Derivative Pricing Shan Zhao and G. W. Wei Department of Computational Science National University of Singapore, . 1. Introduction. Major numerical approaches for option pricing Binomial tree model Finite difference method Monte Carlo simulation.

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High-accuracy PDE Method for Financial Derivative Pricing Shan Zhao and G. W. Wei Department of Computational Science

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  1. High-accuracy PDE Method for Financial Derivative PricingShan Zhao and G. W. WeiDepartment of Computational ScienceNational University of Singapore,

  2. 1. Introduction Major numerical approaches for option pricing Binomial tree model Finite difference method Monte Carlo simulation Simple, flexible, and convergent The speed of convergence usually slow.

  3. Strike price Towards accuracy improvements:  The adaptive mesh model (Trinomial model) Reason Local Adaptive

  4.  Coordinate transformation (Finite difference) Strike price

  5. 2. The adaptive mesh for PDE methods Strike price

  6. Numerical valuation of European call options by using FD

  7. PDE Methods Global Unified Local Examples Spectral DSC Finite difference Approximation style Accuracy High High Low Handling complex boundary conditions Inflexible Flexible Flexible 3. Discrete singular convolution (DSC) algorithm

  8. Numerical valuation of European call options by using DSC >4

  9. 4. Conclusion I. To achieve more accurate valuation Higher resolution meshes Higher order methods II. Higher order PDE methods for financial derivative pricing Rarely used High accuracy and efficient Promising

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