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 PricingShan Zhao and G. W. WeiDepartment of Computational ScienceNational University of Singapore,
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.
Towards accuracy improvements:
The adaptive mesh model (Trinomial model)
Coordinate transformation (Finite difference)
2. The adaptive mesh for PDE methods
Numerical valuation of European call options by using FD
Handling complex boundary conditions
3. Discrete singular convolution (DSC) algorithm
Numerical valuation of European call options by using DSC
I. To achieve more accurate valuation
Higher resolution meshes
Higher order methods
II. Higher order PDE methods for financial derivative pricing
High accuracy and efficient