High-accuracy PDE Method for Financial Derivative Pricing
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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,


1 introduction
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.


Strike price

Towards accuracy improvements:

 The adaptive mesh model (Trinomial model)

Reason

Local

Adaptive


Coordinate transformation (Finite difference)

Strike price




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



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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