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, PowerPoint PPT Presentation


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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 Pricing Shan Zhao and G. W. Wei Department of Computational Science National University of Singapore,

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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

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.


High accuracy pde method for financial derivative pricing shan zhao and g w wei department of computational science national university of singapore

Strike price

Towards accuracy improvements:

 The adaptive mesh model (Trinomial model)

Reason

Local

Adaptive


High accuracy pde method for financial derivative pricing shan zhao and g w wei department of computational science national university of singapore

 Coordinate transformation (Finite difference)

Strike price


High accuracy pde method for financial derivative pricing shan zhao and g w wei department of computational science national university of singapore

2. The adaptive mesh for PDE methods

Strike price


High accuracy pde method for financial derivative pricing shan zhao and g w wei department of computational science national university of singapore

Numerical valuation of European call options by using FD


High accuracy pde method for financial derivative pricing shan zhao and g w wei department of computational science national university of singapore

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


High accuracy pde method for financial derivative pricing shan zhao and g w wei department of computational science national university of singapore

Numerical valuation of European call options by using DSC

>4


High accuracy pde method for financial derivative pricing shan zhao and g w wei department of computational science national university of singapore

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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