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Convergence Rates of Moving Mesh Rannacher Methods for PDEs of Asian Options Pricing

Convergence Rates of Moving Mesh Rannacher Methods for PDEs of Asian Options Pricing
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Year:    2016

Author:    Jingtang Ma, Zhiqiang Zhou

Journal of Computational Mathematics, Vol. 34 (2016), Iss. 3 : pp. 240–261

Abstract

This paper studies the convergence rates of a moving mesh implicit finite difference method with interpolation for partial differential equations (PDEs) with moving boundary arising in Asian option pricing. The moving mesh scheme is based on Rannacher time-stepping approach whose idea is running the implicit Euler schemes in the initial few steps and continuing with Crank-Nicolson schemes. With graded meshes for time direction and moving meshes for space direction, the fully discretized scheme is constructed using quadratic interpolation between two consecutive time level for the PDEs with moving boundary. The second-order convergence rates in both time and space are proved and numerical examples are carried out to confirm the theoretical results.  

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1601-m2014-0217

Journal of Computational Mathematics, Vol. 34 (2016), Iss. 3 : pp. 240–261

Published online:    2016-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

Keywords:    Asian option pricing Moving mesh methods Crank-Nicolson schemes Rannacher time-stepping schemes Convergence analysis.

Author Details

Jingtang Ma

Zhiqiang Zhou

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