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Volume 34, Issue 3
Convergence Rates of Moving Mesh Rannacher Methods for PDEs of Asian Options Pricing

Jingtang Ma & Zhiqiang Zhou

DOI: 10.4208/jcm.1601-m2014-0217

J. Comp. Math., 34 (2016), pp. 240-261.

Published online: 2016-06

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  • 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.  

  • Keywords

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

  • AMS Subject Headings

65M06, 65M12, 91G20, 91G60, 91G80.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

mjt@swufe.edu.cn (Jingtang Ma)

zqzhou_hu@yahoo.com (Zhiqiang Zhou)

  • BibTex
  • RIS
  • TXT
@Article{JCM-34-240, author = {Ma , Jingtang and Zhou , Zhiqiang}, title = {Convergence Rates of Moving Mesh Rannacher Methods for PDEs of Asian Options Pricing}, journal = {Journal of Computational Mathematics}, year = {2016}, volume = {34}, number = {3}, pages = {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.  

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1601-m2014-0217}, url = {http://global-sci.org/intro/article_detail/jcm/9794.html} }
TY - JOUR T1 - Convergence Rates of Moving Mesh Rannacher Methods for PDEs of Asian Options Pricing AU - Ma , Jingtang AU - Zhou , Zhiqiang JO - Journal of Computational Mathematics VL - 3 SP - 240 EP - 261 PY - 2016 DA - 2016/06 SN - 34 DO - http://doi.org/10.4208/jcm.1601-m2014-0217 UR - https://global-sci.org/intro/article_detail/jcm/9794.html KW - Asian option pricing, Moving mesh methods, Crank-Nicolson schemes, Rannacher time-stepping schemes, Convergence analysis. AB -

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.  

Ma , Jingtang and Zhou , Zhiqiang. (2016). Convergence Rates of Moving Mesh Rannacher Methods for PDEs of Asian Options Pricing. Journal of Computational Mathematics. 34 (3). 240-261. doi:10.4208/jcm.1601-m2014-0217
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