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 - <p style="text-align: justify;">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. &nbsp;</p>