TY - JOUR
T1 - Finite Element Method for American Option Pricing: A Penalty Approach
AU - SAJID MEMON
JO - International Journal of Numerical Analysis Modeling Series B
VL - 3
SP - 345
EP - 370
PY - 2012
DA - 2012/03
SN - 3
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnamb/289.html
KW - Penalty method
KW - American options
KW - variational inequality
KW - finite element method
KW - error analysis
AB - The model for pricing of American option gives rise to a parabolic variational inequality. We first use penalty function approach to reformulate it as an equality problem. Since the
problem is defined on an unbounded domain, we truncate it to a bounded domain and discuss
error due to truncation and penalization. Finite element method is then applied to the penalized
problem on the truncated domain. By coupling the penalty parameter and the discretization
parameters, error estimates are established when the initial data in H^1_0 . Finally, some numerical
experiments are conducted to confirm the theoretical findings.