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Volume 3, Issue 3
Finite Element Method for American Option Pricing: A Penalty Approach

SAJID MEMON

Int. J. Numer. Anal. Mod. B, 3 (2012), pp. 345-370

Published online: 2012-03

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  • Abstract
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.
  • Keywords

Penalty method American options variational inequality finite element method error analysis

  • AMS Subject Headings

35R35 49J40 60G40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAMB-3-345, author = {SAJID MEMON}, title = {Finite Element Method for American Option Pricing: A Penalty Approach}, journal = {International Journal of Numerical Analysis Modeling Series B}, year = {2012}, volume = {3}, number = {3}, pages = {345--370}, abstract = {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.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnamb/289.html} }
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.
SAJID MEMON. (2012). Finite Element Method for American Option Pricing: A Penalty Approach. International Journal of Numerical Analysis Modeling Series B. 3 (3). 345-370. doi:
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