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Volume 5, Issue 2
The Regularization Method for a Degenerate Parabolic Variational Inequality Arising from American Option Valuation

G. Wang & X. Yang

Int. J. Numer. Anal. Mod., 5 (2008), pp. 222-238.

Published online: 2008-05

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  • Abstract

In this paper, we present a regularization method to a degenerate variational inequality of parabolic type arising from American option pricing. Main difficulty in actually analyzing this kind of problem is caused by the presence of a non-smoothing initial value function in the formulation of the problem. We first use a smoothing technique with small parameter $\varepsilon > 0$ to non-smoothing initial value function; and then we derive the error estimates for regularized continuous problem and regularized discrete problem, respectively. Numerical tests are given to confirm our theoretical results.

  • Keywords

regularization method, variational inequality, American option valuation, finite element and error estimates.

  • AMS Subject Headings

35R35, 49J40, 60G40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-5-222, author = {}, title = {The Regularization Method for a Degenerate Parabolic Variational Inequality Arising from American Option Valuation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2008}, volume = {5}, number = {2}, pages = {222--238}, abstract = {

In this paper, we present a regularization method to a degenerate variational inequality of parabolic type arising from American option pricing. Main difficulty in actually analyzing this kind of problem is caused by the presence of a non-smoothing initial value function in the formulation of the problem. We first use a smoothing technique with small parameter $\varepsilon > 0$ to non-smoothing initial value function; and then we derive the error estimates for regularized continuous problem and regularized discrete problem, respectively. Numerical tests are given to confirm our theoretical results.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/808.html} }
TY - JOUR T1 - The Regularization Method for a Degenerate Parabolic Variational Inequality Arising from American Option Valuation JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 222 EP - 238 PY - 2008 DA - 2008/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/808.html KW - regularization method, variational inequality, American option valuation, finite element and error estimates. AB -

In this paper, we present a regularization method to a degenerate variational inequality of parabolic type arising from American option pricing. Main difficulty in actually analyzing this kind of problem is caused by the presence of a non-smoothing initial value function in the formulation of the problem. We first use a smoothing technique with small parameter $\varepsilon > 0$ to non-smoothing initial value function; and then we derive the error estimates for regularized continuous problem and regularized discrete problem, respectively. Numerical tests are given to confirm our theoretical results.

G. Wang & X. Yang. (1970). The Regularization Method for a Degenerate Parabolic Variational Inequality Arising from American Option Valuation. International Journal of Numerical Analysis and Modeling. 5 (2). 222-238. doi:
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