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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 = {G. Wang and X. Yang}, 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 AU - G. Wang & X. Yang 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 and X. Yang. (2008). 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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