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 - <p style="text-align: justify;">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 $\varepsilon &gt; 0$ 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.</p>