The Regularization Method for a Degenerate Parabolic Variational Inequality Arising from American Option Valuation

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.