A Simple Numerical Method for Pricing an American Put Option

We present a simple numerical method to find the optimal exercise boundary in an American put option. We formulate an intermediate function with the fixed free boundary that has Lipschitz character near optimal exercise boundary. Employing it, we can easily determine the optimal exercise boundary by solving a quadratic equation in time-recursive way. We also present several numerical results which illustrate a comparison to other methods

Semi-tractability of optimal stopping problems via a weighted stochastic mesh algorithm

In this article we propose a Weighted Stochastic Mesh (WSM) algorithm for approximating the value of discrete and continuous time optimal stopping problems. It is shown that in the discrete time case the WSM algorithm leads to semi-tractability of the corresponding optimal stopping problem in the sense that its complexity is bounded in order by $\varepsilon^{-4}\log^{d+2}(1/\varepsilon)$ with $d$ being the dimension of the underlying Markov chain. Furthermore we study the WSM approach in the context of continuous time optimal stopping problems and derive the corresponding complexity bounds. Although we can not prove semi-tractability in this case, our bounds turn out to be the tightest ones among the complexity bounds known in the literature. We illustrate our theoretical findings by a numerical example