Finite Difference Methods for Early Exercise Options

Abstract

Usually, options with early exercise possibility like American and Bermudan options have to be priced numerically. In this article, approaches based on partial differential operators and their finite difference discretization are considered. The early exercise possibility leads to an inequality constraint for the price of the option. Linear complementarity problem (LCP) and other formulations incorporating this constraint are discussed. Fairly standard finite difference discretizations can be used for the underlying partial differential operator. Several solution and approximation methods including the projected successive over relaxation (PSOR) method and penalty methods are described. As an example, an American put option is priced using different methods under the Black–Scholes model.

Finite Difference Methods for nonlinear American Option Pricing models: Numerical Analysis and Computing

“…A numerical solution has to be found on infinite domain [0; ∞) × [0; T ] for all regimes. In accordance with [66], [106] the domain in original variable S can be truncated about three or four times the exercise price. It is sufficient to take the numerical domain for the transformed problem .…”