Accessible Requires Authentication Published by De Gruyter January 1, 2012

Error Estimates for Approximations of American Put Option Price

David Šiška

Abstract

Finite difference approximations to multi-asset American put option price are considered. The assets are modelled as a multi-dimensional diffusion process with variable drift and volatility. Approximation error of order one quarter with respect to the time discretisation parameter and one half with respect to the space discretisation parameter is proved by reformulating the corresponding optimal stopping problem as a solution of a degenerate Hamilton-Jacobi-Bellman equation. Furthermore, the error arising from restricting the discrete problem to a finite grid by reducing the original problem to a bounded domain is estimated.

Received: 2011-05-16
Revised: 2011-08-23
Accepted: 2011-09-15
Published Online: 2012
Published in Print: 2012

© Institute of Mathematics, NAS of Belarus