Sensitivity of American Option Prices with Respect to the Variations of Local Volatility

Abstract

In mathematical finance there are two well known and traditional technique s to deal American options: Solving parabolic partial differential equations and using the probabilistic approach. In this paper, we use purely probabilistic approach. We consider standard one-dimensional diffusion model with local volatility that is a func tion of time and current stock price and where the risk-free interest rate is constant. We estimate the continuity of American option prices w ith respect to the corresponding local volatilities.