An Asymptotic Analysis of an American Call Option with Small Volatility N. P. Firth

Abstract

this paper we present an asymptotic analysis of an American call option where the di#usion term (volatility) is small compared to the drift terms (interest rate and continuous dividend yield). We show that in the limit where di#usion is negligible, relative to drift, then, at leading order, the American call's behaviour is the same as a perpetual American call option (except in a boundary layer about the option's expiry date).