An Asymptotic Analysis of an American Call Option with Small Volatility

N. P. Firth: OCIAM, Mathematical Institute, 24-29 St. Giles’, Oxford, OX1 3LB UK firth@maths.ox.ac.uk

J. N. Dewynne: OCIAM, Oxford dewynne@maths.ox.ac.uk

S. J. Chapman: OCIAM, Oxford chapman@maths.ox.ac.uk

Abstract

In this paper we present an asymptotic analysis of an American call option where the diffusion term (volatility) is small compared to the drift terms (interest rate and continuous dividend yield). We show that in the limit where diffusion 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).