An Asymptotic Analysis of an American Call Option with Small Volatility
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 callâ€™s behaviour is the same as a perpetual American call option (except in a boundary layer about the optionâ€™s expiry date).
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