43 research outputs found
Back to basics: historical option pricing revisited
We reconsider the problem of option pricing using historical probability
distributions. We first discuss how the risk-minimisation scheme proposed
recently is an adequate starting point under the realistic assumption that
price increments are uncorrelated (but not necessarily independent) and of
arbitrary probability density. We discuss in particular how, in the Gaussian
limit, the Black-Scholes results are recovered, including the fact that the
average return of the underlying stock disappears from the price (and the
hedging strategy). We compare this theory to real option prices and find these
reflect in a surprisingly accurate way the subtle statistical features of the
underlying asset fluctuations.Comment: 14 pages, 2 .ps figures. Proceedings, to appear in Proc. Roy. So
An Asymptotic Analysis of an American Call Option with Small Volatility N. P. Firth
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).