Back to basics: historical option pricing revisited

Details Back to basics: historical option pricing revisited Back to basics: historical option pricing revisited

1998-08-19

arxiv.org/abs/cond-mat/9808206v1

Physics

Condensed Matter

14 pages, 2 .ps figures. Proceedings, to appear in Proc. Roy. Soc

Scientific paper

10.1098/rsta.1999.0414

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.

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