Back to basics: historical option pricing revisited

Jean-Philippe Bouchaud and Marc Potters ()
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Jean-Philippe Bouchaud: Science & Finance, Capital Fund Management

No 500036, Science & Finance (CFM) working paper archive from Science & Finance, Capital Fund Management

Abstract: 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.

JEL-codes: G10 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-cfn, nep-fin and nep-rmg
Date: 1998-08
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Published in Philosophical Transactions: Mathematical, Physical & Engineering Sciences 357, 2019 - 2028 (1999)

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Persistent link: http://EconPapers.repec.org/RePEc:sfi:sfiwpa:500036

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