Option pricing and hedging with temporal correlations

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

No 500030, Science & Finance (CFM) working paper archive from Science & Finance, Capital Fund Management

Abstract: We consider the problem of option pricing and hedging when stock returns are correlated in time. Within a quadratic-risk minimisation scheme, we obtain a general formula, valid for weakly correlated non-Gaussian processes. We show that for Gaussian price increments, the correlations are irrelevant, and the Black-Scholes formula holds with the volatility of the price increments on the scale of the re-hedging. For non-Gaussian processes, further non trivial corrections to the `smile' are brought about by the correlations, even when the hedge is the Black-Scholes Delta-hedge. We introduce a compact notation which eases the computations and could be of use to deal with more complicated models.

JEL-codes: G10 (search for similar items in EconPapers)
Date: 2000-11
New Economics Papers: this item is included in nep-cfn, nep-fin and nep-rmg
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Published in International Journal of Theoretical and Applied Finance 5 (3) (2002) 307-320

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Persistent link: https://EconPapers.repec.org/RePEc:sfi:sfiwpa:500030

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