OPTION PRICING AND HEDGING WITH TEMPORAL CORRELATIONS

Lorenzo Cornalba, Jean-Philippe Bouchaud and Marc Potters
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Lorenzo Cornalba: Laboratoire de Physique Théorique de l'École Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 5, France
Jean-Philippe Bouchaud: Service de Physique de l'État Condensé, Centre d'études de Saclay, Orme des Merisiers, 91191 Gif-sur-Yvette Cedex, France;
Marc Potters: Science & Finance, The Research division of Capital Fund Management, 109-111 rue Victor-Hugo, 92532 Levallois Cedex, France

International Journal of Theoretical and Applied Finance (IJTAF), 2002, vol. 05, issue 03, 307-320

Abstract: We consider the problem of option pricing and hedging when stock returns are correlated in time. Within a quadratic-risk minimisation scheme with history-dependent hedging strategies, 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 calculated 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 Δ-hedge. We introduce a compact notation which eases the computations and could be of use to deal with more complicated models.

Keywords: Option pricing; hedging; non-Gaussian processes (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (3)

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DOI: 10.1142/S0219024902001444

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