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Option Pricing and Hedging with Temporal Correlations

Lorenzo Cornalba·Jean-Philippe Bouchaud·Marc Potters
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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.

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Lorenzo Cornalba, Jean-Philippe Bouchaud, Marc Potters. 2000-11-29. Option Pricing and Hedging with Temporal Correlations. https://arxiv.org/abs/cond-mat/0011506

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