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29 March 2024
 
  » arxiv » cond-mat/0011506

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Option Pricing and Hedging with Temporal Correlations
Lorenzo Cornalba ; Jean-Philippe Bouchaud ; Marc Potters ;
Date 29 Nov 2000
Journal International Journal of Theoretical and Applied Finance 5 (3) (2002) 307-320
Subject cond-mat
Affiliation2,3) and Marc Potters ( ENS Paris, CEA Saclay, Science & Finance, CFM
AbstractWe 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.
Source arXiv, cond-mat/0011506
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