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Option pricing and hedging with temporal correlations

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  • Lorenzo Cornalba
  • Jean-Philippe Bouchaud

    (Science & Finance, Capital Fund Management
    CEA Saclay;)

  • Marc Potters

    (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.

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Paper provided by Science & Finance, Capital Fund Management in its series Science & Finance (CFM) working paper archive with number 500030.

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Date of creation: Nov 2000
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Publication status: Published in International Journal of Theoretical and Applied Finance 5 (3) (2002) 307-320
Handle: RePEc:sfi:sfiwpa:500030

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