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Option Pricing And Hedging With Temporal Correlations

Author

Listed:
  • 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;
    Science & Finance, The Research division of Capital Fund Management, 109-111 rue Victor-Hugo, 92532 Levallois Cedex, France)

  • MARC POTTERS

    (Science & Finance, The Research division of Capital Fund Management, 109-111 rue Victor-Hugo, 92532 Levallois Cedex, France)

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.

Suggested Citation

  • Lorenzo Cornalba & Jean-Philippe Bouchaud & Marc Potters, 2002. "Option Pricing And Hedging With Temporal Correlations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 307-320.
    • Handle: RePEc:wsi:ijtafx:v:05:y:2002:i:03:n:s0219024902001444
    DOI: 10.1142/S0219024902001444
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    Citations

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    Cited by:

    1. Tung-Lam Dao & Trung-Tu Nguyen & Cyril Deremble & Yves Lemp'eri`ere & Jean-Philippe Bouchaud & Marc Potters, 2016. "Tail protection for long investors: Trend convexity at work," Papers 1607.02410, arXiv.org.
    2. Dowd, Kevin & Buckner, Dean & Blake, David & Fry, John, 2019. "The valuation of no-negative equity guarantees and equity release mortgages," Economics Letters, Elsevier, vol. 184(C).
    3. Bruno R'emillard & Sylvain Rubenthaler, 2012. "Optimal hedging in discrete time," Papers 1211.5035, arXiv.org.

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