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Limit Theorem for a Modified Leland Hedging Strategy under Constant Transaction Costs rate

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  • Sebastien Darses

    (LATP - Laboratoire d'Analyse, Topologie, Probabilités - Université Paul Cézanne - Aix-Marseille 3 - Université de Provence - Aix-Marseille 1 - CNRS - Centre National de la Recherche Scientifique)

  • Emmanuel Denis

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

Abstract

We study the Leland model for hedging portfolios in the presence of a constant proportional transaction costs coefficient. The modified Leland's strategy recently defined by the second author, contrarily to the classical one, ensures the asymptotic replication of a large class of payoff. In this setting, we prove a limit theorem for the deviation between the real portfolio and the payoff. As Pergamenshchikov did in the framework of the usual Leland's strategy, we identify the rate of convergence and the associated limit distribution. This rate turns out to be improved using the modified strategy and non periodic revision dates.

Suggested Citation

  • Sebastien Darses & Emmanuel Denis, 2010. "Limit Theorem for a Modified Leland Hedging Strategy under Constant Transaction Costs rate," Working Papers hal-00467704, HAL.
    • Handle: RePEc:hal:wpaper:hal-00467704
    Note: View the original document on HAL open archive server: https://hal.science/hal-00467704
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    References listed on IDEAS

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    1. Yuri M. Kabanov & (*), Mher M. Safarian, 1997. "On Leland's strategy of option pricing with transactions costs," Finance and Stochastics, Springer, vol. 1(3), pages 239-250.
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    Cited by:

    1. Peili Lu & Jiaqi Shen & Liheng Zhao & Haoyang Qin & Xunzhi Liu & Zhongxing Ye, 2020. "Price risk management by using dynamic hedging based on advanced Black–Scholes model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 1-14, March.

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    Keywords

    Asymptotic hedging; Leland-Lott strategy; Transaction costs; Martingale limit theorem.; Martingale limit theorem;
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