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Beyond the Leland strategies

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  • Emmanuel Lepinette
  • Amal Omrani

Abstract

In the Black and Scholes model with proportional transaction costs, the Leland strategy allows to asymptotically super-replicate the European Call option as the number of revision dates converges to + infinity and the transaction costs rate tends rapidly to 0. This method relies heavily on the explicit expression of the delta-hedging strategy in the Black and Scholes model where the volatility is enlarged to compensate for the transaction costs. We solve the same problem of super-hedging but for a general model with an arbitrary fixed number of revision dates and arbitrary fixed transaction costs rates. Moreover, our approach does not need the existence of a risk-neutral probability measure and is (almost) model free and easily implementable from real data.

Suggested Citation

  • Emmanuel Lepinette & Amal Omrani, 2025. "Beyond the Leland strategies," Papers 2503.02419, arXiv.org.
    • Handle: RePEc:arx:papers:2503.02419
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    References listed on IDEAS

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    1. repec:dau:papers:123456789/4654 is not listed on IDEAS
    2. 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.
    3. Emmanuel Denis & Yuri Kabanov, 2010. "Mean square error for the Leland–Lott hedging strategy: convex pay-offs," Finance and Stochastics, Springer, vol. 14(4), pages 625-667, December.
    4. Meriam El Mansour & Emmanuel Lépinette, 2020. "Conditional Interior and Conditional Closure of Random Sets," Journal of Optimization Theory and Applications, Springer, vol. 187(2), pages 356-369, November.
    5. Thai Huu Nguyen & Serguei Pergamenshchikov, 2017. "Approximate Hedging Problem With Transaction Costs In Stochastic Volatility Markets," Mathematical Finance, Wiley Blackwell, vol. 27(3), pages 832-865, July.
    6. Emmanuel Denis, 2010. "Approximate Hedging of Contingent Claims under Transaction Costs for General Pay-offs," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(6), pages 491-518.
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