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Conservative Delta Hedging under Transaction Costs

In: Recent Advances In Financial Engineering 2011

Author

Listed:
  • Masaaki Fukasawa

    (Department of Mathematics, Osaka University, Japan)

Abstract

Explicit robust hedging strategies for convex or concave payoffs under a continuous semimartingale model with uncertainty and small transaction costs are constructed. In an asymptotic sense, the upper and lower bounds of the cumulative volatility enable us to super-hedge convex and concave payoffs respectively. The idea is a combination of Mykland's conservative delta hedging and Leland's enlarging volatility. We use a specific sequence of stopping times as rebalancing dates, which can be superior to equidistant one even when there is no model uncertainty. A central limit theorem for the super-hedging error as the coefficient of linear transaction costs tends to zero is proved. The mean squared error is also studied.

Suggested Citation

  • Masaaki Fukasawa, 2012. "Conservative Delta Hedging under Transaction Costs," World Scientific Book Chapters, in: Akihiko Takahashi & Yukio Muromachi & Hidetaka Nakaoka (ed.), Recent Advances In Financial Engineering 2011, chapter 4, pages 55-72, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789814407335_0004
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    Citations

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    Cited by:

    1. Romuald Elie & Emmanuel Lépinette, 2015. "Approximate hedging for nonlinear transaction costs on the volume of traded assets," Finance and Stochastics, Springer, vol. 19(3), pages 541-581, July.
    2. Masaaki Fukasawa, 2012. "Efficient Discretization of Stochastic Integrals," Papers 1204.0637, arXiv.org.
    3. Masaaki Fukasawa, 2014. "Efficient discretization of stochastic integrals," Finance and Stochastics, Springer, vol. 18(1), pages 175-208, January.
    4. Jiatu Cai & Masaaki Fukasawa, 2014. "Asymptotic replication with modified volatility under small transaction costs," Papers 1408.5677, arXiv.org.
    5. Jiatu Cai & Masaaki Fukasawa, 2016. "Asymptotic replication with modified volatility under small transaction costs," Finance and Stochastics, Springer, vol. 20(2), pages 381-431, April.

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