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Rebalancing static super-replications

Author

Listed:
  • Akihiko Takahashi

    (Graduate School of Economics, University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan)

  • Yukihiro Tsuzuki

    (Graduate School of Economics, University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan)

Abstract

This paper proposes a trading strategy that dynamically rebalances static super-replicating portfolios, which is very useful for both investment and hedging strategies. In order to investigate general properties of the strategy, we derive the Doob–Meyer decomposition for the value process without any specifications of models under the continuous processes of the underlying variables. In particular, we find that the increasing part of the decomposition characterizes the performance of the strategy. Also, we obtain more concrete features for cross-currency and one-touch options based on our general framework. Moreover, numerical examples for cross-currency options demonstrate the effectiveness of our strategy for investment and hedging.

Suggested Citation

  • Akihiko Takahashi & Yukihiro Tsuzuki, 2017. "Rebalancing static super-replications," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-23, March.
    • Handle: RePEc:wsi:ijfexx:v:04:y:2017:i:01:n:s2424786317500037
    DOI: 10.1142/S2424786317500037
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    References listed on IDEAS

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    1. Yukihiro Tsuzuki, 2012. "On the Optimal Super- and Sub-Hedging Strategies," CARF F-Series CARF-F-300, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Aug 2013.
    2. Chung, San-Lin & Wang, Yaw-Huei, 2008. "Bounds and prices of currency cross-rate options," Journal of Banking & Finance, Elsevier, vol. 32(5), pages 631-642, May.
    3. Haydyn Brown & David Hobson & L. C. G. Rogers, 2001. "Robust Hedging of Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 11(3), pages 285-314, July.
    4. Yukihiro Tsuzuki, 2013. "On Optimal Super-Hedging And Sub-Hedging Strategies," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(06), pages 1-17.
    5. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-186, March.
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    Cited by:

    1. Robin Dee & Armin Fügenschuh & George Kaimakamis, 2021. "The Unit Re-Balancing Problem," Mathematics, MDPI, vol. 9(24), pages 1-19, December.

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