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Model independent hedging strategies for variance swaps

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  • David Hobson
  • Martin Klimmek
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    Abstract

    A variance swap is a derivative with a path-dependent payoff which allows investors to take positions on the future variability of an asset. In the idealised setting of a continuously monitored variance swap written on an asset with continuous paths it is well known that the variance swap payoff can be replicated exactly using a portfolio of puts and calls and a dynamic position in the asset. This fact forms the basis of the VIX contract. But what if we are in the more realistic setting where the contract is based on discrete monitoring, and the underlying asset may have jumps? We show that it is possible to derive model-independent, no-arbitrage bounds on the price of the variance swap, and corresponding sub- and super-replicating strategies. Further, we characterise the optimal bounds. The form of the hedges depends crucially on the kernel used to define the variance swap.

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    File URL: http://arxiv.org/pdf/1104.4010
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1104.4010.

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    Date of creation: Apr 2011
    Date of revision: May 2011
    Handle: RePEc:arx:papers:1104.4010

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    Web page: http://arxiv.org/

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    1. Robert Jarrow & Younes Kchia & Martin Larsson & Philip Protter, 2013. "Discretely sampled variance and volatility swaps versus their continuous approximations," Finance and Stochastics, Springer, vol. 17(2), pages 305-324, April.
    2. Ian Martin, 2011. "Simple Variance Swaps," NBER Working Papers 16884, National Bureau of Economic Research, Inc.
    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.
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    Cited by:
    1. B. Acciaio & M. Beiglb\"ock & F. Penkner & W. Schachermayer & J. Temme, 2012. "A trajectorial interpretation of Doob's martingale inequalities," Papers 1202.0447, arXiv.org, revised Jul 2013.

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