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Model-independent hedging strategies for variance swaps

  • David Hobson

    ()

  • Martin Klimmek

    ()

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    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. Copyright Springer-Verlag 2012

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    File URL: http://hdl.handle.net/10.1007/s00780-012-0190-3
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    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 16 (2012)
    Issue (Month): 4 (October)
    Pages: 611-649

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    Handle: RePEc:spr:finsto:v:16:y:2012:i:4:p:611-649
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    1. Ian Martin, 2011. "Simple Variance Swaps," NBER Working Papers 16884, National Bureau of Economic Research, Inc.
    2. David G. Hobson, 1998. "Robust hedging of the lookback option," Finance and Stochastics, Springer, vol. 2(4), pages 329-347.
    3. Peter Carr & Roger Lee & Liuren Wu, 2012. "Variance swaps on time-changed Lévy processes," Finance and Stochastics, Springer, vol. 16(2), pages 335-355, April.
    4. Bick, Avi & Willinger, Walter, 1994. "Dynamic spanning without probabilities," Stochastic Processes and their Applications, Elsevier, vol. 50(2), pages 349-374, April.
    5. Mark Broadie & Ashish Jain, 2008. "The Effect Of Jumps And Discrete Sampling On Volatility And Variance Swaps," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(08), pages 761-797.
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