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The Effect Of Jumps And Discrete Sampling On Volatility And Variance Swaps

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  • MARK BROADIE

    ()
    (Columbia University, Graduate School of Business, 3022 Broadway, New York, NY, 10027-6902, USA)

  • ASHISH JAIN

    ()
    (Columbia University, Graduate School of Business, 3022 Broadway, New York, NY, 10027-6902, USA)

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    Abstract

    We investigate the effect of discrete sampling and asset price jumps on fair variance and volatility swap strikes. Fair discrete volatility strikes and fair discrete variance strikes are derived in different models of the underlying evolution of the asset price: the Black-Scholes model, the Heston stochastic volatility model, the Merton jump-diffusion model and the Bates and Scott stochastic volatility and jump model. We determine fair discrete and continuous variance strikes analytically and fair discrete and continuous volatility strikes using simulation and variance reduction techniques and numerical integration techniques in all models. Numerical results show that the well-known convexity correction formula may not provide a good approximation of fair volatility strikes in models with jumps in the underlying asset. For realistic contract specifications and model parameters, we find that the effect of discrete sampling is typically small while the effect of jumps can be significant.

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    Bibliographic Info

    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

    Volume (Year): 11 (2008)
    Issue (Month): 08 ()
    Pages: 761-797

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    Handle: RePEc:wsi:ijtafx:v:11:y:2008:i:08:p:761-797

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    Related research

    Keywords: Variance swaps; volatility swaps; VIX; stochastic volatility; jump models;

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    Cited by:
    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. Jan Novotny, 2010. "Price Jumps in Visegrad Country Stock Markets: An Empirical Analysis," CERGE-EI Working Papers wp412, The Center for Economic Research and Graduate Education - Economic Institute, Prague.
    3. Jan Hanousek & Evzen Kocenda & Jan Novotny, 2011. "The Identification of Price Jumps," CERGE-EI Working Papers wp434, The Center for Economic Research and Graduate Education - Economic Institute, Prague.
    4. Jan Hanousek & Evžen Kočenda & Jan Novotný, 2013. "Price Jumps on European Stock Markets," William Davidson Institute Working Papers Series wp1059, William Davidson Institute at the University of Michigan.
    5. Jan Novotný & Jan Hanousek & Evžen Kočenda, 2013. "Price Jump Indicators: Stock Market Empirics During the Crisis," William Davidson Institute Working Papers Series wp1050, William Davidson Institute at the University of Michigan.
    6. Kaeck, Andreas & Alexander, Carol, 2012. "Volatility dynamics for the S&P 500: Further evidence from non-affine, multi-factor jump diffusions," Journal of Banking & Finance, Elsevier, vol. 36(11), pages 3110-3121.
    7. David Hobson & Martin Klimmek, 2012. "Model-independent hedging strategies for variance swaps," Finance and Stochastics, Springer, vol. 16(4), pages 611-649, October.
    8. Hynek Lavicka & Tomas Lichard & Jan Novotny, 2014. "Sand in the Wheels or Wheels in the Sand? Tobin Taxes and Market Crashes," CERGE-EI Working Papers wp511, The Center for Economic Research and Graduate Education - Economic Institute, Prague.
    9. 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.
    10. Carol Alexander & Johannes Rauch, 2014. "Discretisation-Invariant Swaps," Papers 1404.1351, arXiv.org.
    11. Martin Keller-Ressel & Johannes Muhle-Karbe, 2013. "Asymptotic and exact pricing of options on variance," Finance and Stochastics, Springer, vol. 17(1), pages 107-133, January.

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