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Pricing options on realized variance

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Author Info

  • Peter Carr
  • Hélyette Geman

    ()

  • Dilip Madan

    ()

  • Marc Yor

    ()

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    Abstract

    Models which hypothesize that returns are pure jump processes with independent increments have been shown to be capable of capturing the observed variation of market prices of vanilla stock options across strike and maturity. In this paper, these models are employed to derive in closed form the prices of derivatives written on future realized quadratic variation. Alternative work on pricing derivatives on quadratic variation has alternatively assumed that the underlying returns process is continuous over time. We compare the model values of derivatives on quadratic variation for the two types of models and find substantial differences. Copyright Springer-Verlag Berlin/Heidelberg 2005

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    File URL: http://hdl.handle.net/10.1007/s00780-005-0155-x
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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 9 (2005)
    Issue (Month): 4 (October)
    Pages: 453-475

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    Handle: RePEc:spr:finsto:v:9:y:2005:i:4:p:453-475

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    Web page: http://www.springerlink.com/content/101164/

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    Related research

    Keywords: Options on variance swaps; options on time changes; self decomposability and its hierarchy;

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    Citations

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    Cited by:
    1. Leunglung Chan & Eckhard Platen, 2010. "Exact Pricing and Hedging Formulas of Long Dated Variance Swaps under a $3/2$ Volatility Model," Papers 1007.2968, arXiv.org, revised Jan 2011.
    2. Nicolas Merener, 2009. "Swap Rate Variance Swaps," Business School Working Papers 2009-02, Universidad Torcuato Di Tella.
    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. Pospisil, Libor & Vecer, Jan & Xu, Mingxin, 2007. "Tradable measure of risk," MPRA Paper 5059, University Library of Munich, Germany.
    5. Peter Carr & Roger Lee, 2013. "Variation and share-weighted variation swaps on time-changed Lévy processes," Finance and Stochastics, Springer, vol. 17(4), pages 685-716, October.
    6. Giovanni Salvi & Anatoliy V. Swishchuk, 2012. "Modeling and Pricing of Covariance and Correlation Swaps for Financial Markets with Semi-Markov Volatilities," Papers 1205.5565, arXiv.org.
    7. Andrey Itkin & Peter Carr, 2010. "Pricing swaps and options on quadratic variation under stochastic time change models—discrete observations case," Review of Derivatives Research, Springer, vol. 13(2), pages 141-176, July.
    8. Ole E. Barndorff-Nielsen & Neil Shephard, 2005. "Variation, jumps, market frictions and high frequency data in financial econometrics," OFRC Working Papers Series 2005fe08, Oxford Financial Research Centre.
    9. Dotsis, George & Psychoyios, Dimitris & Skiadopoulos, George, 2007. "An empirical comparison of continuous-time models of implied volatility indices," Journal of Banking & Finance, Elsevier, vol. 31(12), pages 3584-3603, December.
    10. Lan Zhang, 2012. "Implied and realized volatility: empirical model selection," Annals of Finance, Springer, vol. 8(2), pages 259-275, May.
    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.
    12. Jan Baldeaux & Alexander Badran, 2012. "Consistent Modeling of VIX and Equity Derivatives Using a 3/2 plus Jumps Model," Papers 1203.5903, arXiv.org, revised Aug 2012.
    13. Jesús P. Colino, 2008. "New stochastic processes to model interest rates : LIBOR additive processes," Statistics and Econometrics Working Papers ws085316, Universidad Carlos III, Departamento de Estadística y Econometría.
    14. Andrey Itkin & Peter Carr, 2012. "Using Pseudo-Parabolic and Fractional Equations for Option Pricing in Jump Diffusion Models," Computational Economics, Society for Computational Economics, vol. 40(1), pages 63-104, June.
    15. Akihiko Takahashi & Yukihiro Tsuzuki & Akira Yamazaki, 2009. "Hedging European Derivatives with the Polynomial Variance Swap under Uncertain Volatility Environments," CARF F-Series CARF-F-161, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    16. Peter Carr & Roger Lee, 2010. "Hedging variance options on continuous semimartingales," Finance and Stochastics, Springer, vol. 14(2), pages 179-207, April.
    17. Chourdakis, Kyriakos & Dotsis, George, 2011. "Maximum likelihood estimation of non-affine volatility processes," Journal of Empirical Finance, Elsevier, vol. 18(3), pages 533-545, June.
    18. Jesús P. Colino & Francisco J. Nogales & Winfried Stute, 2008. "LIBOR additive model calibration to swaptions markets," Statistics and Econometrics Working Papers ws085619, Universidad Carlos III, Departamento de Estadística y Econometría.

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