IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1103.2310.html
   My bibliography  Save this paper

Convex order of discrete, continuous and predictable quadratic variation & applications to options on variance

Author

Listed:
  • Martin Keller-Ressel
  • Claus Griessler

Abstract

We consider a square-integrable semimartingale and investigate the convex order relations between its discrete, continuous and predictable quadratic variation. As the main results, we show that if the semimartingale has conditionally independent increments and symmetric jump measure, then its discrete realized variance dominates its quadratic variation in increasing convex order. The results have immediate applications to the pricing of options on realized variance. For a class of models including time-changed Levy models and Sato processes with symmetric jumps our results show that options on variance are typically underpriced, if quadratic variation is substituted for the discretely sampled realized variance.

Suggested Citation

  • Martin Keller-Ressel & Claus Griessler, 2011. "Convex order of discrete, continuous and predictable quadratic variation & applications to options on variance," Papers 1103.2310, arXiv.org, revised Oct 2012.
    • Handle: RePEc:arx:papers:1103.2310
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1103.2310
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Peter Carr & Hélyette Geman & Dilip B. Madan & Marc Yor, 2003. "Stochastic Volatility for Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 345-382, July.
    2. 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.
    3. repec:dau:papers:123456789/1380 is not listed on IDEAS
    4. repec:dau:papers:123456789/1392 is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Carole Bernard & Zhenyu Cui, 2013. "Prices and Asymptotics for Discrete Variance Swaps," Papers 1305.7092, arXiv.org.
    2. Carole Bernard & Zhenyu Cui & Don McLeish, 2013. "Convergence of the discrete variance swap in time-homogeneous diffusion models," Papers 1310.0099, arXiv.org.
    3. Bernard, Carole & Jiang, Xiao & Wang, Ruodu, 2014. "Risk aggregation with dependence uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 93-108.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wendong Zheng & Chi Hung Yuen & Yue Kuen Kwok, 2016. "Recursive Algorithms For Pricing Discrete Variance Options And Volatility Swaps Under Time-Changed Lévy Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(02), pages 1-29, March.
    2. Anatoliy Swishchuk, 2013. "Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8660, December.
    3. Leonidas S. Rompolis & Elias Tzavalis, 2017. "Pricing and hedging contingent claims using variance and higher order moment swaps," Quantitative Finance, Taylor & Francis Journals, vol. 17(4), pages 531-550, April.
    4. Todorov, Viktor & Zhang, Yang, 2023. "Bias reduction in spot volatility estimation from options," Journal of Econometrics, Elsevier, vol. 234(1), pages 53-81.
    5. Aleksandar Mijatovi'c & Martijn Pistorius, 2009. "Exotic derivatives under stochastic volatility models with jumps," Papers 0912.2595, arXiv.org, revised Oct 2010.
    6. Fu, Qi & So, Jacky Yuk-Chow & Li, Xiaotong, 2024. "Stable paretian distribution, return generating processes and habit formation—The implication for equity premium puzzle," The North American Journal of Economics and Finance, Elsevier, vol. 70(C).
    7. Zura Kakushadze, 2016. "Volatility Smile as Relativistic Effect," Papers 1610.02456, arXiv.org, revised Feb 2017.
    8. Martijn Pistorius & Johannes Stolte, 2012. "Fast computation of vanilla prices in time-changed models and implied volatilities using rational approximations," Papers 1203.6899, arXiv.org.
    9. Panov, Vladimir, 2019. "Some properties of the one-dimensional subordinated stable model," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 80-84.
    10. Alexander, Carol & Rauch, Johannes, 2021. "A general property for time aggregation," European Journal of Operational Research, Elsevier, vol. 291(2), pages 536-548.
    11. Igor Halperin & Andrey Itkin, 2013. "USLV: Unspanned Stochastic Local Volatility Model," Papers 1301.4442, arXiv.org, revised Mar 2013.
    12. Hanousek, Jan & Novotný, Jan, 2012. "Price jumps in Visegrad-country stock markets: An empirical analysis," Emerging Markets Review, Elsevier, vol. 13(2), pages 184-201.
    13. Shaw, Charles, 2018. "Regime-Switching And Levy Jump Dynamics In Option-Adjusted Spreads," MPRA Paper 94154, University Library of Munich, Germany, revised 27 May 2019.
    14. Dilip B. Madan & Sofie Reyners & Wim Schoutens, 2019. "Advanced model calibration on bitcoin options," Digital Finance, Springer, vol. 1(1), pages 117-137, November.
    15. Kim, Seong-Tae & Kim, Jeong-Hoon, 2020. "Stochastic elasticity of vol-of-vol and pricing of variance swaps," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 420-440.
    16. Hanousek Jan & Kočenda Evžen & Novotný Jan, 2012. "The identification of price jumps," Monte Carlo Methods and Applications, De Gruyter, vol. 18(1), pages 53-77, January.
    17. Hounyo, Ulrich & Varneskov, Rasmus T., 2017. "A local stable bootstrap for power variations of pure-jump semimartingales and activity index estimation," Journal of Econometrics, Elsevier, vol. 198(1), pages 10-28.
    18. Brignone, Riccardo & Gonzato, Luca & Lütkebohmert, Eva, 2023. "Efficient Quasi-Bayesian Estimation of Affine Option Pricing Models Using Risk-Neutral Cumulants," Journal of Banking & Finance, Elsevier, vol. 148(C).
    19. Geman, Hélyette, 2005. "From measure changes to time changes in asset pricing," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2701-2722, November.
    20. Ilze Kalnina & Dacheng Xiu, 2017. "Nonparametric Estimation of the Leverage Effect: A Trade-Off Between Robustness and Efficiency," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 384-396, January.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1103.2310. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.