IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0174133.html
   My bibliography  Save this article

A note on contracts on quadratic variation

Author

Listed:
  • Carl Lindberg

Abstract

Given a Black stochastic volatility model for a future F, and a function g, we show that the price of 1 2 ∫ 0 T g ( t , F ( t ) ) F 2 ( t ) σ 2 ( t ) d t can be represented by portfolios of put and call options. This generalizes the classical representation result for the variance swap. Further, in a local volatility model, we give an example based on Dupire’s formula which shows how the theorem can be used to design variance related contracts with desirable characteristics.

Suggested Citation

  • Carl Lindberg, 2017. "A note on contracts on quadratic variation," PLOS ONE, Public Library of Science, vol. 12(3), pages 1-5, March.
    • Handle: RePEc:plo:pone00:0174133
    DOI: 10.1371/journal.pone.0174133
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0174133
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0174133&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0174133?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Tim Bollerslev & George Tauchen & Hao Zhou, 2009. "Expected Stock Returns and Variance Risk Premia," Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4463-4492, November.
    2. Tim Bollerslev & Viktor Todorov, 2011. "Tails, Fears, and Risk Premia," Journal of Finance, American Finance Association, vol. 66(6), pages 2165-2211, December.
    3. Bekaert, Geert & Hoerova, Marie, 2014. "The VIX, the variance premium and stock market volatility," Journal of Econometrics, Elsevier, vol. 183(2), pages 181-192.
    4. Filipović, Damir & Gourier, Elise & Mancini, Loriano, 2016. "Quadratic variance swap models," Journal of Financial Economics, Elsevier, vol. 119(1), pages 44-68.
    5. Itamar Drechsler & Amir Yaron, 2011. "What's Vol Got to Do with It," Review of Financial Studies, Society for Financial Studies, vol. 24(1), pages 1-45.
    6. Egloff, Daniel & Leippold, Markus & Wu, Liuren, 2010. "The Term Structure of Variance Swap Rates and Optimal Variance Swap Investments," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 45(5), pages 1279-1310, October.
    7. Peter Carr & Liuren Wu, 2009. "Variance Risk Premiums," Review of Financial Studies, Society for Financial Studies, vol. 22(3), pages 1311-1341, March.
    Full references (including those not matched with items on IDEAS)

    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. Hollstein, Fabian & Wese Simen, Chardin, 2020. "Variance risk: A bird’s eye view," Journal of Econometrics, Elsevier, vol. 215(2), pages 517-535.
    2. Konstantinidi, Eirini & Skiadopoulos, George, 2016. "How does the market variance risk premium vary over time? Evidence from S&P 500 variance swap investment returns," Journal of Banking & Finance, Elsevier, vol. 62(C), pages 62-75.
    3. Konstantinidi, Eirini & Skiadopoulos, George, 2016. "How does the market variance risk premium vary over time? Evidence from S&P 500 variance swap investment returns," Journal of Banking & Finance, Elsevier, vol. 62(C), pages 62-75.
    4. Filipović, Damir & Gourier, Elise & Mancini, Loriano, 2016. "Quadratic variance swap models," Journal of Financial Economics, Elsevier, vol. 119(1), pages 44-68.
    5. Rombouts, Jeroen V.K. & Stentoft, Lars & Violante, Francesco, 2020. "Variance swap payoffs, risk premia and extreme market conditions," Econometrics and Statistics, Elsevier, vol. 13(C), pages 106-124.
    6. Rombouts, Jeroen V.K. & Stentoft, Lars & Violante, Francesco, 2020. "Dynamics of variance risk premia: A new model for disentangling the price of risk," Journal of Econometrics, Elsevier, vol. 217(2), pages 312-334.
    7. Jeroen V.K. Rombouts & Lars Stentoft & Francesco Violante, 2017. "Dynamics of Variance Risk Premia, Investors' Sentiment and Return Predictability," CREATES Research Papers 2017-10, Department of Economics and Business Economics, Aarhus University.
    8. Bardgett, Chris & Gourier, Elise & Leippold, Markus, 2019. "Inferring volatility dynamics and risk premia from the S&P 500 and VIX markets," Journal of Financial Economics, Elsevier, vol. 131(3), pages 593-618.
    9. Andreou, Elena & Ghysels, Eric, 2021. "Predicting the VIX and the volatility risk premium: The role of short-run funding spreads Volatility Factors," Journal of Econometrics, Elsevier, vol. 220(2), pages 366-398.
    10. Erik Vogt, 2014. "Option-implied term structures," Staff Reports 706, Federal Reserve Bank of New York.
    11. Amengual, Dante & Xiu, Dacheng, 2018. "Resolution of policy uncertainty and sudden declines in volatility," Journal of Econometrics, Elsevier, vol. 203(2), pages 297-315.
    12. Caporin, Massimiliano & Kolokolov, Aleksey & Renò, Roberto, 2017. "Systemic co-jumps," Journal of Financial Economics, Elsevier, vol. 126(3), pages 563-591.
    13. Bollerslev, Tim & Todorov, Viktor & Xu, Lai, 2015. "Tail risk premia and return predictability," Journal of Financial Economics, Elsevier, vol. 118(1), pages 113-134.
    14. Peter Van Tassel & Erik Vogt, 2016. "Global variance term premia and intermediary risk appetite," Staff Reports 789, Federal Reserve Bank of New York.
    15. Aït-Sahalia, Yacine & Karaman, Mustafa & Mancini, Loriano, 2020. "The term structure of equity and variance risk premia," Journal of Econometrics, Elsevier, vol. 219(2), pages 204-230.
    16. Buss, Adrian & Vilkov, Grigory & ,, 2018. "Expected Correlation and Future Market Returns," CEPR Discussion Papers 12760, C.E.P.R. Discussion Papers.
    17. Andersen, Torben G. & Todorov, Viktor & Ubukata, Masato, 2021. "Tail risk and return predictability for the Japanese equity market," Journal of Econometrics, Elsevier, vol. 222(1), pages 344-363.
    18. K. Victor Chow & Wanjun Jiang & Bingxin Li & Jingrui Li, 2020. "Decomposing the VIX: Implications for the predictability of stock returns," The Financial Review, Eastern Finance Association, vol. 55(4), pages 645-668, November.
    19. Held, Matthias & Kapraun, Julia & Omachel, Marcel & Thimme, Julian, 2020. "Up- and downside variance risk premia in global equity markets," Journal of Banking & Finance, Elsevier, vol. 118(C).
    20. Oikonomou, Ioannis & Stancu, Andrei & Symeonidis, Lazaros & Wese Simen, Chardin, 2019. "The information content of short-term options," Journal of Financial Markets, Elsevier, vol. 46(C).

    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:plo:pone00:0174133. 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: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    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.