IDEAS home Printed from https://ideas.repec.org/a/kap/revdev/v27y2024i1d10.1007_s11147-023-09200-x.html
   My bibliography  Save this article

Martingale defects in the volatility surface and bubble conditions in the underlying

Author

Listed:
  • Philip Stahl

    (Technische Universität Darmstadt
    Deka Investment GmbH
    IQAM Research GmbH)

  • Jérôme Blauth

    (Deka Investment GmbH
    IQAM Research GmbH)

Abstract

The martingale theory of bubbles enables testing for asset price bubbles by analyzing option prices. As recently shown by Piiroinen et al. (Asset price bubbles: an option-based indicator, 2018), the SABR model is a strict local martingale when its parameterization implies a positive correlation between stock and option prices. We operationalize this theoretical result and analyze stock price bubbles in 2576 stocks over 26 years. Martingale defect conditions are absorbed quickly by options markets, but identify high proportions in significant and permanent changes in distribution of price returns, option trading activity, short interest in the underlying, and institutional ownership. These results confirm many common assumptions about stock price bubbles. These bubbles are temporally clustered, and tend to occur in periods of positive market development. Martingale defects are rare in market corrections, which indicates that they are a result of overoptimistic speculation.

Suggested Citation

  • Philip Stahl & Jérôme Blauth, 2024. "Martingale defects in the volatility surface and bubble conditions in the underlying," Review of Derivatives Research, Springer, vol. 27(1), pages 85-111, April.
    • Handle: RePEc:kap:revdev:v:27:y:2024:i:1:d:10.1007_s11147-023-09200-x
    DOI: 10.1007/s11147-023-09200-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11147-023-09200-x
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11147-023-09200-x?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Mark Loewenstein & Gregory A. Willard, 2000. "Local martingales, arbitrage, and viability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 16(1), pages 135-161.
    2. Hannes Mohrschladt & Judith C. Schneider, 2021. "Idiosyncratic volatility, option-based measures of informed trading, and investor attention," Review of Derivatives Research, Springer, vol. 24(3), pages 197-220, October.
    3. Robert A. Jarrow, 2008. "Market Manipulation, Bubbles, Corners, and Short Squeezes," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 6, pages 105-130, World Scientific Publishing Co. Pte. Ltd..
    4. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    5. John R. Conlon, 2004. "Simple Finite Horizon Bubbles Robust to Higher Order Knowledge," Econometrica, Econometric Society, vol. 72(3), pages 927-936, May.
    6. Alexander Cox & David Hobson, 2005. "Local martingales, bubbles and option prices," Finance and Stochastics, Springer, vol. 9(4), pages 477-492, October.
    7. Francesca Biagini & Lukas Gonon & Andrea Mazzon & Thilo Meyer-Brandis, 2022. "Detecting asset price bubbles using deep learning," Papers 2210.01726, arXiv.org, revised Jun 2024.
    8. Camerer, Colin, 1989. "Bubbles and Fads in Asset Prices," Journal of Economic Surveys, Wiley Blackwell, vol. 3(1), pages 3-41.
    9. Cheridito, Patrick & Filipovic, Damir & Kimmel, Robert L., 2007. "Market price of risk specifications for affine models: Theory and evidence," Journal of Financial Economics, Elsevier, vol. 83(1), pages 123-170, January.
    10. Francesca Biagini & Hans Föllmer & Sorin Nedelcu, 2014. "Shifting martingale measures and the birth of a bubble as a submartingale," Finance and Stochastics, Springer, vol. 18(2), pages 297-326, April.
    11. Robert A. Jarrow & Simon S. Kwok, 2021. "Inferring financial bubbles from option data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(7), pages 1013-1046, November.
    12. Francesca Biagini & Andrea Mazzon & Ari-Pekka Perkkio, 2020. "Optional projection under equivalent local martingale measures," Papers 2003.09940, arXiv.org.
    13. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    14. Petteri Piiroinen & Lassi Roininen & Tobias Schoden & Martin Simon, 2018. "Asset Price Bubbles: An Option-based Indicator," Papers 1805.07403, arXiv.org, revised Jul 2018.
    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. Robert A. Jarrow, 2015. "Asset Price Bubbles," Annual Review of Financial Economics, Annual Reviews, vol. 7(1), pages 201-218, December.
    2. Martin HERDEGEN & Martin SCHWEIZER, 2015. "Economics-Based Financial Bubbles (and Why They Imply Strict Local Martingales)," Swiss Finance Institute Research Paper Series 15-05, Swiss Finance Institute.
    3. Fergusson, Kevin, 2020. "Less-Expensive Valuation And Reserving Of Long-Dated Variable Annuities When Interest Rates And Mortality Rates Are Stochastic," ASTIN Bulletin, Cambridge University Press, vol. 50(2), pages 381-417, May.
    4. Robert A. Jarrow & Simon S. Kwok, 2021. "Inferring financial bubbles from option data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(7), pages 1013-1046, November.
    5. repec:uts:finphd:40 is not listed on IDEAS
    6. Kevin John Fergusson, 2018. "Less-Expensive Pricing and Hedging of Extreme-Maturity Interest Rate Derivatives and Equity Index Options Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2018, January-A.
    7. Constantinos Kardaras, 2012. "Valuation and parities for exchange options," Papers 1206.3220, arXiv.org, revised Nov 2014.
    8. Petteri Piiroinen & Lassi Roininen & Tobias Schoden & Martin Simon, 2018. "Asset Price Bubbles: An Option-based Indicator," Papers 1805.07403, arXiv.org, revised Jul 2018.
    9. Martin Herdegen & Martin Schweizer, 2016. "Strong Bubbles And Strict Local Martingales," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-44, June.
    10. Robert A. Jarrow & Simon S. Kwok, 2023. "An explosion time characterization of asset price bubbles," International Review of Finance, International Review of Finance Ltd., vol. 23(2), pages 469-479, June.
    11. Hardy Hulley, 2009. "Strict Local Martingales in Continuous Financial Market Models," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 19, July-Dece.
    12. Robert Jarrow & Philip Protter, 2011. "Foreign currency bubbles," Review of Derivatives Research, Springer, vol. 14(1), pages 67-83, April.
    13. Alexander M. G. Cox & Zhaoxu Hou & Jan Obloj, 2014. "Robust pricing and hedging under trading restrictions and the emergence of local martingale models," Papers 1406.0551, arXiv.org, revised Jun 2015.
    14. Francesca Biagini & Lukas Gonon & Andrea Mazzon & Thilo Meyer-Brandis, 2022. "Detecting asset price bubbles using deep learning," Papers 2210.01726, arXiv.org, revised Jun 2024.
    15. Weihan Li & Jin E. Zhang & Xinfeng Ruan & Pakorn Aschakulporn, 2024. "An empirical study on the early exercise premium of American options: Evidence from OEX and XEO options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(7), pages 1117-1153, July.
    16. Boyarchenko, Svetlana & Levendorskii[caron], Sergei, 2007. "Optimal stopping made easy," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 201-217, February.
    17. Robert C. Merton, 2006. "Paul Samuelson and Financial Economics," The American Economist, Sage Publications, vol. 50(2), pages 9-31, October.
    18. Ammann, Manuel & Kind, Axel & Wilde, Christian, 2003. "Are convertible bonds underpriced? An analysis of the French market," Journal of Banking & Finance, Elsevier, vol. 27(4), pages 635-653, April.
    19. Kim, Amy M. & Li, Huanan, 2020. "Incorporating the impacts of climate change in transportation infrastructure decision models," Transportation Research Part A: Policy and Practice, Elsevier, vol. 134(C), pages 271-287.
    20. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    21. Jobst, Andreas A., 2014. "Measuring systemic risk-adjusted liquidity (SRL)—A model approach," Journal of Banking & Finance, Elsevier, vol. 45(C), pages 270-287.

    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:kap:revdev:v:27:y:2024:i:1:d:10.1007_s11147-023-09200-x. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.