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A market-induced mechanism for stock pinning


  • Marco Avellaneda
  • Michael Lipkin


We propose a model to describe stock pinning on option expiration dates. We argue that if the open interest on a particular contract is unusually large, delta-hedging in aggregate by floor market-makers can impact the stock price and drive it to the strike price of the option. We derive a stochastic differential equation for the stock price which has a singular drift that accounts for the price-impact of delta-hedging. According to this model, the stock price has a finite probability of pinning at a strike. We calculate analytically and numerically this probability in terms of the volatility of the stock, the time-to-maturity, the open interest for the option under consideration and a 'price elasticity' constant that models price impact.

Suggested Citation

  • Marco Avellaneda & Michael Lipkin, 2003. "A market-induced mechanism for stock pinning," Quantitative Finance, Taylor & Francis Journals, vol. 3(6), pages 417-425.
  • Handle: RePEc:taf:quantf:v:3:y:2003:i:6:p:417-425
    DOI: 10.1088/1469-7688/3/6/301

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    Cited by:

    1. Rama Cont & Lakshithe Wagalath, 2016. "Institutional Investors And The Dependence Structure Of Asset Returns," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(02), pages 1-37, March.
    2. Görgens, Maik & Thulin, Måns, 2014. "Bias-correction of the maximum likelihood estimator for the α-Brownian bridge," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 78-86.
    3. Xiaoyan Ni, Sophie & Pearson, Neil D. & Poteshman, Allen M., 2005. "Stock price clustering on option expiration dates," Journal of Financial Economics, Elsevier, vol. 78(1), pages 49-87, October.
    4. Marc Jeannin & Giulia Iori & David Samuel, 2008. "Modeling stock pinning," Quantitative Finance, Taylor & Francis Journals, vol. 8(8), pages 823-831.
    5. Lakshithe Wagalath, 2014. "Modelling the rebalancing slippage of leveraged exchange-traded funds," Quantitative Finance, Taylor & Francis Journals, vol. 14(9), pages 1503-1511, September.
    6. repec:wsi:ijtafx:v:10:y:2007:i:03:n:s0219024907004287 is not listed on IDEAS
    7. Stivers, Chris & Sun, Licheng, 2013. "Returns and option activity over the option-expiration week for S&P 100 stocks," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4226-4240.
    8. repec:cai:finpug:fina_372_0039 is not listed on IDEAS
    9. Baurdoux, Erik J. & Chen, Nan & Surya, Budhi & Yamazak, Kazutoshi, 2015. "Optimal double stopping of a Brownian bridge," LSE Research Online Documents on Economics 61618, London School of Economics and Political Science, LSE Library.
    10. Erik J. Baurdoux & Nan Chen & Budhi A. Surya & Kazutoshi Yamazaki, 2014. "Optimal double stopping of a Brownian bridge," Papers 1409.2226,, revised Dec 2014.
    11. Christoph Kuhn & Budhi Arta Surya & Bjorn Ulbricht, 2014. "Optimal Selling Time of a Stock under Capital Gains Taxes," Papers 1501.00026,
    12. Golez, Benjamin & Jackwerth, Jens Carsten, 2012. "Pinning in the S&P 500 futures," Journal of Financial Economics, Elsevier, vol. 106(3), pages 566-585.

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