A Market-Induced Mechanism for Stock Pinning

New York University Courant Institute Working Paper

20 Pages Posted: 22 Nov 2003

See all articles by Marco Avellaneda

Marco Avellaneda

New York University (NYU) - Courant Institute of Mathematical Sciences; Finance Concepts LLC

Mike Lipkin

Columbia University; Katama Trading, LLC

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Abstract

We propose a model to describe stock pinning on option expiration dates. We argue that if the open interest in 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.

Keywords: Stock clustering, options, open interest, volume, pinning

Suggested Citation

Avellaneda, Marco and Lipkin, Michael D., A Market-Induced Mechanism for Stock Pinning. New York University Courant Institute Working Paper, Available at SSRN: https://ssrn.com/abstract=458020 or http://dx.doi.org/10.2139/ssrn.458020

Marco Avellaneda (Contact Author)

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Michael D. Lipkin

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