PinningPaper - RE S E A R C H PA P E R Q U A N T I T A T I...

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QUANTITATIVE FINANCE VOLUME 3 (2003) 417–425 R ESEARCH P APER INSTITUTE OF PHYSICS PUBLISHING A market-induced mechanism for stock pinning Marco Avellaneda 1 and Michael D Lipkin 2 1 Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA 2 Katama Trading, LLC, American Stock Exchange, 2 Rector Street, New York, NY 10006, USA E-mail: and Received 18 March 2003, in ±nal form 11 July 2003 Published 5 September 2003 Online at Abstract 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 ²oor 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 ±nite 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. 1. Introduction This paper analyses a phenomenon observed in equity options markets known as ‘stock pinning’. Only minutes before options expire, many stock prices are near or at option strike prices. For some stocks, the subsequent evolution of the price until expiration is remarkably different from a random walk. Stock prices will experience a sudden rush to the vicinity of the strike, coupled with the appearance of an unusually high availability of stock offered just above the strike price and similar large size bid just below the strike. Unless important stock-speci±c news reaches the market, these stocks become pinned , i.e. the closing price at expiration will be within a few cents from the strike price. Historically and, in particular, during the speculative bubble of the late 1990s, traders saw frequent pinning in technology stocks such as Microsoft and Intel. With open interest being very high in several strikes, and with high stock prices and high volatility, several strikes would be ‘visited’ in a single day. Pinning became apparent only at the very end of the option’s lifetime. Krishnan and Nelken (2001) present signi±cant statistical evidence of pinning of Microsoft stock using historical data. More recently, hedge funds have engaged in trades consisting of selling thousands of put or call options on the same strike in stocks that have normally a much smaller open interest. One example of this activity occurred in the stock J D Edwards (JDEC, option symbol QJD) in 2001. Typical front-month open interests in JDEC are on the order of a few hundred contracts. Nevertheless, over a period of six expirations in 2001, the same hedge fund sold repeatedly more than 25 000 contracts on a single strike in the front-month expiration each time. The stock actually pinned at that strike
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This note was uploaded on 12/08/2011 for the course CIS 625 taught by Professor Michaelkearns during the Spring '12 term at Pennsylvania State University, University Park.

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PinningPaper - RE S E A R C H PA P E R Q U A N T I T A T I...

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