A Market-Induced Mechanism for Stock Pinning

Marco Avellaneda and Michael Lipkin
Working Paper, March 2003

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.