A reader asked: “Do you have any research on the phenomenon of ‘pinning’ during options expiration? The theory is that there is a Max Pain price where options sellers stand to lose the least, and that they manipulate prices towards these levels.” A search of the Social Science Research Network (SSRN) separately for “pinning” and “expiration” yields the following studies, in descending order of number of downloads:
“Stock Price Clustering on Option Expiration Dates” from August 2004: “This paper presents striking evidence that option trading changes the prices of underlying stocks. In particular, we show that on expiration dates the closing prices of stocks with listed options cluster at option strike prices. On each expiration date, the returns of optionable stocks are altered by an average of at least 16.5 basis points, which translates into aggregate market capitalization shifts on the order of $9 billion. We provide evidence that hedge re-balancing by option market-makers and stock price manipulation by firm proprietary traders contribute to the clustering.”
“The Effects of Option Expiration on NSE Volume and Prices” from November 2004: “This paper studies the effect of stock options expiration day on the underlying shares traded on the National Stock Exchange (NSE). Overall we tested for abnormal trading volume, abnormal price movement, individual stock reversal and stock pinning on expiration days. To the best of our knowledge, this is a first such study done on the Indian market.” Within the paper there is the following statement (underlining added): “Stock pinning behavior on expiration days also was not suggested by the data for the five stocks considered…”
“A Market-Induced Mechanism for Stock Pinning” from November 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.”
“Modeling Stock Pinning” from July 2006: “The paper investigates the effect of hedging strategies on the so called pinning effect, i.e. the tendency of stock’s prices to close near the strike price of heavily traded options as the expiration date nears. In the paper we extend the analysis of Avellaneda and Lipkin (2003) who propose an explanation of stock pinning in terms of delta hedging strategies for long option positions. We adopt a model introduced by Frey and Stremme (1997) and show that in this case pinning is driven by two effects: a hedging dependent drift term that pushes the stock price toward the strike price and a hedging dependent volatility term that constrains the stock price near the strike as it approaches it. Finally we show that pinning can be generated by dynamic hedging strategies under more realistic market conditions by simulating trading in a double auction model.”
The first paper is probably the most relevant, but the stock price distortions it describes appear to be too small for exploitation, at least by individual traders. Moreover, the ascendancy of high-frequency trading (acceleration of dynamic hedging) since the sample periods used in these studies may have affected the speeds with which prices react to any apparent imbalances between options and their underlying assets.
