Gamma Squeeze

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In the stock market, a gamma squeeze occurs when the underlying price of a stock increases within a very short timeframe. A higher amount of money moving into call options results in greater buying activity and can push the stock price up as a result.
Overview
A gamma squeeze is driven by a large number of out of the money (OTM) option buying. When option contracts expire, they quickly approach a delta of 1 or 0 based on if the option is in the money (ITM) or out of the money (OTM). Given this fast change in delta, the gamma moves rapidly. This phenomenon leads to market makers purchasing additional shares to cover the increase in delta from the new in the money (ITM) call options. Simultaneously, the market makers will sell shares for contracts whose delta is decreasing. The market makers are essentially hedging to remain as neutral as possible.
The effect of the squeeze comes from a mass amount of call option contracts expiring in the money (ITM). As the delta approaches 1 per contract, the gamma of each contract rises hence the term “squeeze”. In certain scenarios, this squeeze is emphasized when there are limited to no out of the money (OTM) contracts being sold on the market and market makers can only buy more shares to cover their short contract positions. This cycle of continuous buying is ongoing, where covering delta results in share prices increasing and delta going up and up, pushing gamma up along with it. The entire option chain must expire in the money (ITM) for the full squeeze to execute. A gamma squeeze can occur in different sizes, but multiple gamma squeezes are unlikely to occur consecutively. This is because once a successful squeeze occurs, the option contracts will be much more expensive to purchase thus creating a smaller demand and a subsequent reduction in purchasing trends.
The gamma squeeze will most commonly occur during regular trading hours. Market makers actively hedge into the close of the market and the vast number of call and put options will only hit their expiration date at the close of the market. These options, expiring in the money (ITM) or out of the money (OTM), will expire with a delta of zero because the market makers will have preemptively accounted for the increase in option purchases. The market makers take real time purchasing volume data into account and hedge their position by buying more shares to cover their short position. The only exception is at the money (ATM) options. At the money (ATM) options expire with a non zero delta and the stock tied to the options can see change after-hours.
Related definitions
Delta
The greek option that measures the expected increase or decrease in the value of a stock contract determined by the $1 move of the underlying asset. Call options that speculate that the stock price will increase in the future, have deltas of 0 to 1. Put options that speculate that the stock price will decrease in the future have negative deltas.
Gamma
The greek option that measures the rate of change of delta. Long position options tend to have a positive gamma, while short position options have negative gamma. Gamma determines how quickly change occurs in delta. Mathematically, gamma is the 2nd derivative of the options value function.
Market maker
An individual or firm that acts as a liquidity provider to the market. A market maker quotes both bid and ask prices of an asset and takes profit on bid-ask spreads, which represent the amount the ask price exceeds the bid price of the market value. Market makers track how delta and gamma changes throughout the trading day and as the price moves they continue to hedge positions into the market close. This exacerbates a gamma squeeze as a market maker will often continue to buy up shares as the price approaches the strike price. Market makers are commonly referred to as neutral brokerage houses and are compensated for the risk of holding assets whose value might change with the market value of the security before it can be bought and sold by another party.
Out of the money (OTM)
The term relates to options in which the underlying price of the stock is less than the strike price of the option in the case of a call and greater than the strike price in the case of a put. Out of the money (OTM) options are commonly used for covered call strategies and are typically less expensive than in the money (ITM) options.
Stock option
An option is the right an investor has to purchase a stock contract of 100 shares at a certain price called a strike price, where the trader pays a premium fee for the opportunity to purchase the stock at a later date.
Short squeeze
A short squeeze occurs when a short seller who has borrowed and sold shares in hopes that the stock price will go down, sees the price go up. Therefore, the short seller is obligated to go out into the open market and buy back those shares because as the stock price increases, the short seller loses money due to the stock selling at a price point greater than what they shorted at. So many individuals and firms buying back the stock to reduce losses, pushes up the stock price and results in severely leveraged companies. Historically, the short hedge funds will generate counterfeit shares and disregard the failures to deliver, which continuously accrue, creating what many refer to as the "mother of all short squeezes" (MOASS). Simultaneously, the hedge funds attempt to extend this squeeze as long as possible hoping individual investors will give in and sell their positions.
Examples
In October 2008, Porsche Automobile Manufacturer bought enough of Volkswagen's stock on the open market that it caused Volkswagon's stock price to skyrocket. The hedge funds held a heavily shorted position against the company and the squeeze that occurred cost them an estimated US$30 billion in the span of only a few days of trading.
In January 2021, several individuals on the Reddit forum Wallstreetbets pointed towards why investors should purchase GameStop stock and execute long call options on GameStop. These users acknowledged that a large percentage of GME common stock shares were shorted by hedge funds. The key data that these subreddit users unraveled was that there were more shorts on the GameStop stock than total shares outstanding. In GameStop's case, the short position would grow up to 140% more than shares outstanding. With GameStop stock in particular, there was relatively low implied volatility and a mass amount of same day out of the money (OTM) call options available which led to a frenzy of call options being purchased. This price movement from individual share buying, option buying, and social media spotlight pushed the share price well above strike prices and resulted in an increase in option contract values. The short squeeze and gamma squeeze resulted an all time intraday high of US$483 on January 28, 2021.

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