What do you mean by market makers needing to buy more shares to hedge their position

In the context of a gamma squeeze, "market makers needing to buy more shares to hedge their position" refers to the process of hedging risk that market makers employ when they sell call options. Here's a breakdown of the scenario:

1. **Initial Positioning**: Market makers sell call options to investors, hoping to profit from the premium they receive. This creates an obligation for the market maker to buy shares of the underlying stock if the options are exercised.
2. **Rise in Stock Price**: As the stock price increases, the call options held by investors move closer to being "in the money." This means the investors have the right, but not the obligation, to buy the stock at the predetermined strike price.
3. **Hedging Requirements**: To hedge their risk, market makers need to buy additional shares of the stock. This is because the higher stock price increases the likelihood that the call options will be exercised, and the market maker needs to have enough shares on hand to fulfill their obligations.
4. **Gamma and Delta**: The need for market makers to buy more shares is related to the concepts of gamma and delta in options trading. Gamma measures the rate of change of delta for a 1% move in the underlying stock. As the delta changes, the market maker must adjust their hedge by buying or selling shares of stock to maintain a neutral position.
5. **Feedback Loop**: The buying pressure from market makers to hedge their positions can fuel further price increases, creating a self-reinforcing cycle. This is the essence of a gamma squeeze: the more the stock price rises, the more market makers are forced to buy shares to hedge their options, which in turn pushes the stock price even higher.

In essence, market makers hedge their risk by purchasing shares of the underlying stock to offset their short call option positions. This buying activity can contribute to a rapid increase in the stock price, as seen in a gamma squeeze.