To The Moon

Today, this post will cover Gamma Squeeze in options. The reason why $Tesla Motors(TSLA)$ rise is mainly caused by gamma squeeze.

If you don't want to read thousand of words, the next paragraph will explains gamma squeeze in short words.

"In simple words, the Gamma effect is that when the stock price rises, the traders of the investment bank need to buy more stocks to hedge the short exposure of the option. When the volume of these hedging orders is large enough, a large number of buy orders enter the market and push up the stock price, forming a positive feedback."

To fully understand gamma squeeze, you need to know delta and gamma first. ( What is Delta in Options? and What is Gamma in Options? )

Delta & Gamma

Buy call options with positive delta and positive gamma. Sell call options with negative delta, negative gamma.

If an option has a positive delta, then when the stock rises, the price of the option will rise accordingly, and vice versa. How much the option's price rises depends on what the Delta is. If it is 0.1 delta, then for every $1 increase in the stock price, the option price will increase by $0.1.

The delta size of an option is not constant and will change with the price of the stock. As for how much the delta changes, it depends on the Gamma of the option. The characteristic of Gamma is that the value of Gamma determines how much the option Delta changes as the stock changes. As the stock fluctuates, the larger the Gamma value of the option, the larger the change in its Delta.

The Gamma of an option is also not constant and will vary with the price of the stock and other factors.

Delta Neutral

Investopedia explains, "Delta neutral is a portfolio strategy utilizing multiple positions with balancing positive and negative deltas so that the overall delta of the assets in question totals zero."

For example, there are investor and dealer trading Tesla options. Investors are prepared to buy 1 million call options expiring in 3 months with a strike price of $110. Tesla stock is currently trading at $100. 

If this order is filled, the Delta and Gamma risks of the investor and dealer option positions are just the opposite.

When dealer uses the model to calculate the order, assuming that the Delta of this option is 0.1 and the Gamma is 0.02. (To simplify this example, we assume Gamma is unchanged here.) Due to the dealer is the seller of options, the delta risk on the trader's trading account is displayed as -100k (1 million options * -0.1Delta), which means that the current Delta is equal to shorting 100,000 Tesla shares .

In order to hedge directional delta risk, so he planned to buy 100,000 Tesla shares in the stock market. 

If this order executed, sell 1 million Tesla call contracts, with buying 100,000 Tesla shares, the overall delta risk is zero. This type of position is also commonly referred to as delta neutral which is also the usual position of market makers. It is market makers that cause the Gamma squeeze to ensure the delta neutrality principle.

Gamma Squeeze

With Tesla still trading at $100, the dealer immediately placed a buy order for 100,000 shares at $100. 

Generally, Tesla options has better liquidity, the order will be filled quickly. However, today's market is a bit strange. After the dealer placed the order, he noticed that similar large buy orders appear frequently in the market, which soon pushed the stock price to $101.

The order was not filled, which made the dealer start to be vigilant. The dealer thinks these buy orders are likely due to investors buying similar options from other banks, causing dealers at other banks to start similar hedging transactions.

The dealer uses the model to calculate the order one more time. As the stock has risen by $1, the delta of the option has risen from 0.1 to 0.12 (0.1 + 0.02gamma). It means the dealer's latest risk to options now amounts to a short 120,000 shares of Tesla, 20,000 more shares than his previous order. In order to completely hedge the delta risk, the dealer now need to buy 20,000 more Tesla shares than the original 100,000 shares.

This newly added 20,000 shares is the core point to understand Gamma effect. When the stock price rises from $101 to 102, 103... and so on, the delta of the options in the dealer's hands keeps getting bigger (that is, the number of sell call Tesla shares is increasing) until delta to 1. This means that the dealer's hedging position in Tesla stock will increase from the initial 100,000 shares to a maximum of 1 million shares as the stock price rises. 

Gamma squeeze does not change the direction of the market. Due to the existence of a wave of hedgers buy at high & sell at low, it will only expand the volatility that has already occurred in the market.