Thread by @asitbaran

Brief write-up on Gamma. Hope you hv few takeaways

1 - Gamma is one of the Option Greeks. It measures the rate of change of the Delta of the option with respect to a move in the underlying asset. Specifically, the Gamma of an option tells us by how much the delta of an option

2 -would increase by when the underlying moves by 1 unit. Since Delta is a first derivative, Gamma is a second derivative of the price of the option.

A : Gamma Characteristics:

Gamma is a +ve function. If we own options, we own Gamma. If we are short options, we must have

3 - short Gamma.
Gamma is what makes Delta go from mild to ferocious, from small to large. The instability of that Delta depends on the option’s Gamma

a) Long Option Benefits of Gamma

Gamma is friendliest to long option holders. It accelerates profits for every 1point, the

4 -underlying moves in our favor, and decelerates losses for every 1 point the underlying moves against us. Since Delta is the rate of change of an option’s price, and Gamma increases an option’s Delta as it moves closer to, or further in the money, the delta

5 - would just continue to increase.

b) Short Option Risks of Gamma

Because it can be beneficial for option buyers, that must mean that it can be risky for option sellers. From the seller’s perspective, it can accelerate losses, and decelerate directional gains. It is just

6 - the opposite side of the coin.

Gamma “manufactures” call Deltas when a stock rallies and put deltas when a stock drop. It “un-manufactures” call deltas when the stock drops and put deltas when the stock rallies

c) Expiration Risk & Gamma

ATM Gamma increases quickly

7 - towards Expiration. However, further OTM / ITM Gamma tends to decrease over time. As we get closer to expiration, the probability curve gets much narrower.

There is not a lot of time for the underlying to move to far OTM strikes, and they will have a lower probability

8 - of being ITM because of that. Since we know the probability curve is narrower, that also means the Delta distribution is more narrow. The result is a more aggressive Gamma. This can be good for option buyers, but especially bad for option sellers.

9 - It can quickly turn trades into losers, or losing trades into winners.

d) Additive in Nature

Gamma is additive for options struck on the same underlying, regardless of their expiration. If we have BN 23000 CE & 23200 PE, the portfolio Gamma is just the sum of the

10 - Gammas from both the strikes.

B : Factors Affecting Gamma

a) Strike price relative to Spot:

Likewise, gamma itself isn’t constant. The closer an Option is to being ATM (.40 - .60) the greater its Gamma. ATM options have the highest Gamma of any Option within an

11 - expiration. Options whose strikes are a long away from the current SPOT price will have less or even ZERO Gamma. (Delta of an option very far away from current spot price is unlikely to change greatly for a small or moderate change in SPOT, hence less sensitivity of

12 - Gamma at OTM strikes. Deep-in-the-money or far-out-of-the-money options have lower Gamma than at- the-money options. The deep ITM Options already have a high positive or negative Delta. If the options become deeper ITM, the Delta will move towards

13 - 1.00 (or -1.00 for puts) and the Gamma will decrease because the Delta cannot move past 1.00. If the stock were to move toward the strike of the deep ITM option, the Gamma will increase and the Delta moves

14 - lower approximately by the amount of the current Gamma.

b) Time to Expiration:

Options with less DTE have greater Gamma than longer dated Options. A change in the SPOT price is more significant for a shorter dated option than a longer dated option and so the effect on

15 - the option’s Delta will be greater. In the long scheme of things, the change in SPOT price is inconsequential for long Option’s Delta.

c) IV of the Option

The higher the IV, the lower the Gamma, and the lower the IV, the higher the Gamma; other things being equal. As IV

16 - decreases, Gamma of at-the-money calls and puts increases. When implied volatility goes higher, the Gamma of both in-the-money and out-of-the-money calls and puts will be decreasing. This occurs because low IV
options will have a more dramatic change in Delta when the

17 - underlying moves. A high implied volatility underlying product will see less of a Delta change with movement as the possibility of more movement is foreseen. An ATM option where IV is very high, a small change in the underlying would not impact the Delta

18 - hence insignificant changes to Gamma

Gamma Scalp / Trading

Gamma scalping hedges the Deltas manufactured by gamma as the price of the stock moves up and down. Traditionally, Gamma scalping is done with a long straddle, which has relatively low deltas, because the ATM call

19 - and put have deltas close to 0.50. So the +0.50 delta from the call offsets the -0.50 Delta from the put. But the straddle has a lot of gamma and negative Theta. Gamma scalping hedges the straddle’s delta with stock when it reaches some amount

Gamma scalping can also be

20 - done from the short straddle side, but the stock hedges lose money against the short straddle’s positive theta. Either way, gamma scalping is capital intensive, and it isn’t a simple strategy.

Gamma profits (and losses) are an exponential function (NOT A LINEAR) of the

21 - change in SPOT price. Double the move in the SPOT price and the Gamma profits/losses quadruple. Gamma p/l is explosive.
To Trade Gamma, an options position typically Delta-neutral, is

22 - established. The position will either be long/short Gamma. Which is determined by whether the Gamma from the long option positions is greater than or less than the short Gamma arising from short option positions

23 - The above is just a summarized takeaways

Suggestive Further Readings:

tastytrade.com/tt/learn/gamma

Trading Options Greeks: How Time, Volatility, and Other Pricing Factors Drive Profits by Dan Passarelli

Option Volatility and Pricing: Advanced Trading Strategies

24 - and Techniques by Sheldon Natenberg

The Option Trader Handbook: George Jabbour
Trading Options to Win: S. A. Johnston
Dynamic Hedging: Taleb

Happy Reading
Cheers