Gamma is the first and widely expected most important second order derivative. Other second order derivatives won’t be touched on for a while, as they are more important as traders get involved with volatility trading and complex position structures.
Gamma is the change in the option’s Delta for a change in the underlying value. What this means is that if you are long a $17.5 call that is 50 Delta and has 10 Gamma, the Delta of the call will be 60 on a rally to $18.5.
Gamma is the curvature of the option PnL graph. For example, we will look at the changing value of a $17.5 call with 50% Implied Volatility and 30 days to expiration:
If the option payout were linear, then there would be no gamma. Because the slope of the call payout graph changes over price, we can see the impact of gamma. Gamma is generally paired with Theta when traders categorize Greeks. This is because if you have Gamma and a desire to be Delta neutral (as many Volatility Traders do), then the cost of being long Gamma is your Theta. That trader can scalp the underlying as the price changes because the Delta of their position will increase on a rally and decrease on a break. If the range of the stock is wide enough, they can buy and sell shares on the same day and day trade enough to make up for their Theta without taking a directional bias.
Gamma is also higher in shorter dated options. As an equity rallies, the call Delta increases because the call is more likely to finish in-the-money and is closer to acting like a long underlying position. Shorter dated options increase their probability of finishing in-the-money more rapidly because they have less time to work (or fail to work).
There are many details regarding Gamma that we will want to dive into as we increase the complexity of our trade such as the change in Gamma given a change in Implied Volatility and how to manage a Gamma position even if you are trading directionally, and we will get into those topics and many others down the line.
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