I know that the gamma for a long non derivative asset is going to be 0, since delta does not change with price of this item.

However, I am wondering how you could tell if the Gamma on the option of the stock is going to be positive or negative? How can we tell this information?

The short answer: Gamma is the change in the delta as the underlying changes. For long calls/puts gamma is > 0 and short calls/puts gamma is < 0.

If you are delta hedge with a short call, then given that a stock’s delta is always 1, its gamma is 0. A delta-hedged portfolio with a long position in stocks and a short position in calls will have negative gamma exposure.

If you’re delta hedge with a long put, then you guess!

How is there a positive change in delta when the price is going down? Even though this is a short position, this is still a call option, thus the delta would increase as the option becomes more in the money (as the stock price rises), and this would create a positive gamma, even on the short position

That would imply that the delta s higher than a higher underlying price and thus make the relationship between delta and the underlying price positive.

I drew a picture, it is essentially the opposite of the long call position. What I am confused on is in a long call position, the 80 would have a higher delta than the price at 20.

I know a short call position is different than the long call position, but the stock price at 80 would still be in the money for the counter party in the option contract. So even though we may be short the call, the overall delta on the option would still be higher at 80 than at 20 (if that makes sense).

Basically, from the short call position (since the payoff will be the opposite of the long call position) the delta will decrease as the option becomes more in the money.

As such, the delta in a short call would decrease as the underlying price increases, which means the GAMMA on this position would be negative.

So essentially, the gamma on a short position is going to be the exact opposite of the long position, since we are “betting” on the opposite side of the long position on a option contract.

Does this same philosophy follow for put options as well?