Estimating Dealer Gamma Imbalance from Option Open Interest

# Index with negative gamma


# Index with negative gamma












I understand the principal of being gamma negative or positive, but what I struggle to understand is that how can we say that an index options for example SPY is gamma negative ? how do we do this calculations ?

We can see here $QQQ short gamma now, how do we calculate this ?

this is from spotgamma*

## Answer by oronimbus (score 2)

https://quant.stackexchange.com/a/63625

An index itself doesn‘t have any gamma. Even for the options on an index (spot? futures? ETF?) it‘s a zero sum game since for every long position you have a matching short position. Now it gets a bit more interesting if you look into the type of players that trade options. Very simplified you have two main players. Firstly, there are real money investors buying downside protection & selling upside. Naturally they buy puts as hedges but won‘t further delta hedge those. On the other side of the trade you have market makers (MM) who take that flow to generate income. Since the MM is not using options to create a view, they will hedge their risk for every option that the sell/buy.

The type of chart that you’re looking at is based on this very simplified assumption that all puts are sold and calls bought by the MM (and thus delta hedged). Hence for every put, they will sell some of the underlying and for every call the will buy some. If you aggregate the net delta exposure by strike (bucket) you will eventually end up with a chart like yours. This is sometimes referred to gamma imbalance (remember this from a JPM publication).

Using a bit of maths, the \$ Gamma per contract is: $$\Gamma_{\\\$} = \Gamma_{BS} \times F \times S$$

Where $F$ is your contract multiplier (often 100) and $S$ the spot price.

Rinse and repeat for every contract and scale the \$ Gamma by the open interest of every option in the chain. Then simply subtract call gamma from put gamma and there you go!

Now obviously this gross simplification limits the usefulness of such a chart. Nonetheless it‘s a fun exercise and might show a thing or two. There are more sophisticated approaches where you‘d identify for every trade whether its a dealer buying or selling. This could be done via an IV approach where you mark each trade relative to its fair value (dealer buys cheap and sells rich). That‘s a lot of data to process though and requires some proper thought.

Some people make a living out of selling gamma exposure data in a ready made and easily digestible format (not me!). I do recommend having a look at the „white paper“ from above link.

## Answer by user42108 (score 1)

https://quant.stackexchange.com/a/63524

"how can we say that an index options for example SPY is gamma negative ?"

I believe the chart shows an estimate of dealers' net gamma position for QQQ as a function of price. It is not the gamma for a single option on an index.

This kind of analysis has been discussed elsewhere, and I believe previously on StackExchange.