Gamma Explainer

TVC:SPX   S&P 500 Index
I was asked, why I think dealer selling will abate at strikes lower than 3800. Let me explain the thinking behind it and consider the charts above. The answer comes at the end of this piece :).

Assume a simplified model, where option dealers buy calls and sell puts.

Both positions are long positions (delta positive), so the dealer has to sell futures against them. How many futures he has to sell or buy back after the initial hedge is set and the market starts moving, is determined by their respective gamma values.

Short puts have negative gamma, long calls have positive gamma.

Let’s go through two simplified scenarios.

1) For simplicity assume the dealer sells one put with a delta of 10 and the market moves lower:

Initially the dealer needs to short 10 shares of the underlying, but as the market declines and the delta increases in a non-linear way, he has to sell more shares at an ever faster pace, until the put is at the money. At this point the hedging pressure abates again, until the delta of the contract reaches 100, which means that the dealer is now fully hedged by shorting 100 shares.

The rate of the delta-hedge adjustment is expressed by gamma. To understand this concept take a look at the chart in the lower left corner.

If on the other hand side the market moves higher again, the dealer is forced to buy back shares in order to stay market neutral.

2) Now assume another scenario, where the dealer buys one call option with a delta of 10 and the market moves higher.

Initially the dealer has to short 10 shares of the underlying, but as delta increases he has to sell even more shares at a faster pace, until delta reaches 50 and gamma (the need for hedging adjustments) slowly abates again. When the call has reached a delta of 100 the dealer is fully hedged.

If the market moves lower again, the dealer has to buy back shares in order to stay market neutral. Take a look at the chart in the lower right corner to get the idea.

Now put both scenarios together and imagine a situation where the options dealer owns one short put and one long call.

If you combine the gamma curves of both contracts (bottom left chart & bottom right chart) and blend them together you would get a curve that has the same characteristics as the one in the big chart with the black background above.

To compute this graph I take all SPX options into consideration to calculate an implied dealer gamma curve.

If the chart is positive, that means dealers have to sell into strength and buy into weakness (they provide liquidity, stabilize the markets), if it turns negative dealers have to sell into weakness and buy into strength (they take liquidity, destabilize the markets).

At both tails, the curve starts to flatten out, that’s the point where dealers are fully hedged and dealer flows come to a stop (before they reverse again - not depicted in chart). And this is the answer to the initial question :).

Sorry for the long explanation, I am just stringing this together really fast and I hope I am not too sloppy and you get the basic concept.


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