[qeternity]

Not exactly. It depends how the market is positioned. Right now put/call ratios are very low meaning the market is long upside gamma, so when stocks fall, convexity means that market makers hedging decelerates as the market falls, but accelerates as it mean reverts.

This gives rise to a phenomenon known as pinning where stocks prices tend to oscillate around strikes with high OI and thus high convexity.

[ironSkillet]

Would you mind explaining the market dynamics in more detail? My understanding is that the positive gamma causes long market makers to put pressure on prices to mean revert, but I don't quite grok the rest of the dynamics.

[qeternity]

Well, it's negative gamma from the MM's perspective (this is ultimately what they're being paid to provide in a purely Black-Scholes sense). It's less about whether gamma is positive or negative because that just depends on which side of the trade you're looking at.

The simple reason is that like delta, gamma is also not constant. Gamma is our derivative of delta with respect to underlying, but there exists another measure called speed which is the derivative of gamma with respect to underlying (gamma of gamma). This is normally distributed around the strike price of the option, so as you deviate from the strike, the gamma of an option decreases which means that MM hedging decelerates as you move away from the strike. It also means that MM hedging accelerates as you approach the strike. Convexity cuts both ways.

Let's say a MM is short a $100 call in some asset X. When we are below $100, any move towards $100 means we have to buy increasing amounts of X in order to remain delta neutral. This pushes prices towards $100. But as we move through $100 this force decelerates. So let's presume that market momentum takes us to $110, at this point, a $1 drop to $109 results in more selling than an increase to $111 results in buying. These forces can become self fulfilling whereby the selling that we have to do when we drop from $110 to $109 contributes to downward pressure and pushes us to $108. And recall that our hedging accelerates as we move towards the strike. So we have to sell even more now than we did before, which further contributes to downward momentum. This pressure peaks at $100 at which point is starts to decelerate again, providing a natural tendency to revert to high OI strikes where there is substantial outstanding gamma.