9A.6 Pinning: dealer gamma and the evidence

Motivation

There is a real mechanism by which option positions can pull a price toward a strike near expiry. It does not run through "writers' pain"; it runs through the delta hedging of whoever holds the options and the price impact of their hedges.

9A.6.1Dealer hedging feedback#

A one-line model Let $G(S,t)$ be the aggregate gamma, in units of the underlying per point, of option positions held by delta-hedging intermediaries (dealers). A dealer who is long gamma holds a delta that rises with $S$ , so to stay hedged she sells $G\,dS$ units when $S$ rises by $dS$ . Suppose order flow moves the price linearly: a net purchase of $q$ units moves the price by $\lambda q$ points. Let $dS^0$ be the move that the rest of the market would produce.

Proposition 9A.4hedging feedback

In this linear model the realised move is

dS=\frac{dS^0}{1+\lambda G},\qquad \sigma_{\text{eff}}=\frac{\sigma}{1+\lambda G}\quad(1+\lambda G>0). \tag{9A.6}

Proof

The dealers' hedge flow is $-G\,dS$ , which moves the price by $-\lambda G\,dS$ . So $dS=dS^0-\lambda G\,dS$ ; solve for $dS$ . Volatility scales with the move.∎

With dealers long gamma ( $G>0$ ) volatility is damped. Gamma of options at strike $K$ is concentrated within about $\pm F\sigma\sqrt\tau$ of $K$ and grows like $\tau^{-1/2}$ at the money (M09 Proposition 9.10). So as expiry approaches, $\lambda G$ grows near the strike and the local volatility there shrinks: paths that come near the strike tend to stay. That is pinning. With dealers short gamma ( $G<0$ ) the same algebra gives amplification, and the model explodes as $\lambda|G|\to1$ : hedging chases the price.

Avellaneda and Lipkin (2003) build this into a diffusion with a singular drift toward the strike and show that, when OI at a strike is unusually large and market makers are long options in aggregate, the stock has a positive, but not certain, probability of finishing exactly at the strike. The sign of dealer gamma decides everything, and it is not observable in public data.

9A.6.2Pinning evidence and Indian data#

Evidence

Ni, Pearson and Poteshman (2005) show that on US option expiration dates the closing prices of optionable stocks cluster at strike prices, and attribute this to delta-hedge rebalancing by market makers and to stock-price manipulation by firm proprietary traders.
Golez and Jackwerth (2012) find that S&P 500 futures tend to settle near the at-the-money strike on days when serial futures options expire, and estimate the associated shift in futures notional at no less than $115 million per expiration day.
For Nifty, the 31 expiries of 9A.16 show no clustering at 50- or 100-point strikes: the mean distance of the settlement from the nearest multiple of 100 was 24.7 points, against 25 for a uniform distribution (z = −0.11), and from the nearest multiple of 50 it was 14.0 against 12.5 (z = +1.18, the wrong direction for pinning).

What Indian data can and cannot tell you About 97% of individual F&O traders bought options in FY26 (SEBI FY26 study; M01 · 1.11 Case 1). Their counterparties are partly delta-hedging intermediaries, which suggests dealers are often short gamma in the strikes retail buys, the amplifying case. But the participant-wise OI file (9A.11) counts contracts by category across all strikes and expiries; it cannot give gamma. Any claim about "dealer gamma" on Nifty is an estimate built on assumptions about who holds what.

Settlement design matters Expiry settlement computed as an average over a window (from 7 Dec 2026, the index value computed from the constituents' VWAPs over the last 30 minutes of continuous trading; SEBI circular of 15 Oct 2026, para 4.9; M01 · 1.2) makes the payoff depend on an average, which reduces the gamma at the very end and the reward for moving one print (M05 · 5.6).