What Is Dealer Delta Exposure (DEX)?

Dealer delta exposure, usually shortened to DEX, measures the aggregate directional position options dealers carry in an underlying across its listed options. Delta is what an option's price does per dollar the underlying moves, and DEX adds that up across every strike and expiry. It describes a positioning backdrop rather than a signal.

Options dealers take the other side of what investors want to trade, and the delta that arrives with those trades gets hedged in the underlying as ordinary business. Dealer delta exposure is an estimate of how large that hedged position is at a point in time. This page covers what delta is, how a book-wide delta figure is built from open interest, the sign convention the figure uses and why it differs from the gamma one, and how delta and gamma answer different questions. It is descriptive throughout.

What delta measures

If calls and puts are new to you, start with what a call option and a put option are. Delta is the first derivative of an option's value with respect to the underlying: how much the option's price changes for a one dollar move in the underlying.

In the closed form Black-Scholes model this figure is built on, with no dividend yield assumed, a call's delta is N(d1) and a put's delta is N(d1) minus 1, where N is the standard normal cumulative distribution function and d1 = (ln(S/K) + (r + s^2/2)T) / (s sqrt(T)), where S is the spot price, K the strike, r the rate, s the volatility and T the time to expiry in years. Because N returns a value between 0 and 1, a call delta lands between 0 and 1 and a put delta lands between -1 and 0. That range carries the whole sign story: a call gains value as the underlying rises and a put loses it, so the two sides of the chain arrive with opposite signs already attached.

Delta is also read as a share equivalent. One listed contract covers 100 shares, so a contract's delta times 100 is the share count that contract currently behaves like, and that is the position a dealer offsets in order to be flat.

From one contract to a whole book

A single contract's delta is a per share sensitivity, so turning it into a book-wide figure takes three multiplications. By open interest, the count of contracts outstanding at that strike and expiry. By the contract multiplier of 100. And by the spot price S, which turns a share count into dollars. The stored quantity is delta times open interest times 100 times spot, a delta-dollar notional.

That product is computed contract by contract and summed across every strike and expiry in the listed chain, then reported three ways: the call leg, the put leg, and the net. Open interest comes from the prior session's end of day chain snapshot, which is why the result is a positioning estimate as of a session and not a live book.

The sign convention, and the one exception

The figure is signed by the standard naive dealer positioning assumption, a modeling convention rather than a measured book. Across the exposure families the net is the call leg minus the put leg: that is how gamma, vega, vanna, charm, theta, vomma, speed and zomma exposures are combined. Delta is the single exception:

`net DEX = call DEX + put DEX`

The suite treats this as part of its stated sign convention rather than a law of nature. Gamma, vega and the higher order terms that descend from them take the same value on a call and a put at the same strike and expiry, and apart from delta itself, whose two sides differ by a constant, theta is the only one whose sides differ, by an exact rate-only term. For those families the direction of the book has to be imposed, so the put leg is subtracted. Delta is the exception the suite makes: the sign already lives in delta itself, since put delta is negative, so the two legs are added as they stand.

The practical consequence is that a page showing both families has to name which rule it applies to each. Read a DEX net under the gamma rule, or a gamma net under the delta rule, and the number that comes back is a different quantity wearing the same label.

Delta and gamma answer different questions

Delta is the level of the hedge. Gamma is how fast that level changes as the underlying moves. A dealer who is delta hedged at one price is no longer hedged after the market moves, because every option's delta has shifted, and gamma is the size of that shift.

That makes the two readings different in kind. Dealer delta exposure describes how large the hedged position already is and which way it points. Dealer gamma exposure describes how much rehedging the next move forces, and which way that rehedging pushes. A book can carry a large delta with very little gamma, when its options sit deep in the money, or a small delta with a lot of gamma, when they sit right on it. Neither reading substitutes for the other.

What dealer delta exposure does not tell you

Hedging delta is routine dealer business. A desk that buys a call from a customer sells shares against it, and that hedge is a mechanical consequence of the trade rather than a view on the name. So the size of the aggregate delta position describes what the hedging backdrop looks like, not what it is about to do.

Three limits are worth holding on to. The figure is modeled, not measured: it is built from listed open interest and a pricing model with assumptions stated, and no exchange publishes an actual dealer book. The side of the book is a convention rather than an observation, which is why the rules above are stated as conventions. And open interest counts contracts outstanding rather than contracts traded, so a large reading does not say anything changed hands in the last session.

How Kresmion computes it

Kresmion computes modeled dealer greeks exposure nightly for a curated universe of US names from listed option open interest, using closed form Black-Scholes with the assumptions stated, and delta exposure is one of those families: call leg, put leg and net, per name and per session. The live SPY snapshot on this page is that computation for a single session, printed with the as of date it was drawn from. The full suite across every covered name, including the implied volatility tab, lives in Kresmion's greeks tool with a free account.

Key takeaways

Frequently asked questions

What is the difference between dealer delta exposure and dealer gamma exposure?

Delta exposure is the level of the hedge: how large a share equivalent dollar position dealers carry at this snapshot. Gamma exposure is how fast that level changes as the underlying moves, which is what forces a hedged desk to keep trading. The two can look unrelated on the same book, so they are read alongside each other rather than one standing in for the other.

Why is net DEX call plus put when the other greeks are call minus put?

Because delta already carries its own sign. A call delta sits between 0 and 1 and a put delta between -1 and 0, so the put leg arrives negative and adding it keeps the direction intact. Gamma, vega and the terms descending from them take the same value on both sides of the chain, so their nets have to impose a direction by subtracting the put leg instead.

Does dealer delta exposure predict which way a market moves?

No, it describes the backdrop. Hedging the delta that arrives with customer trades is ordinary dealer business, so the aggregate says how large the hedged position is and which way it points, not what happens next. Treating a positioning measure as a forecast asks it a question it was never built to answer.

Is this a real dealer book?

No. It is a modeled estimate, built from listed option open interest and a closed form pricing model with assumptions stated, then signed by the standard dealer positioning assumption. No exchange publishes actual dealer inventories, so every published dealer exposure figure of this kind is a model output and is read as one.

This page is information, not investment advice.

---

Source: closed form Black-Scholes greeks, with the modeling assumptions stated on Kresmion's greeks exposure tool; Kresmion modeled dealer positioning data.

Kresmion Research.