11. Three Forces: gamma, vanna, charm

11. Three Forces: gamma, vanna, charm

The SPX market has habits that puzzled observers for years. A quiet Friday afternoon — no news, thin volume — and the index stubbornly crawls higher. Volatility drains away after an event has passed — and the market rises on its own, as if someone were methodically buying up every dip. Who is buying? Look at the tape — nobody special. The answer hides not in the tape but in the schedule: the dealer is buying, and buying not because he wants to — because he must.

By lesson 4 we knew one reason for his obligations — the movement of price. Time to complete the picture: there are three.

One obligation, three causes

The dealer's rule has not changed since lesson 4: keep the book's delta at zero. But the book's delta is a living quantity, and price is not the only thing that can push it off zero.

Price moves — the book's delta is shifted by the force of gamma. Volatility moves — by the force of vanna. Nothing moves at all, the clock simply runs — delta drifts because of charm. Three different causes, one consequence: the book has slid off zero, and the dealer must trade futures. Gamma we have already taken apart inside and out — its GEX map shows where hedging brakes price and where it accelerates it. That leaves the two quiet forces to meet. Both work through the same mechanism, so let's take it apart once, on a concrete book.

Take the market's most typical book: clients bought puts at strikes below the market — the insurance from lesson 1 — and the dealer, accordingly, sold those puts. A put's delta is negative, so the dealer's short position carries positive delta: his book is being pulled upward, and to stay neutral he holds short futures. Remember this starting arrangement — both forces will play out on it.

Vanna: the force of fear

Vanna answers the question: what happens to delta if volatility shifts.

Suppose the frightening event has passed and IV heads lower — the bell of expectations from lesson 2 contracts. Out-of-the-money puts that had real chances under the wide bell are now nearly hopeless: their delta melts before your eyes. And with it melts the positive delta of the dealer book — the futures short that balanced it has become excessive. The dealer must trim it: buy futures. Across the whole market, at every dealer, at the same time.

There is the answer to the "causeless" rally after fear subsides: the decline in volatility by itself generates dealer buying. The market calls this mechanism a vanna rally. It works in reverse too, and more viciously: a spike in IV inflates put deltas, the dealers are suddenly short of short, and they sell futures into a falling market — on top of all the other selling.

The VEX map from the previous lesson shows this force by strike: exactly where the dealer book is most sensitive to a move in volatility — and, therefore, which levels will "wake up" when VIX shifts.

Charm: the force of time

Charm answers a question stranger still: what happens to delta if nothing happens at all.

Back to the same book. The market is frozen, IV stands still — but the clock runs, and the out-of-the-money puts are aging. Every hour brings expiration closer, at which an out-of-the-money option is worth zero — and its delta is already drifting toward zero (look once more at the gamma chart from lesson 3: the delta curve presses closer to the step with every passing day). You know the melody from here: the book's delta melts — the futures short is excessive — the dealer buys. From the passage of time alone.

Hence the second answer: the Friday afternoon drift. Toward the end of the week large series expire, delta decay accelerates — recall theta from lesson 3, the final days burn fastest — and the dealers' buying back of their hedges turns into a steady tailwind. The effect is so regular it has a name — charm flow. Just don't file it away as "the force that pulls upward": the direction is set by the book. On the typical book, where clients sit in protective puts, the decay pulls the market up — hence the reputation of quiet pre-expiration days with their "strange" lean. But if the client overweight is in calls, the same mechanics run mirrored: call deltas melt, dealers sell down their long hedge, and the drift points down.

Now overlay the 0DTE world from lesson 7. Charm used to gather strength once a month, into the big Friday expiration. Now some series expires every single day — and the same picture repeats daily: after lunch, the deltas of options expiring today melt ever faster, the forced dealer flow builds and peaks right at the close. The CEX map shows it by strike: exactly where the passage of time will make dealers trade, and in which direction.

How to read the three forces together

The three maps answer in different registers, and this is worth saying out loud. GEX describes the market's character: viscous here or slippery — with no direction; we discussed this in lesson 4. Vanna and charm are built differently: they are conditional directional flows. The reading formula goes: "if IV declines, dealers will buy this much at these levels"; "if the day passes quietly, by evening dealers will have bought back this much". The condition is mandatory: if the scenario reverses, the flow reverses too. Charm is in this sense the most honest of the trio: its condition — the passage of time — always comes true.

And the shared property the whole exercise was for: none of the three forces asks the dealer's opinion. Given the book, all three can be computed — and the book, minute by minute and without guesswork, is what the feed from lesson 9 gave us.

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Now we have both the data and the language of forces. What remains is to see how it looks on a chart. The next lesson covers the strike indicators of the new pack: a positioning profile that leafs through history like a book, and a heatmap where every strike lives its own life in time.