metrics & theory

Options are levered and convex. They can be used to express a view on direction and volatility. Due to their capital efficiency and flexibility, they have made up an increasing proportion of market activity. (cf. Cboe)

An option is a contract between a buyer and a seller. It is a convex exposure that participants must actively manage. If options control a substantial portion of the notional value transacted in an asset, participant repositioning will influence the underlying price. But underlying price influences options prices too! We specialize in capturing and visualizing these feedback loops (such as the infamous "gamma squeeze").

In order to understand the effect of options, a natural intuition is to wonder how many there are. If we know that, we should be able to model how option prices will behave to understand how participants will reposition. It turns out that "how many" is a difficult question. And that what we really care about, "Where is the risk?" is a slightly different question.

Approaches to Measuring Exposure

1. Open Interest (OI)

The most reliable metric of "how many" is open interest. After each trading day, the OCC (Options Clearing Corporation) tallies up option orders "to open" and orders "to close." They report the results of the tally before the next trading day. So from one day to the next we know "how many." In general, opening and closing order data is not available intraday. Additionally, since options spreads are wide, and most transactions take place at the mid-price, it can be difficult to discern from Time & Sales data whether an option has been bought or sold. Open interest may not tell us anything about who holds the inventory but it does tell us how much notional risk is coming from the options world in aggregate.

2. Volume

We can enrich our picture by using volume in conjunction with open interest. Wherever volume is greater than open interest, we can guess that new contracts are being added, or at the very least, glean an intraday picture of where the activity is. Volume is not directional, and is at best a blunt measure of notional risk.

3. Participant Flow Tagging

A common industry approach relies on participant flow tagging. Tagged datasets categorize volume by participant type (such as customer, broker-dealer, or market maker) and trade origin (open versus close). Some feeds provide this data through end-of-day reports or intraday batch snapshots.

Tagging appeals to traders because it attempts to track cumulative inventory over the life of a contract. However, cumulative inventory does not reliably show current hedging behavior. Desks frequently absorb, re-hedge, or net older positions across other books.

Additionally, even if one assumes that only market makers hedge, models that rely on participant tags face key structural limitations:

• Decay of Historical Inventory: Tracking inventory over the contract lifecycle assumes that old positions exert active hedging pressure. In reality, traders absorb, re-hedge, or net older positions over time. Cumulative tallies treat stale inventory as active risk.
• Single-Exchange Asset Limitation: Full-scale tagging only works for single-exchange assets. Consolidated feeds for multiply-listed equities and ETFs trade across many venues without unified participant tags.
• Cross-Product Risk Budgets: Dealers operate multiple trading desks across correlated products like index options, ETFs, and futures. Central risk desks net exposures internally between these products. Tagging contracts in isolation misses these shared risk budgets.
• Non-Linear Hedging & Execution Timing: Participants do not hedge continuously according to theoretical Greeks. They adjust risk at discrete intervals and trade within hedging bands. Traders also rebalance during high-volume periods to reduce market impact.
• Risk Sensitivity: Tagging does not reveal how risk-sensitive the holders of the inventory are.
• Batch Reporting: Tagged data often arrives in periodic batch snapshots rather than reflecting continuous, real-time quote repricing.

More fundamentally, participant flow tagging relies on an oversimplified framework. Traditional models assume that only dealers hedge while all other participants stay passive. In reality, many market participants actively reposition based on their own risk incentives.

4. Classified Volume as a Measure of Volatility Supply

The problem becomes simpler once we stop asking "how many" and ask instead, "where is the risk?" That reframing doesn't require knowing who is trading; it requires measuring what flow does to price.

A dealer's immediate concern is not whether an order opens or closes a position, but how it changes their exposure. If a buyer and a seller can be matched, the dealer captures the spread and inventory stays flat. Whenever one side can't be matched, the dealer reprices instead of rushing to hedge: left short calls, for example, they raise the price to buy those calls back and raise the price to sell more, so the next order is more likely to hand the position back to them, closing the loop before it ever reaches the underlying.

That logic isn't limited to designated dealers. Providing liquidity and taking it are roles, not identities tied to an account type. Whoever absorbs the other side of a trade without moving the price is providing liquidity in that moment. Whoever pays up to transact immediately is taking it — a hedge fund can take liquidity, and a retail trader can provide it. In practice the broader market behaves like a distributed market maker, matching buyers with sellers and repricing where it cannot.

So instead of tracking any one firm's book, we measure that function across the whole market: we observe how prices react to orders as they happen, to see whenever demand outpaces supply, and vice versa. When the surface absorbs volume without price distortion, trading is elastic. When one-sided flow forces quotes to adjust, we call that surface inelasticity—a sign that supply and demand have distorted the volatility surface.

This is like learning to play blackjack by counting cards: tracking the composition of the deck, not guessing each player's hand (cf. Hau Volatility). The same idea underlies classic price-impact theory (cf. Kyle).

Under the hood, we measure trades against a proprietary theoretical valuation benchmark. The model assumes extracted edge always favors the liquidity provider. The direction of the edge a trade pays tells us which side is providing liquidity (makers) and which is taking it (takers):

• Taker Buys (Above Theo): Takers concede edge to buy immediately. Volatility is undersupplied, leaving makers warehousing short volatility risk at that strike.
• Taker Sells (Below Theo): Takers concede edge to exit immediately. Volatility is oversupplied, leaving makers warehousing long volatility risk at that strike.

Our maker-taker framework is designed to map where risk concentrates, and update that map in real time. Risk that makers warehouse shows up in price, so we measure how the surface is absorbing flow now instead of reconstructing the full stock of positions. We highlight what matters: prices and how they change.

Pipeline

Our pipeline processes data as follows:

 ┌────────────────────────────────────────────────────────────────────────┐
 │                      1. THE RAW OBSERVATION                            │
 │ Trades execute across strikes and expirations.                         │
 └───────────────────────────────────┬────────────────────────────────────┘
                                     │
                                     ▼
 ┌────────────────────────────────────────────────────────────────────────┐
 │                 2. MEASURING VOLATILITY SUPPLY                         │
 │ gexbot measures aggressive order flow to map net maker inventory:      │
 │ • Taker Buy  → Maker Short Volatility (Undersupplied strike)           │
 │ • Taker Sell → Maker Long Volatility (Oversupplied strike)             │
 └───────────────────────────────────┬────────────────────────────────────┘
                                     │
                                     ▼
 ┌────────────────────────────────────────────────────────────────────────┐
 │                 3. GREEKS FILTER                                       │
 │ The model filters risk-sensitive inventory via options greeks:         │
 ├───────────────────────────────────┬────────────────────────────────────┤
 │ • DEX (Delta)                     │ Directional capital exposure       │
 │ • GEX (Gamma / Convexity)         │ Second-order price curvature       │
 │ • Vanna / Charm                   │ Volatility and time decay risk     │
 └───────────────────────────────────┬────────────────────────────────────┘
                                     │
                                     ▼
 ┌────────────────────────────────────────────────────────────────────────┐
 │                  4. THE HOLISTIC STRUCTURAL MAP                        │
 │ A spatial map shows where volatility is scarce or well supplied, and   │
 │ how inventory responds to spot, volatility, and time.                  │
 └────────────────────────────────────────────────────────────────────────┘

Conclusion

gexbot measures risk-sensitive inventory across the market by tracking the elasticity of the volatility surface.

This approach separates flow into liquidity makers and liquidity takers. The greeks then act like a lens that helps map the most relevant levels from options-space onto underlying price-space. They model the likely systemic response of participants as spot price, volatility, and time change.

Much like transacted volume, what matters most is the flow that has yet to be fully digested. What is most recently measured is most relevant, because it reflects the latest state of price elasticity at that part of the surface.

What we truly want to know is not "how many?", but instead, "where is there not enough?"