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Dollar Gamma Exposure: Units, Scenario P/L, and Inferred GEX

Convert Gamma into position curvature, local P/L and cash-Gamma measures with explicit units, signed inventory, joint scenarios, full repricing, and dealer-GEX inference controls.

Updated

For educational purposes only; not investment advice. Investing may result in loss.

Direct answer

Dollar Gamma, Cash Gamma, and GEX are not universally standardized labels. A report may mean position Gamma, the local second-order P/L for a stated move, the Gamma-induced change in Dollar Delta for a 1% move, or an open-interest-based estimate. Values are comparable only after the exact formula, price unit, return scale, 0.5 convention, signed quantity, multiplier, currency, and timestamp are disclosed.

Raw Gamma is local model curvature, not executable P/L. Large moves, volatility-surface changes, time, dividends, exercise boundaries, gaps, and discrete hedging require full repricing and a complete cash and hedge ledger.

From unit Gamma to named monetary measures

Let unsigned long-option unit Gamma be Gamma = partial Delta / partial S, quoted per share for a $1 underlying move. Let q be signed contracts, M the compatible multiplier, S spot, Delta S the absolute price shock, and r = Delta S / S the decimal return. Position Gamma is G_pos = Gamma x q x M, measured in share-equivalent Delta per $1 move.

Local curvature P/L is P/L_Gamma ~= 0.5 x G_pos x (Delta S)^2 = 0.5 x G_pos x S^2 x r^2. Define CashGamma = G_pos x S^2; then P/L_Gamma ~= 0.5 x CashGamma x r^2. A separate common measure, G_pos x S^2 x 0.01, estimates the Gamma component of the Dollar-Delta change for a 1% spot move. It is not 1% Gamma P/L and omits the existing-Delta component of the full change in S x Delta shares.

  1. Lock the account or inference purpose, timestamp, underlying, exact series, strike, expiry, type, style, settlement, multiplier, deliverable, currency, model, and volatility-surface version.
  2. Identify whether each feed is per share, per contract, per point, already signed, or already position-scaled. Normalize to one unsigned unit Gamma plus signed q, and apply quantity, multiplier, deliverable, point value, and FX exactly once.
  3. Name the output before calculating it: G_pos, P/L_Gamma, CashGamma, 1% Dollar-Delta Gamma component, or a vendor-specific GEX. State whether 0.5 is included and whether returns use decimal or percentage-point units.
  4. Freeze spot, absolute or percentage shock, joint cross-underlying scenario, surface dynamics, time, rates, dividends, borrow, and FX. Use separate up, down, and gap scenarios rather than assuming symmetry.
  5. Calculate leg-level gross and same-underlying net measures first. Aggregate across underlyings only as monetary P/L under an explicit joint scenario and FX conversion; retain gross exposure, Delta, Theta, Vega, and costs.
  6. Validate local results with finite differences and full repricing. Prewrite hedge fills, spread and impact, liquidity, expiration, exercise, assignment, cash or physical settlement, adjustment, halt, and remaining-inventory branches.
  7. Separate known account positions from public-OI-based dealer estimates. Disclose direction heuristics and missing OTC or exotic inventory, version the data, and reconcile fills, hedges, settlements, model P/L, actual P/L, and records.

Vanilla unit calls and puts normally have positive Gamma for a long holder; signed q makes a short position negative. If a vendor feed is already signed or aggregated, applying the sign or multiplier again is an error. Index, futures-option, adjusted, and cash-settled products may use points or non-share deliverables.

Worked examples

  • One position, four different numbers. Let S = $100, Gamma = 0.04, q = +10, and M = 100. Then G_pos = 40 shares/$. A 1% move has Delta S = $1: Gamma P/L is 0.5 x 40 x 1^2 = $20, Gamma-induced Delta change is 40 shares, the frozen-spot Dollar-Delta component is $4,000, and CashGamma = $400,000. For a 5% move with Gamma artificially frozen, P/L is 0.5 x 40 x 5^2 = $500, or 25 times the 1% result.
  • Same-underlying gross exposure can net to zero. At S = $250, 20 long calls with Gamma = 0.018 and 15 short puts with Gamma = 0.024, all M = 100, produce G_A = +36 shares/$ and G_B = -36 shares/$. A 2% move has Delta S = $5; leg Gamma P/L is +$450 and -$450, net zero. The two 1% Dollar-Delta Gamma components are +$22,500 and -$22,500, so gross is $45,000 despite zero net.
  • Cross-underlying aggregation needs a joint scenario. Underlying A has S_A = $50, G_A = +200 shares/$, and r_A = +2%, giving Delta S_A = $1 and +$100 Gamma P/L. Underlying B has S_B = $200, G_B = -20 shares/$, and r_B = -1%, giving Delta S_B = -$2 and -$40. This declared joint scenario totals +$60; the raw sum 200 - 20 has no cross-underlying monetary meaning.
  • Open interest cannot choose the dealer sign. At S = $400 and M = 100, calls with Gamma = 0.0025 and OI = 10,000 have G magnitude 2,500 shares/$ and a 1% Dollar-Delta Gamma magnitude of $4.00 million. Puts with Gamma = 0.0030 and OI = 8,000 have magnitude 2,400 shares/$ and $3.84 million. A call-positive, put-negative heuristic reports +$160,000; both long reports +$7.84 million, and both short -$7.84 million. Public OI alone cannot select among them.

Risks and controls

  • Dollar Gamma, Cash Gamma, Gamma P/L, and GEX labels can conceal different formulas.
  • Gamma can be per share, per contract, per point, or already position-scaled.
  • Signed quantity or feed sign can be applied twice or omitted.
  • Quantity, multiplier, point value, deliverable, or FX can be multiplied twice.
  • Omitting or duplicating the Taylor 0.5 changes Gamma P/L by a factor of two.
  • Decimal returns, percentage points, and percentages can create factors of 100 or 10,000.
  • A $1 move and a 1% move differ whenever spot is not $100.
  • Omitting S^2 confuses raw position Gamma with a cash-scaled measure.
  • Gamma P/L can be confused with the Gamma component or total change in Dollar Delta.
  • Stale spot, model, surface, rates, dividends, borrow, or timestamp corrupts the result.
  • Frozen Gamma becomes unreliable for large moves, gaps, or long scenario horizons.
  • Up and down full repricing can differ because volatility skew and surface dynamics move.
  • Near-expiry and 0DTE Gamma can change sharply within minutes.
  • American exercise, discrete dividends, halts, and corporate actions can create boundaries or adjustments.
  • Equity shares, index points, futures contracts, and cash settlement use different units.
  • Cross-underlying sums require explicit joint shocks, currencies, FX, and correlation assumptions.
  • Small net Gamma can hide large gross, legging, liquidity, and model exposure.
  • Delta, Theta, Vega, Vanna, Charm, financing, hedges, and costs can dominate total P/L.
  • Public OI lacks dealer direction, opening or closing flow, OTC inventory, and dynamic hedges.
  • Hedge fills, gaps, impact, settlement, model P/L, actual P/L, and records can fail to reconcile.

Common misconceptions

  • “Dollar Gamma has one standard formula.” Vendors use different scaling, signs, moves, and 0.5 conventions.
  • “1% Cash Gamma equals 1% Gamma P/L.” One may measure Dollar-Delta change while the other is quadratic P/L.
  • “Positive Gamma guarantees positive total P/L.” Delta, Theta, Vega, surface changes, hedging, and costs remain.
  • “Raw Gamma can be added across stocks.” Only a declared joint monetary scenario creates an interpretable sum.
  • “Public dealer GEX reveals dealer inventory or predicts direction.” OI does not identify ownership, flow, OTC books, or hedges.

Authoritative sources

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