Net Greeks: Aggregating Delta, Gamma, Theta, and Vega

For educational purposes only; not investment advice.

Direct answer

Net Greeks are the signed, scaled sums of local option sensitivities across every leg of a position or portfolio. They answer questions such as: how many share-equivalents of directional exposure exist now; how quickly that Delta may change; how much model value may change with one day passing; and how sensitive value is to an implied-volatility move.

For Greek (G), a basic aggregation is:

G_net = sum_i(position sign_i × contracts_i × multiplier_i × G_i)

Long positions use a positive position sign and shorts a negative one. Stock contributes Delta directly, usually +1 per long share and −1 per short share, but normally has zero option Gamma, Theta, and Vega. Aggregation is valid only after every input uses compatible units, underlying risk factor, valuation time, and scenario convention.

What the totals mean

Net Delta is the first-order change in portfolio value for a small underlying-price move. After multiplier scaling it is often read as share-equivalent exposure. Net Gamma estimates the change in net Delta for an underlying move and adds curvature to P&L. Net Theta estimates change from passage of time with other model inputs fixed. Net Vega estimates change for an implied-volatility move.

A second-order local approximation is:

Delta V ≈ Delta_net Delta S + 0.5 Gamma_net (Delta S)^2 + Vega_net Delta IV + Theta_net Delta t

This is a local model expansion, not a payoff guarantee. Greeks change as spot, time, volatility surface, rates, dividends, and exercise assumptions change. Cross-Greeks and higher-order terms matter for large or simultaneous shocks.

Units must be stated. A platform may show Delta per share or already multiplied by 100; Gamma may describe Delta change per $1 or per 1%; Theta may be per calendar day, trading day, or year; Vega may be per one volatility percentage point or per 1.00 decimal change. Adding unmatched displays can produce errors of 100 times or more.

A four-component portfolio

Assume all options share one underlying and use a 100 multiplier:

Long 3 calls: Delta 0.55, Gamma 0.025, Theta −$0.06 per day, Vega $0.12 per volatility point, each quoted per share.
Short 2 calls: Delta 0.30, Gamma 0.018, Theta −$0.04 per day, Vega $0.09 per point, each before applying the short sign.
Short 50 shares.

The scaled totals are:

Net Delta = (3×100×0.55−2×100×0.30−50=55) share-equivalents.
Net Gamma = (3×100×0.025−2×100×0.018=3.9) Delta units per $1 move.
Net Theta = (3×100×(-0.06)−2×100×(-0.04)=-$10) per day.
Net Vega = (3×100×0.12−2×100×0.09=$18) per volatility point.

For a local scenario in which the stock rises $2, IV falls 3 percentage points, and one day passes:

Delta V ≈ 55 × 2 + 0.5 × 3.9 × 2^2 + 18 × (-3) - 10 = $53.80

This estimate ignores changes in Greeks during the move, volatility skew reshaping, cross-effects, Bid/Ask spreads, and discrete execution. Revalue every leg under the full scenario for a stronger check.

Portfolio Greek checklist

Inventory every option and share position by underlying, expiration, strike, type, side, quantity, multiplier, and deliverable.
Preserve signs: a short position reverses the option’s displayed Greek; a put’s raw Delta is generally negative before position sign.
Confirm whether the platform already applies quantity and multiplier. Never multiply twice.
Record the unit for each Greek, especially Theta time basis and Vega volatility basis.
Aggregate only like risk factors. Delta in one stock cannot be mechanically added to Delta in another without defining a common dollar, beta, or factor exposure.
Separate expirations and volatility-surface nodes. Equal total Vega can hide long near-term volatility and short long-term volatility.
Recalculate after spot, IV, time, dividends, rates, fills, exercise, assignment, or corporate actions.
Inspect gross as well as net exposure. Large offsetting legs can show small net Greeks while retaining liquidity, basis, jump, and execution risk.
Stress price and IV together, not only one at a time. Equity declines often coincide with skew and volatility changes.
Include nonlinear scenarios near expiration, where Gamma can change quickly and a small net Delta can become large.
Check sign conventions for Theta and Rho; vendors do not always report the same bump direction.
Use full repricing for large shocks and compare it with the Greek approximation to measure approximation error.
Include Bid/Ask, fees, margin, early exercise, assignment, settlement, and inability to close all legs simultaneously.
Treat calculated Greeks as model outputs. Different rates, dividends, volatility surfaces, clocks, and American-exercise models can produce different values.
Do not infer maximum loss from Greeks; use the actual payoff and stress scenarios.

Common misconceptions

“Net Delta of zero means no risk.” Gamma, Vega, Theta, jumps, basis, and liquidity can remain substantial.
“Greeks are fixed contract attributes.” They are recalculated model sensitivities.
“A positive Greek is always beneficial.” Its desirability depends on the market move, cost, horizon, and other exposures.
“Netting removes gross exposure.” Offsetting sensitivities do not remove legging, margin, assignment, or surface-basis risk.
“Vega from every expiration is interchangeable.” Different maturities and strikes respond to different parts of the volatility surface.
“Theta is guaranteed daily cash income.” It is a model partial derivative, not a booked payment.
“The Taylor estimate is exact.” It is local and omits higher-order and cross-effects.
“All platforms use the same units.” Scaling and bump conventions vary.
“Greeks reveal maximum loss.” Payoff, path, exercise, settlement, and execution determine realized loss.