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

Learn how to aggregate signed option Greeks across legs, contracts, multipliers, and stock, interpret the units, and stress a portfolio beyond a single snapshot.

Canonical: https://wiki.fcontext.com/options/net-greeks/
Fact checked: 2026-07-22

> For educational purposes only; not investment advice.

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## 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.

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## 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.

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## 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.

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## 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.

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## 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.

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## Related topics

- [Delta and Gamma](/options/delta-and-gamma/)
- [Theta](/options/theta/)
- [Vega](/options/vega/)
- [Delta-Gamma approximation](/options/delta-gamma-approximation/)

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## Primary sources

- [Cboe: Learning the Greeks—An Expert's Perspective](https://www.cboe.com/insights/posts/learning-the-greeks-an-experts-perspective)
- [Cboe: Options Calculator](https://www.cboe.com/education/tools/options-calculator/)
- [OCC: Industry Services—Delta Values](https://www.theocc.com/clearance-and-settlement/industry-services)
- [Black and Scholes (1973): The Pricing of Options and Corporate Liabilities](https://doi.org/10.1086/260062)