OPTIONS FIELD GUIDE · 03

The Greeks

Greeks are model-based sensitivities. They estimate how theoretical option value may respond when one input changes while the others are held constant.

10 min READFOUNDATIONALUPDATED JUL 2026
ΔDeltaUNDERLYING PRICE

Approximate option-price change for a $1 move in the underlying. Calls usually have positive delta; puts negative.

ΓGammaDELTA CHANGE

Approximate change in delta for a $1 underlying move. Delta changes as the underlying moves.

ΘThetaPASSAGE OF TIME

Approximate value change for one day passing, with other inputs unchanged. Long options commonly have negative theta.

VVegaIMPLIED VOLATILITY

Approximate value change for a one-volatility-point IV move. Long calls and puts commonly have positive vega.

ρRhoINTEREST RATES

Approximate value change for a one-percentage-point rate move. Usually more material for longer-dated contracts.

Read the units before reading the number

GREEKSHOCKROUGH INTERPRETATION
Delta 0.45Underlying +$1Option value about +$0.45
Gamma 0.04Underlying +$1Delta about +0.04
Theta −0.08One day passesOption value about −$0.08
Vega 0.12IV +1 pointOption value about +$0.12

These local approximations can diverge from actual P/L. Larger shocks make curvature and interactions between inputs increasingly important.

Where the sensitivities concentrate

NEAR ATMGamma can be largest

Especially close to expiration, delta can change quickly around the strike.

MORE TIMEVega can be larger

Longer-dated options generally have more exposure to changes in IV.

NEAR EXPIRYTheta can accelerate

Extrinsic value has less time remaining and can decay nonlinearly.

Portfolio Greeks add position direction and size

A short contract reverses the sign of the option’s quoted Greeks; each standard equity contract usually represents 100 shares. Portfolio values therefore aggregate approximately as quoted Greek × contracts × 100 × position sign. Multi-leg positions can neutralize one sensitivity while retaining another.

Greeks depend on their inputs

The pricing model, implied-volatility input, rate and dividend assumptions, and quote quality all influence the result. Recalculate them as spot, time, and volatility change.

APPLY IT

See the Greeks of a complete position.

Build multiple option legs plus an aggregate stock position, then inspect portfolio Delta, Gamma, Theta, and Vega.

Authoritative reading

Options Industry Council: Understanding Options Greeks ↗Options Industry Council: Volatility and the Greeks ↗
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