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Delta (Δ)

Delta measures how much an option's price changes when the underlying moves $1.

Interactive Delta Curve​

Explore how delta changes across spot prices for different positions.

Position:
Days to Expiry30d
1d90d
Implied Volatility50%
10%150%
Positive delta: profits when price rises. Click or drag to move spot price.
ITMOTMATM1.00.50.00.00.0$70kStrike $100k$130kSpot PriceDelta
Spot Price
$100.0k
Delta
+0.540
Moneyness
ATM
Hedge Ratio
54%
Gamma Risk
Low
Delta = +0.540 → For every $1,000 move in spot, the option moves $540 in the same direction

Values by Position​

Option
Delta Range
Example
Long call
0 to +1
Δ = 0.5 means +$0.50 per $1 up
Long put
-1 to 0
Δ = -0.5 means +$0.50 per $1 down
Short call
0 to -1
Opposite of long call
Short put
0 to +1
Opposite of long put

Delta by Moneyness​

Moneyness
Call Δ
Put Δ
Deep ITM
~1.0
~-1.0
ATM
~0.5
~-0.5
Deep OTM
~0.0
~0.0

Interpretations​

Delta has multiple useful interpretations:

  1. Price sensitivity: A 0.5 delta call gains 0.50whenunderlyingrises0.50 when underlying rises 1
  2. Hedge ratio: To delta-hedge 10 calls with 0.5 delta, short 5 units of underlying
  3. Probability proxy: ~50% delta ≈ roughly 50% chance of expiring ITM (approximation)

Delta Changes​

Delta isn't constant. It changes based on:

  • Underlying price - Moving ITM increases delta, OTM decreases it
  • Time to expiry - Near expiry, delta snaps to 0 or 1
  • Volatility - Higher vol spreads delta more evenly across strikes
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The rate at which delta changes is measured by gamma. High gamma means delta is unstable.

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