In options trading, Delta (Δ) measures how much an option’s price changes when the underlying stock moves by $1.
What Is Delta?
Mathematically:
Δ
=
∂
𝑉
∂
𝑆
Δ=
∂S
∂V
Where:
V = Option price
S = Underlying stock price
👉 Delta tells you the sensitivity of the option price to stock movement.
🔹 Simple Example
If a call option has:
Delta = 0.60
Then:
If the stock rises $1 → option gains ~$0.60
If the stock falls $1 → option loses ~$0.60
Since 1 contract = 100 shares:
$0.60 × 100 = $60 change per contract
🔹 Delta Range
Option Type Delta Range
Call Option 0 to +1
Put Option -1 to 0
ATM options ≈ 0.50 (calls) or -0.50 (puts)
Deep ITM calls ≈ 0.80–0.99
Deep OTM calls ≈ 0.01–0.20
🔹 What Delta Also Represents
1️⃣ Probability Approximation
Delta roughly represents the probability the option expires ITM.
Example:
Delta 0.70 ≈ 70% chance of expiring in-the-money.
(Not exact, but commonly used as a quick estimate.)
2️⃣ Share Equivalent (Hedge Ratio)
Delta shows how many shares your option behaves like.
Example:
1 call with Delta 0.60 ≈ 60 shares of stock exposure.
So:
10 contracts × 0.60 × 100 = 600 share equivalent
🔹 How Delta Changes (Gamma Effect)
Delta is not fixed. It changes when the stock price moves.
4
As calls move ITM → Delta approaches 1
As calls move OTM → Delta approaches 0
Gamma controls how fast delta changes.
🔹 Why Delta Matters
Delta helps you:
Estimate profit/loss from stock moves
Choose strike prices
Manage risk
Hedge positions
Build neutral strategies (delta-neutral trading)
🔹 Quick Intuition
Think of Delta like:
The “speed” of the option relative to the stock.
If the stock moves fast and your delta is high → your option moves almost as much as the stock.
If you'd like, I can also explain how delta works together with theta and gamma in real trades, or show examples of delta-based strategy selection.
