delta

 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.