Call Option Delta

Options
Updated Apr 2026 • Has calculator

The rate of change in a call option's price for a $1 move in the underlying stock.

What is Delta (Call)?

Delta (Δ) measures how much a call option's price changes when the underlying stock price moves by $1. Call delta ranges from 0 to 1: a delta of 0.60 means the call gains $0.60 for every $1 rise in the stock. At-the-money calls have delta near 0.50. Deep in-the-money calls approach delta 1.0; far out-of-the-money calls approach 0. Delta also approximates the probability that the option expires in the money.

Formula

Δ_call = N(d₁)

Worked Example

Worked example — Apple Inc. (AAPL) — ATM call, representative Q1 2024

Representative Q1 2024 market conditions

Step 1  Stock price (S): $185.00, Strike (K): $185.00
Step 2  Risk-free rate: 5.25%, Volatility: 28%, T = 0.25 yrs
Step 3  d₁ = [ln(1) + (0.0525 + 0.0392)×0.25] / (0.28×0.50) = 0.163
Step 4  Δ_call = N(0.163) ≈ 0.565
Step 5  → If AAPL rises $1.00, this call gains approximately $0.57
Step 6  → Delta ≈ 56.5% probability the option expires in the money

Source: Hull, J.C. — Options, Futures, and Other Derivatives, 11th ed., Ch. 19 (2024-01-15)

Calculate Delta (Call)

Current market price of the underlying stock

Option strike price

Annual risk-free rate

Time to expiration in years

Annualised implied volatility

Call Delta

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Not investment advice.

How to Interpret Delta (Call)

< 0.25
Far OTM — low sensitivity, ~15–25% ITM probability
0.25 – 0.45
Slightly OTM — moderate sensitivity
0.45 – 0.55
At-the-money — delta ≈ 0.50
> 0.55
In-the-money — high sensitivity to stock moves

📚 Options Basics — Complete the path

  1. Delta (Call)
  2. Gamma
  3. Theta (Call)
  4. Vega
  5. BS Call
Sources
  1. Hull, J.C. — Options, Futures, and Other Derivatives, 11th ed.
  2. Investopedia — Delta
  3. CBOE Education Center