Call Option Delta Calculator

Updated on 15-Jul-2025

Call Option Delta Calculator to understand how much the price of a call option will change when the underlying asset’s price changes.

Stock Price ($):

Strike Price ($):

Time to Expiration (years):

yrs

Volatility (%):

Risk-Free Rate (%):

Option Delta Calculation

Call Option Delta

0.00

Delta Interpretation

Enter values to calculate

About Call Option Delta

• Delta measures how much an option's price changes when the underlying stock moves $1
• Call delta ranges from 0 to 1 (0% to 100% probability of being in-the-money)
• Delta = N(d1) in the Black-Scholes model
• At-the-money options typically have delta ~0.5

What is Call Option Delta?

Call Option Delta is a measure of how much the price of a call option will change when the price of the underlying asset changes by $1.

It ranges from 0 to 1, where:

A delta close to 0 means the option is deep out-of-the-money.
A delta close to 1 means the option is deep in-the-money.

If a call option has a delta of 0.68, it means that for every $1 increase in the stock price, the option price increases by approximately $0.68.

Call Option Delta Formula (Black-Scholes)

To calculate the delta of a European call option, we use the following formula:

$Call Delta = N (d_{1})$

Where:

$N (d_{1})$ is the cumulative distribution function (CDF) of the standard normal distribution.
$d_{1}$ is calculated using:

$d_{1} = \frac{ln (\frac{S}{K}) + (r + \frac{σ^{2}}{2}) T}{σ \sqrt{T}}$

Example: Call Delta Calculation

Let’s calculate the delta using the following values:

Stock Price (S) = 100
Strike Price (K) = 95
Time to Expiry (T) = 0.5 years
Volatility (σ) = 30% = 0.30
Risk-Free Rate (r) = 5% = 0.05

Step 1: Calculate $d_{1}$

$d_{1} = \frac{ln (\frac{100}{95}) + (0.05 + \frac{{0.30}^{2}}{2}) \times 0.5}{0.30 \times \sqrt{0.5}} \approx 0.466$

Step 2: Find the Call Delta

$Call Delta = N (0.466) \approx 0.6793$

Symbol	Meaning
$S$	Current Stock Price
$K$	Strike Price of the Option
$T$	Time to Expiry (in years)
$σ$	Volatility (as a decimal, e.g. 30% = 0.30)
$r$	Risk-Free Interest Rate (as a decimal, e.g. 5% = 0.05)

Final Answer:

The call option delta is approximately 0.679.

This means for every $1 increase in the stock price, the call option price is expected to increase by $0.68 to $0.68, assuming all other factors remain constant.

Interpretation:

Delta helps estimate price movement of the option.
A delta of 0.679 means there is also a 67.9% probability that the option will expire in the money, under the Black-Scholes model.