Delta: Measuring Option Price Sensitivity

What is Delta?

Delta is one of the most important Option Greeks.

It measures the expected change in an option's premium for a change in the price of the underlying asset.

In simple terms:

Delta tells you how sensitive an option premium is to changes in the underlying price.

For example, if a Call Option has a Delta of 0.5, a ₹10 rise in the underlying may result in approximately a ₹5 increase in the option premium, assuming other factors remain unchanged.

Similarly, a ₹10 fall may result in approximately a ₹5 decrease in the premium.

The relationship can be expressed as:

Expected Change in Premium = Delta × Change in Underlying Price

This is an approximation, because other factors can also affect the premium.

Delta of a Call Option

A Call Option has a positive Delta.

Its Delta generally ranges from:

0 to +1

A higher Delta means the Call Option tends to respond more strongly to changes in the underlying.

Example

Suppose:

• Call Option Delta = 0.40
• Underlying rises by 20 points

Expected change in premium:

0.40 × 20 = 8 points

So, the option premium may increase by approximately 8 points.

If the underlying falls by 20 points, the premium may decrease by approximately 8 points.

Delta of a Put Option

A Put Option has a negative Delta.

Its Delta generally ranges from:

-1 to 0

The negative sign indicates that the Put premium generally moves in the opposite direction to the underlying.

Example

Suppose:

• Put Option Delta = -0.40
• Underlying falls by 20 points

Expected change in premium:

-0.40 × (-20) = +8 points

So, the Put premium may increase by approximately 8 points.

If the underlying rises, the Put premium generally falls.

Why is Call Delta Positive and Put Delta Negative?

The sign of Delta reflects the direction in which the option premium generally moves.

Call Option

When the underlying price rises, a Call becomes more valuable.

Therefore, Call Delta is positive.

Put Option

When the underlying price rises, a Put generally becomes less valuable.

Therefore, Put Delta is negative.

This makes Delta useful for quickly understanding the directional behaviour of an option.

Delta and Moneyness

The value of Delta also changes depending on whether an option is ITM, ATM or OTM.

These are approximate ranges, not fixed values.

Why is ATM Delta Around 0.5?

An ATM option is close to the current market price of the underlying.

Its Delta is generally around:

• +0.50 for an ATM Call
• -0.50 for an ATM Put

This means an ATM option usually responds to changes in the underlying more than a deep OTM option, but less like a deep ITM option.

Why Can't Call Delta Go Above 1?

Consider a Call Option with a Delta greater than 1.

If the underlying rises by 10 points and the Delta is 1.5, the option premium would theoretically rise by 15 points.

That would mean the derivative is moving more than the underlying itself.

The source explains why this does not make sense for a Call Option.

Therefore, Call Delta is capped at +1.

Similarly, it cannot fall below 0.

So:

Call Delta = 0 to +1