Δ
Option Greek

Delta

How much your option follows the stock

Category Direction

What is Delta?

Think of Delta like a speedometer. It doesn't tell you where you're going — it tells you how fast your option price is moving right now relative to the stock.

Delta gauges how much the price of an option contract is expected to change for every ₹1 (or $1) move in the underlying asset. A call with delta 0.60 gains approximately ₹0.60 when the stock rises ₹1. It is the most-used number in options trading — simple, direct, and immediately actionable.

Formula
Δ = ∂V / ∂S
∂Vchange in the option's price
∂Schange in the underlying asset's price
partial derivative — rate of change at a given moment

Delta ranges from 0 to 1 for call options and 0 to −1 for put options. Put options carry negative delta because they gain value as the stock falls. Deep in-the-money options behave almost like the stock itself (delta near ±1.0), while far out-of-the-money options barely move (delta near 0).

The One Rule to Know

Delta × stock move ≈ option P&L per share. A 0.40 delta call on a $3 stock move gains approximately 0.40 × $3 = $1.20 per share, or $120 per contract. This is the most-used calculation in options trading — every professional trader does this math constantly.

Moneyness Call Delta Put Delta What it means
Deep ITM 0.80 – 1.00 −1.00 – −0.80 Behaves almost exactly like owning the stock
Slightly ITM 0.55 – 0.80 −0.80 – −0.55 Closely tracks the stock with less capital
At-the-Money (ATM) ≈ 0.50 ≈ −0.50 Moves about half as much as the stock
Slightly OTM 0.25 – 0.45 −0.45 – −0.25 Leveraged but less responsive to small moves
Far OTM 0.05 – 0.20 −0.20 – −0.05 Barely moves — needs a big rally to matter

Delta also gives you a quick read on the probability of expiring in-the-money. A call option with delta 0.70 has roughly a 70% chance of finishing in the money at expiry. It is not mathematically exact, but professional traders use this rule of thumb daily for strike selection and position sizing. A 0.20 delta is a low-probability bet; a 0.70 delta is a higher-conviction, lower-leverage trade.

Delta vs Stock Price

Delta value
0 +1 -1 ATM Call Delta Put Delta OTM ITM
Stock Price (relative to strike) →

How to Read This Chart

  • Green curve (calls) starts near 0 far OTM, crosses 0.50 at ATM, and approaches 1.0 deep ITM.
  • Red curve (puts) mirrors it — starts near −1 deep ITM and rises to 0 far OTM.
  • The white dot marks ATM — both calls and puts have delta ≈ ±0.50 here.
  • Both curves have an S-shape — delta accelerates fastest near ATM. That acceleration is measured by Gamma.

Frequently Asked

What does delta 0.40 mean in practice?

For 1 contract (100 shares), a delta of 0.40 means a $1 rise in the stock gains approximately $40. A $5 rise gains roughly $200. This approximation holds well for small moves but breaks down for large moves — that's where gamma matters.

Can I use delta as probability of profiting?

Approximately. Delta ≈ probability of expiring in-the-money. A 0.25 delta call has roughly a 25% chance of being ITM at expiry. Traders use this constantly for strike selection — selling 0.15–0.20 delta options is a popular premium-collecting strategy because statistically, they expire worthless ~80% of the time.

Why is put delta negative?

Puts profit when price falls — the opposite direction of stock. The negative sign captures this. A put with delta −0.35 gains $35 per contract for every $1 the stock drops. Don't be confused by the sign — it's just showing you the direction, not that the option is losing value.

Does delta change while I hold the position?

Constantly. Delta is not static — it shifts with every price tick, every day that passes, every change in volatility. This is why you check Greeks on your broker platform in real time, not once when you enter. An ATM call at delta 0.50 can become a 0.75 delta call after a 5% rally — the position has fundamentally changed character.

What is "delta neutral" and should I care?

A portfolio is delta neutral when total delta ≈ 0 — it makes money from sources other than direction (like volatility or time). Market makers and professional traders maintain delta-neutral books to isolate other risks. For most retail traders, it's less relevant, but understanding it helps you see why institutions behave the way they do when hedging large option positions.

A Real Example

Scenario

AAPL is trading at $200. You buy 1 contract of the $200 strike call (ATM) for $5.00. Delta = 0.50. You control 100 shares.

1
AAPL rises to $202 (+$2)
Estimated gain: 0.50 × $2 × 100 = +$100. Option worth ≈ $6.00. You're up 20% on a 1% stock move — that's option leverage.
2
AAPL continues to $210 (+$10 total)
As the call goes deeper ITM, delta increased along the way (gamma). Actual gain likely >$550 — more than delta alone predicted because delta kept growing during the rally.
3
Instead, AAPL falls to $195 (−$5)
Estimated loss: 0.50 × $5 × 100 = −$250. But as delta shrinks going OTM, actual loss is a bit less. Option worth ≈ $2.50.

When you're right, gains accelerate (delta grows). When you're wrong, losses decelerate (delta shrinks). This asymmetry — called convexity — is a structural advantage of buying options over owning stock.

What Beginners Get Wrong

Treating delta as fixed. Delta changes with every tick. After a big move, your option behaves completely differently. A 0.30 delta call you bought might be a 0.70 delta call after a 10% rally. Always think delta + gamma together — delta is a snapshot, not a constant.
Getting confused by put delta's negative sign. A put with delta −0.30 is not "30% broken." It means the put gains $0.30 for every $1 the stock falls. Many beginners misread this and think a negative delta means the option is losing money. It just means direction is inverted.
Using only delta to estimate P&L over multiple days. Delta is an instantaneous measure. If you hold an option for a week with the stock flat, theta (time decay) has been silently eating your premium even though delta said you should break even. Always account for the full picture: delta, theta, and vega.
Test Yourself

Quick Quiz

Answer all questions and check your score.

1 A call option has delta 0.60. The stock rises $2. How much does the option price approximately change?

2 What is the approximate delta of an at-the-money (ATM) call option?

3 An option with delta 0.30 has approximately what probability of expiring in-the-money?

4 Which of these call options has the highest delta?

5 Put options have delta values between: