Delta

Key takeaways

• Delta (Δ) measures how much a derivative’s price changes for a $1 move in its underlying asset.
• Call option deltas range from 0 to +1; put option deltas range from 0 to −1.
• Delta can be interpreted as a hedge ratio, a measure of directional risk, and (approximately) the probability an option will finish in the money.
• Traders use delta to hedge, construct delta-neutral positions (delta spreads), and manage portfolio exposure.

What is delta?

Delta is the first derivative of an option’s price with respect to the price of the underlying asset. It estimates how much the option’s price will change for a $1 change in the underlying security and is denoted Δ. Delta is produced by option pricing models and updated continuously by trading systems.

Delta has three common interpretations:
* Price sensitivity — how option value changes with the underlying price.
* Hedge ratio — number of underlying units needed to hedge option exposure to be delta-neutral.
* (Approximate) probability that the option will expire in the money.

Call and put option deltas

Call and put deltas behave predictably depending on moneyness and time to expiration.

Call options:
* Range: 0 to +1.
* At-the-money: about +0.5.
* In-the-money: delta approaches +1 as expiration nears.
* Out-of-the-money: delta approaches 0 as expiration nears.

Put options:
* Range: 0 to −1.
* At-the-money: about −0.5.
* In-the-money: delta approaches −1 as expiration nears.
* Out-of-the-money: delta approaches 0 as expiration nears.

Example interpretations:
* A call with delta +0.65: a $1 increase in the underlying raises the option by about $0.65.
* A put with delta −0.33: a $1 increase in the underlying lowers the option by about $0.33.

Delta is often used together with gamma, which measures the change in delta for a $1 change in the underlying.

Delta spread and delta-neutral strategies

A delta spread is a position constructed so the sum of deltas equals zero. When a position is delta-neutral, small moves in the underlying should not produce immediate directional P&L.

Common implementation:
* Calendar spread — sell near-term options and buy longer-dated options in proportions that offset delta. The trader typically profits from time decay in the near-term options, assuming limited movement in the underlying.

Delta-neutral strategies reduce directional exposure but remain exposed to other risks (volatility, time decay, gamma).

How traders use delta

• Hedging: Delta tells how many shares (or units) to buy or sell to offset option exposure. For example, one equity option typically represents 100 shares. Buying 100 calls with delta +0.40 implies a +4,000 delta; selling 4,000 shares would neutralize that exposure.
• Position sizing and risk management: Delta aggregates across positions to show net directional exposure of a portfolio.
• Probability and trade selection: Traders use delta as one input when assessing the likelihood an option finishes in the money.

Portfolio delta

Sum the deltas of all positions to get the portfolio (book) delta. Example:
* Long one call at +0.10 and two calls at +0.30 each → total delta +0.70.
* Adding a put with delta −0.70 makes the overall portfolio delta-neutral.

Delta of a share of stock

A long share of stock has a delta of +1.0; a short share has a delta of −1.0.

Simple explanation (Explain Like I’m Five)

If an option is a bet on a stock, delta tells you how much the bet’s value will change when the stock moves $1. Call deltas are between 0 and +1, put deltas are between 0 and −1. Bigger deltas mean the option behaves more like the stock itself.

Examples

BigCorp stock at $20:
* Call option with delta +0.35 and price $2: if stock rises to $21, call ≈ $2.35.
* Put option with delta −0.65 and price $2: if stock rises to $21, put ≈ $1.35.

The bottom line

Delta is a fundamental option Greek that quantifies directional sensitivity and serves as a hedge ratio. Understanding delta helps traders and investors manage exposure, construct hedges, and evaluate option behavior as the underlying price changes.