Delta is the option Greek that shows how sensitive an option’s price is to a small change in the underlying asset. A delta of 0.60 means the option is expected to gain about 60p if the share price rises by £1, all else unchanged. For puts, delta is negative because the option gains value when the underlying falls.
Think of delta as the first gear of options pricing. It is the immediate slope of the option price with respect to the underlying price, so it captures direction and the scale of the move on small changes. By convention, call deltas run from 0 to +1 and put deltas from 0 to −1.
What delta reveals about calls and puts
Delta maps closely to moneyness, which is how the strike compares with the current price:
- Deep in-the-money call: delta near +1. The option behaves almost like the underlying.
- At-the-money call: delta around +0.5. Half a share’s worth of exposure per option share.
- Out-of-the-money call: delta closer to 0. Small price sensitivity.
- Deep in-the-money put: delta near −1. Moves almost one-for-one in the opposite direction.
- At-the-money put: delta around −0.5.
- Out-of-the-money put: delta closer to 0.
Time to expiry and implied volatility also shape delta. With more time or higher volatility, deltas are flatter across strikes. Out-of-the-money options pick up a bit more delta, while deep in-the-money options give up some, since there is greater chance of crossing the strike before expiry.
Some trading screens display put delta as a positive absolute value. Others keep the negative sign. Check your platform’s convention, because it changes how you read position totals.
Using delta to size and hedge positions
Delta is the basic hedge ratio. If you hold options and want to offset their immediate directional risk, you trade the underlying in proportion to your net delta. A positive delta means you are long direction. To neutralise that, you would sell underlying. A negative delta means you benefit if the underlying falls. You would buy underlying to flatten it.
Position managers often talk in “deltas” instead of contracts. For equity options with a 100-share multiplier, one call with a 0.40 delta is 40 deltas. Ten such calls are 400 deltas, which is similar to owning 400 shares for small price moves. This makes it easy to compare exposures across strikes and expiries.
Traders also use delta as a rough shortcut for the probability an option expires in the money. A 0.30 call is often spoken of as a 30% call. That is an approximation that comes from common pricing models and specific assumptions. Treat it as a heuristic, not a promise.
Products that mirror the underlying almost one-for-one are called delta one. Examples include the underlying shares themselves, most futures and many contracts for difference. Options rarely sit at exactly one or minus one except when they are very deep in the money and close to expiry.
Worked example: price impact and a delta hedge
Suppose a share trades at £50. A one-month 52 strike call is quoted with a delta of 0.40. You buy 3 contracts, and each contract controls 100 shares. Your net delta is +120 (3 × 100 × 0.40). For small moves, the calls should behave like 120 shares.
If the share price rises by £1 to £51, the option value would be expected to rise by about 40p per share-equivalent. Your position gains roughly £120 in option value (0.40 × £1 × 3 × 100), ignoring the other Greeks and bid-ask effects.
Now imagine the opposite side. You have sold 5 of those calls at the same delta. Your net delta is −200 (5 × 100 × 0.40, with a negative sign because you are short calls). To hedge the immediate directional risk, you could buy 200 shares. If the share price jumps by £1, the short calls lose about £200, but the shares gain about £200, leaving you close to flat for that small move.
That hedge will not stay perfect. As the price moves, delta changes. This is gamma at work. You would need to rebalance from time to time if you want to keep the position close to delta neutral.
Delta conventions across markets and platforms
Be aware of a few variations you will see in practice:
- Underlying reference: Equity options are usually defined on the share price. Options on futures reference the futures price, which already reflects carry. Their deltas can differ slightly from what you would infer off spot.
- Multiplier: Many equity options use a 100-share multiplier, but not all markets do. Index, futures and crypto options often use different contract sizes. Always check the contract specs before turning deltas into hedge quantities.
- Put sign: Some brokers report put delta as negative, others as positive. The risk is the same, but your spreadsheet will not be if you assume the wrong sign.
- FX conventions: In foreign exchange, you will hear about spot delta versus forward delta, and whether option premium is included when quoting strikes. The headline sign logic still holds, but the exact number depends on the convention used.
Platform displays and margin treatments vary by provider. If you are relying on delta for hedging or risk limits, verify how your system calculates and aggregates it across legs and expiries.
How delta interacts with the other Greeks
Delta does not live alone. Three relationships matter in day-to-day trading:
- Gamma is the rate of change of delta as the underlying moves. High gamma means delta will swing quickly, which forces more frequent hedge rebalancing. Gamma tends to be highest near the money and close to expiry.
- Vega measures sensitivity to implied volatility. When implied volatility rises, the delta curve flattens across strikes. Out-of-the-money options gain delta, in-the-money options lose some. When volatility falls, the curve steepens again.
- Theta captures time decay. As days pass, the probability of crossing the strike narrows, so out-of-the-money deltas drift toward zero and deep in-the-money deltas drift toward one in absolute terms, assuming prices and volatility stay the same.
Understanding these links helps you choose strategies that fit your view. For example, a covered call leaves you long shares with a short call overlay. The combined delta starts near one and falls as the share rises toward the strike, since gains in the shares are offset by losses on the short call. A long call option alone starts with a smaller delta, then builds toward one if the share rallies and time runs short.
Finally, remember that delta is a local measure. It is very good at describing what should happen for a small change in price over a short interval. For larger moves or across time, gamma, vega and theta will shift the picture, and real-world execution costs can dominate the tidy numbers.