The three readings
Sensitivity. Delta is the first derivative of option value with respect to the underlying price. A call with delta 0.6 gains about 0.60 when the stock rises 1.
Hedge ratio. To neutralise the directional risk of one call with delta 0.6, short 0.6 shares. This is the operational meaning on a desk, and the basis of delta hedging.
Probability. Delta approximates the risk-neutral probability the option finishes in the money. A 0.25-delta call is roughly a 25% shot - which is why traders talk about "25-delta" strikes as a way of naming moneyness without reference to price.
That third reading is an approximation (formally it is N(d1), while the in-the-money probability is N(d2)), and a good candidate flags the distinction when using it.
Behaviour
- Calls have delta between 0 and 1; puts between -1 and 0.
- At the money, delta is around 0.5.
- Deep in the money, delta approaches 1 - the option behaves like the stock.
- Deep out of the money, delta approaches 0.
Put and call deltas at the same strike differ by 1, which follows directly from put-call parity - differentiate both sides.
Delta changes
The key practical point: delta is not constant. Its rate of change is gamma, which is why a delta hedge must be maintained rather than set once.
As expiry approaches, delta becomes increasingly step-like - near 1 or near 0 - because there is less time for the option to change status. An at-the-money option on expiry day has a delta that swings violently.
In the interview
A common question: "You are long a 0.4-delta call. The stock rises. What happens to your delta?" It increases, because gamma is positive - so you become more long as the market rises, which is the convexity that makes owning options attractive.
Practise in finance and derivatives.