Delta

The first and most used of the option sensitivities collectively called the greeks. A call option's delta runs from zero to one and a put option's from minus one to zero, and the number states how much of the underlying's next move the option's price is expected to capture. An option deep in the money behaves almost like the underlying itself and carries a delta near the boundary; an option far out of the money barely responds and carries one near zero.

Delta is not observed. It is produced by a pricing model from the underlying price, the strike, the time remaining and an assumption about volatility, so two desks using different volatility assumptions calculate different deltas for the same contract on the same screen. It is also unstable: it changes as the underlying moves, as time passes and as implied volatility changes, and gamma is the measure of how fast it changes.

The habit of reading delta as the probability that an option finishes in the money is the common trip. The two numbers are close, and they are not the same quantity: the probability interpretation is a property of the model's assumptions, which include a distribution real prices do not follow. Delta is also a concept that belongs to options and not to every derivative. A contract for difference tracks its underlying one for one by construction, so it has no delta worth quoting.