Delta measures how much an option’s price is expected to change when the underlying asset moves, and the cleanest intuition is that it reflects the probability the option will expire in-the-money. For example, a call with a delta of 0.70 implies that, under market pricing assumptions, there is roughly a 70% risk-chance it finishes in-the-money. Because that probability is high, the option’s price is already very sensitive to the underlying: if the stock rises $1, the call’s value increases by about $0.70.

Deep-in-the-money calls have deltas near 1 because their chance of retaining intrinsic value is extremely high, so they move almost dollar-for-dollar with the stock. Deep-out-of-the-money calls have deltas near 0 because small price changes barely affect their low probability of payoff. At-the-money options cluster near delta 0.50 because their final outcome is essentially a coin flip.

Delta is not static—it evolves with price movements and the passage of time. Gamma measures how quickly delta changes with the underlying’s price. If gamma is 0.08, then a $1 move in the stock shifts delta by about 0.08; a $2 move shifts it by about 0.16. Gamma is highest for at-the-money options, where small price moves meaningfully alter the probability of finishing in-the-money, and lowest for deep ITM or OTM options, where delta is already near 1 or 0 and changes slowly.