# Calculating deltas of call options?

From a continuous standpoint, I understand why an ATM call has delta = 0.5 and for ITM call, the delta approaches 1 since each move in the underlying corresponds to same unit of value change in call option.

Howwever, if we take a discrete case where call option expires in 1 period. If strike price is 100 and the underlying is at 100. If the underlying moves to 105 in 1 period, then dS = 5 and the change in call option is also 5? So then this ratio of $\frac{dc}{dS} = 1$ not 0.5?

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