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How does delta of an option change with time if underlying price is constant?
As the option approaches expiry, the delta will approach zero or one, depending on whether you're in or out of the money. This might be easiest to conceptualise if you look at the option value as a function of the stock price, and then realise that the delta is the slope of that curve. Now, as we get closer to expiry, time value fades away, and we get closer and closer to the intrinsic value, which looks like this hockey stick: __/ As you see, close to expiry, if you're out of the money, you have nothing (with delta zero), while if you're in the money, you have a forward (with delta one).