When the price of the underlying changes, so too does the option's delta! I think that that is why Glen99's "h" must tend to zero. It is wrong to say that delta can predict the change in the value of an option due to a change in the underlying.
The rate of change (infinitesimally) of delta is known as gamma. ... or the second derivative of the option's value with respect to the price of the underlying.
Delta is measured in terms of shares. Gamma is measured in terms of shares per tick.
When delta changes, so too does gamma. There is no word describing the rate of change of gamma.
