The relationship between the movement of an option's price and that of its underlying security is called Delta.  If the ratio is equal to 1 then an increase of $1 of the stock price equals a rise of $1 in the price of the option.  A delta of .7 means a rise of $0.70 for every dollar rise in the price of the underlying security.

 

As an option nears its expiration there is very little in the may of time value left.  Delta at this point is very nearly 1.  Deltas can be both negative and positive.  If the option price goes down when the underlying security price goes up then the delta will be negative, such would be the case with puts.  If the degree of change for the option exceeds that of the underlying stock it is called an 'up delta'.  If it is less than that of the underlying stock it is called a down delta.