Chapter 1: Definitions 13 
This statement is true no matter what the stock price is. The only reservation is 
that with the stock deeply in- or out-of-the-money, the actual difference between the 
January, April, and July calls will be smaller than with XYZ stock selling at the strik­
ing price of 50. 
Time Value Premium Decay. In Figure 1-3, notice that the price of the 9-
month call is not three times that of the 3-month call. Note next that the curve 
in Figure 1-4 for the decay of time value premium is not straight; that is, the rate 
of decay of an option is not linear. An option's time value premium decays much 
more rapidly in the last few weeks of its life ( that is, in the weeks immediately 
preceding expiration) than it does in the first few weeks of its existence. The rate 
of decay is actually related to the square root of the time remaining. Thus, a 3-
month option decays (loses time value premium) at twice the rate of a 9-month 
option, since the square root of 9 is 3. Similarly, a 2-month option decays at 
twice the rate of a 4-month option (-..f4 = 2). 
This graphic simplification should not lead one to believe that a 9-month option 
necessarily sells for twice the price of a 3-month option, because the other factors 
also influence the actual price relationship between the two calls. Of those other fac­
tors, the volatility of the underlying stock is particularly influential. More volatile 
underlying stocks have higher option prices. This relationship is logical, because if a 
FIGURE 1-4. 
Time value premium decay, assuming the stock price remains con­
stant. 
9 4 
Time Remaining Until Expiration 
(Months) 
0