485
AN INTrOduCTION TO OPTIONS ON FuTureS
until expiration, estimated volatility, and interest rates. For any given set of values for these factors, 
delta will equal the absolute difference between the option premium indicated by the model and the 
model-indicated premium if the futures price changes by one point. Table 34.3 illustrates a number 
of important observations regarding theoretical delta values:
 1. Delta values for out-of-the-money options are low. This relationship is a result of the 
fact that there is a high probability that any given price increase
9 will not make any actual differ-
ence to the value of the option at expiration (i.e., the option will probably expire worthless).
 2. Delta values for in-the-money options are relatively high, but less than one. In-
the-money options have high deltas because there is a high probability that a one-point change 
in the futures price will mean a one-point change in the option value at expiration. However, 
since this probability must always be equal to less than one, the delta value will also always be 
equal to less than one.
 3. Delta values for at-the-money options will be near 0.50. Since there is a 50/50 chance 
that an at-the-money option will expire in-the-money, there will be an approximately 50/50 
chance that a one-point increase in the price of futures will result in a one-point increase in the 
option value at expiration.
 4. Delta values for out-of-the-money options will increase as time to expiration 
increases. A longer time to expiration will increase the probability that a price increase in 
futures will make a difference in the option value at expiration, since there is more time for 
futures to reach the strike price.
 5. Delta values for in-the-money options will decrease as time to expiration 
increases. A longer time to expiration will increase the probability that a change in the futures 
price will not make any difference to the option value at expiration since there is more time for 
futures to fall back to the strike price by the time the option expires.
 6. Delta values for at-the-money options are not substantially affected by time to 
maturity until near expiration. This behavioral pattern is true because the probability that 
an at-the-money option will expire in-the-money remains close to 50/50 until the option is 
near expiration.
9 This section implicitly assumes that the option is a call. If the option is a put, read “price decrease” for all refer-
ences to “price increase.”