482
A Complete Guide to the Futures mArket
table 34.2  Option prices as a Function of V olatility in 
e-Mini S&p 500 Futures pricesa
annualized V olatility put or Call premium
10 22.88 ($1,144)
20 45.75 ($2,288)
30 68.62 ($3,431)
40 91.46 ($4,573)
50 114.29 ($5,715)
a At-the-money options at a strike price of 2000 with 30 days to expiration.
8 James Bowe, Option Strategies T rading Handbook (New Y ork, NY: Coffee, Sugar, and Cocoa exchange, 1983).
assumed to be a function of the square root of time. (This relationship is a consequence of the 
typical assumption regarding the shape of the probability curve for prices of the underlying 
futures contract.) Thus, an option with nine months until expiration would have 1.5 times the 
time value of a four-month option with the same strike price 
(; ;. )93 42 32 15== ÷=  
and three times the time value of a one-month option (; ;)93 11 31 3== ÷= .
 3. V olatility. Time value will vary directly with the estimated volatility of the underlying futures 
contract for the remaining lifespan of the option. This relationship is the result of the fact that 
greater volatility raises the probability the intrinsic value will increase by any specified amount 
prior to expiration. In other words, the greater the volatility, the larger the probable range of 
futures prices. As Table 34.2 shows, volatility has a strong impact on theoretical option pre-
mium values.
Although volatility is an extremely important factor in determining option premium values, 
it should be stressed that the future volatility of the underlying futures contract is never pre-
cisely known until after the fact. (In contrast, the time remaining until expiration and the rela -
tionship between the current price of futures and the strike price can be exactly specified at any 
juncture.) Thus, volatility must always be estimated on the basis of historical volatility data. As 
will be explained, this factor is crucial in explaining the deviation between theoretical and actual 
premium values.
 4. Interest rates. The effect of interest rates on option premiums is considerably smaller than 
any of the above three factors. The specific nature of the relationship between interest rates and 
premiums was succinctly summarized by James Bowe
8:
The effect of interest rates is complicated because changes in rates affect not only the 
underlying value of the option, but the futures price as well. Taking it in steps, a buyer 
of any given option must pay the premium up front, and of course the seller receives 
the money. If interest rates go up and everything else stays constant, the opportunity 
cost to the option buyer of giving up the use of his money increases, and so he is will-
ing to bid less. Conversely, the seller of options can make more on the premiums by