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+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