Chapter 34: Futures and Futures Options 685 
There is another way to look at this data, and that is to view the options' implied 
volatility. Implied volatility was discussed in Chapter 28 on mathematical applica­
tions. It is basically the volatility that one would have to plug into his option pricing 
model in order for the model's theoretical price to agree with the actual market price. 
Alternatively, it is the volatility that is being implied by the actual marketplace. The 
options in this example each have different implied volatilities, since their mispricing 
is so distorted. Table 34-2 gives those implied volatilities. The deltas of the options 
involved are shown as well, for they will be used in later examples. 
These implied volatilities tell the same story: The out-of-the-money puts have 
the lowest implied volatilities, and therefore are the cheapest options; the out-of-the­
money calls have the highest implied volatilities, and are therefore the most expen­
sive options. 
So, no matter which way one prefers to look at it - through comparison of the 
option price to theoretical price or by comparing implied volatilities - it is obvious 
that these soybean options are out of line with one another. 
This sort of pricing distortion is prevalent in many commodity options. 
Soybeans, sugar, coffee, gold, and silver are all subject to this distortion from time to 
time. The distortion is endemic to some - soybeans, for example - or may be pres­
ent only when the speculators tum extremely bullish. 
This precise mispricing pattern is so prevalent in futures options that strategists 
should constantly be looking for it. There are two major ways to attempt to profit 
from this pattern. Both are attractive strategies, since one is buying options that are 
relatively less expensive than the options that are being sold. Such strategies, if 
implemented when the options are mispriced, tilt the odds in the strategist's favor, 
creating a positive expected return for the position. 
TABLE 34-2. 
Volatility skewing of soybean options. 
Strike 
525 
550 
575 
600 
625 
650 
675 
Call 
Price 
19 1/2 
11 
53/4 
31/2 
21/4 
Put 
Price 
1/2 
31/4 ; 
12 
28 
Implied Delta 
Volatility Call/Put 
12% /-0.02 
13% /-0.16 
15% 0.59/-0.41 
17% 0.37 /-0.63 
19% 0.21 
21% 0.13 
23% 0.09