Chapter 34: Futures and Futures Options 679 
This will not work well near expiration, since the future expires one week prior to the 
PHLX option. In addition, it ignores the early exercise value of the PHLX options. 
However, except for these small differentials, the shortcut will give theoretical values 
that can be used in strategy-making decisions. 
Example: It is sometime in April and one desires to calculate the theoretical values 
of the June deutsche mark physical delivery options in Philadelphia. Assume that one 
knows four of the basic items necessary for input to the Black-Scholes formula: 60 
days to expiration, strike price of 68, interest rate of 10%, and volatility of 18%. But 
what should be used as the price of the underlying deutsche mark? Merely use the 
price of the June deutsche mark futures contract in Chicago. 
STRATEGIES REGARDING TRADING LIMITS 
The fact that trading limits exist in most futures contracts could be detrimental to 
both option buyers and option writers. At other times, however, the trading limit may 
present a unique opportunity. The following section focuses on who might benefit 
from trading limits in futures and who would not.. 
Recall that a trading limit in a futures contract limits the absolute number of 
points that the contract can trade up or down from the previous close. Thus, if the 
trading limit in T-bonds is 3 points and they closed last night at 7 421132, then the high­
est they can trade on the next day is 7721132, regardless of what might be happening 
in the cash bond market. Trading limits exist in many futures contracts in order to 
help ensure that the market cannot be manipulated by someone forcing the price to 
move tremendously in one direction or the other. Another reason for having trading 
limits is ostensibly to allow only a fixed move, approximately equal to the amount cov­
ered by the initial margin, so that maintenance margin can be collected if need be. 
However, limits have been applied in case~which they are unnecessary. For exam­
ple, in T-bonds, there is too much liquidity for anyone to be able to manipulate the 
market. Moreover, it is relatively easy to arbitrage the T-bond futures contract against 
cash bonds. This also increases liquidity and would keep the future from trading at a 
price substantially different from its theoretical value. 
Sometimes the markets actually need to move far quickly and cannot because of 
the trading limit. Perhaps cash bonds have rallied 4 points, when the limit is 3 points. 
This makes no difference when a futures contract has risen as high as it can go for 
the day, it is bid there (a situation called "limit bid") and usually doesn't trade again 
as long as the underlying commodity moves higher. It is, of course, possible for a 
future to be limit bid, only to find that later in the day, the underlying commodity 
becomes weaker, and traders begin to sell the future, driving it down off the limit.