The Intelligent Investor’s Guide to Option Pricing  •  67
At time A for the OTM option, we see that there is a bit of the range of 
exposure contained within the cone; however, after some time has passed 
and we are at time B, none of the range of exposure is contained within 
the BSM cone. In contrast, at times A and B for the ITM option, the entire 
range of exposure is contained within the BSM cone. Granted, the area of 
the range of exposure is not as great at time B as it was at time A, but still, 
what there is of the area is completely contained within the cone.
Theoretically, time decay is a constant thing, but sometimes actual 
market pricing does not conform well to theory, especially for thinly traded 
options. For example, you might not see any change in the price of an option 
for a few days and then see the quoted price suddenly fall by a nickel even 
though the stock price has not changed much. This is a function of the way 
prices are quoted—often moving in 5-cent increments rather than in 1-cent 
increments—and lack of “interest” in the option as measured by liquidity.
Changing Other Assumptions
The other input assumptions for the BSM (stock market drift and dividend 
yield) have very small effects on the range of predicted future outcomes in 
what I would call “normal” economic circumstances. The reason for this is 
that these assumptions do not change the width of the BSM cone but rather 
change the tilt of the forward stock price line.
Remember that the effect of raising interest rates by a few points is 
simply to tilt the forward stock price line up by a few degrees; increasing 
your dividend assumptions has the opposite effect. As long as interest rates 
and dividend yields stay within typical limits, you hardly see a difference in 
predicted ranges (or option prices) on the basis of a change in these variables. 
Simultaneous Changes in Variables
In all the preceding examples, we have held all variables but one constant 
and seen how the option price changes with a change in the one “free” 
variable. The thing that takes some time to get used to when one is first 
dealing with options is that, in fact, the variables don’t all hold still when 
another variable changes. The two biggest determinants of option price 
are, as we’ve seen, the strike–stock price ratio and the forward volatility