Chapter 38: The Distribution of Stock Prices 
TABLE 38-5. 
Index price movements. 
Total Indices: 135 
Upside Moves: 
Downside Moves: 
TABLE 38-6. 
3cr 
32 
None 
4cr 
15 
Scr 
3 
Index price movements, least volatile period. 
Total Indices: 66 
Upside Moves: 
Downside Moves: 
3cr 
l 
3 
4cr 
l 
0 
Scr 
0 
0 
789 
Dates: 10/22/99-12/7/99 
>6cr 
0 
Total 
50 
Dates: 7/1/93-8/17/93 
>6cr 
0 
0 
Total 
2 
3 
Total number of indices moving >=3cr: 5 (8% of the indices studied) 
indices made oversized moves - probably a bias because of the strong Internet stock 
market during that time period. The low-volatility period showed a more reasonable, 
but still somewhat eye-opening, 8% making moves of greater than three standard 
deviations. So, even selling index options isn't as safe as it's cracked up to be, when 
they can make moves of this size, defying the "normal" probabilities. 
Since that period in 1999 was rather volatile, and all on the upside, the same 
study was conducted, once again using the least volatile period of July 1993. 
In Table 38-6, the numbers are lower than they are for stocks, but still much 
greater than one might expect according to the lognormal distribution. 
These examples of stock price movement are interesting, but are not rigorous­
ly complete enough to be able to substantiate the broad conclusion that stock prices 
don't behave lognormally. Thus, a more complete study was conducted. The follow­
ing section presents the results of this research. 
THE DISTRIBUTION OF STOCK PRICES 
The earlier examples pointed out that, at least in those specific instances, stock price 
movements don't conform to the lognormal distribution, which is the distribution 
used in many mathematical models that are intended to describe the behavior of 
stock and option prices. This isn't new information to mathematicians; papers dating 
back to the mid-1960s have pointed out that the lognormal distribution is flawed. 
However, it isn't a terrible description of the way that stock prices behave, so many 
applications have continued to use the lognormal distribution.