152  •   The Intelligent Option Investor
move randomly, which the BSM does—is the price level at which there is 
an equal chance of the actual future stock price to be above or below. In 
other words, the 50-delta mark represents the forward price of a stock in 
our BSM cones.
Recall now also that each line demarcating the cone represents roughly a 
16 percent probability of the stock reaching that price at a particular time in the 
future. This means that if we find the call strike prices that have deltas closest to 
0.16 and 0.84 (= 1.00 − 0.16) or the put strike prices that have deltas closest to 
−0.84 and −0.16 for each expiration, we can sketch out the BSM cone at points 
in the future (the data I used to derive this graph are listed in tabular format at 
the end of this section).
6/21/201612/24/20156/27/201512/29/20147/2/20141/3/20147/7/20131/8/20137/12/2012
Date
Oracle (ORCL)
Price per Share
45
40
35
30
25
20
5
10
15
-
Obviously, the bottom range looks completely distended compared 
with the nice, smooth BSM cone shown in earlier chapters. This dis-
tension is simply another way of viewing the volatility smile. Like the 
volatility smile, the distended BSM cone represents an attempt by partici-
pants in the options market to make the BSM more usable in real situa-
tions, where stocks really can and do fall heavily even though the efficient 
market hypothesis (EMH) says that they should not. The shape is saying,