Chapter 21 Valuing Options 553
bre44380_ch21_547-572.indd 553 10/05/15 12:53 PM
◗ FIGURE 21.1 This figure shows the possible six-month price changes for Google stock assuming that
the stock makes a single up or down move each six months (Fig. 21.1[a]); 2 moves, one every three months
(Fig. 21.1[b]); or 26 moves, one every week (Fig. 21.1[c]). Beside each tree we show a histogram of the possible
six-month price changes, assuming investors are risk-neutral.
220 125
60
0
10
20
40
30
50
Probability
, %
% price changes % price changes
220 0 125
53
47
2 27.1 0 1 37.1
2 14.6 1 17.09
60
0
10
20
40
30
50
Probability
, %
% price changes % price changes
2 27.1 0 1 37.1
23
50
27
% price changes
268265262258255250246241235230223216280919304255698 5 101 120 140 162 186 212
(a)
(b)
(c)
% price changes
Probability
, %
0
2
4
6
8
10
12
14
16
18
255235215 5 25 45 65 85 105 125 145 165 185 205
We could continue in this way to chop the period into shorter and shorter intervals, until
eventually we would reach a situation in which the stock price is changing continuously and
there is a continuum of possible future stock prices. We demonstrate first with our simple
two-step case in Figure 21.1(b). Then we work up to the situation where the stock price is
changing continuously. Don’t panic; that won’t be as bad as it sounds.