Principles of Corporate Finance_ 12th Edition

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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.

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