In the table in Example 21.3, u and d both get closer to 1 (u is smaller and d is larger) as the time interval Δt shrinks. Why does this make sense? Does the fact that u and d are each closer to 1 mean that the total volatility of the stock over the remaining life of the option is lower?

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Example 21.3 Increasing the Number of Subperiods In Example 21.2, we broke up the year into three subperiods. Let's now look at the cases of 6 and 20 subperiods. Subperiods, n At = Tin u = exp(oAt) d = exp(- At) 3 0.333 exp(0.173) 1.189 exp(-0.173) 0.841 6 20 0.167 exp(0.122) 1.130 exp(-0.122) 0.885 20 0.050 exp(0.067) = 1.069 exp(-0.067)=0.935 We plot the resulting probability distributions in Panels B and C of Figure 21.5.5