Suppose a spot rate has the following probability distribution of possible rates after four months:

a. Calculate the spot rate’s expected logarithmic return and variance. Assume the current rate is 6%.

b. Calculate the spot rate’s annualized variance and mean.

c. What are the spot rate’s u and d values for a period of length one month (h = length of the period in years = 1/12), one week (h = 1/52), and one day (h = 1/360)?

d. Suppose the spot rate’s mean is equal to zero, what are the rate’s u and d values for the periods of lengths one month, week, and day? Comment on the importance of the mean in calculating u and d when n is large.

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Annualized Spot Rate (%) Probability 6.623 .0625 6.332 .2500 6.054 .3750 5.788 .2500 5.534 .0625