Assume a one-period spot rate follows a binomial process, is currently at S0 =

5%, u = 1.02, d = 1/1.02, and the probability of the spot rate increasing in one period is q = .5.

a. Show with a binomial tree the spot rates, logarithmic returns, and probabilities after one period, two periods, and three periods.

b. What are the spot rate’s expected logarithmic return and variance for each period?

c. Define the properties of a binomial distribution.

d. Verify that the u and d formulas yield the u and d values of 1.02 and 1/1.02 given the logarithmic return’s mean and variance after three periods.