Suppose a spot rate has the following rates over the past 13 quarters:

a. Calculate the spot rate’s average logarithmic return and variance.

b. What is the rate’s annualized mean and variance?

c. Calculate the spot rate’s up and down parameters for periods with the following lengths:
(1) One quarter (h = length in years = 1/4)
(2) One month (h = 1/12)
(3) One week (h = 1/52)
(4) One day (h = 1/360)

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Annualized Quarter Spot Rate (%) y 1.1 5.5 y 1.2 5.0 y 1.3 4.7 y 1.4 4.4 y 2.1 4.7 y 2.2 5.0 y 2.3 5.4 y 2.4 5.0 y 3.1 4.7 y 3.2 4.4 y 3.3 4.7 y 3.4 5.0 y 4.1 5.5