Describe the method of producing scenarios used in the historical simulation over the first three decisions (two years).

a) How many yield curves need to be assessed at the beginning of 64 for the years 64, 65, and 66?

b) Draw a decision tree depicting the probability that each of the yield curves indicated in (a) occurs. What use is made of the uncertainty in the estimates of the change in the twenty-year rate (thirty-year rate) as a fraction of the change in the one-year rate? How could this be modified?

c) Show how to compute the parameters of the functional form for each of the yield curves forecast for the start of 65.

d) Explain how you might assess the required information in actual practice, using a model similar to that described in Exercise 1. Draw a distinction between short-term forecasting (3 months) and long-term forecasting (2 years).