Take a Vasicek model with parameters = 1, r = 5%, = 20%, = 1.5, r = 10% and suppose that the current repo rate r(0) = 1%.

1. What is the models best prediction of the repo rate tomorrow (1 business day from now)? That is, what is the E[r(dt)]?

2. What is the model predicted price of a 1.5y Treasury note with a coupon rate of 5%? You might need to use Excel or Python to compute the relevant (0, T) and (0, T).

3. Suppose you want to construct a replicating portfolio for a 7y zero-coupon Treasury note that consists of cash and the 1.5y Treasury note with a coupon rate of 5%. How many of the 1.5y notes you need to have in your replicating portfolio? Feel free to use Excel or Python for these calculations