On December 29, 2017 the Treasury semi-annually compounded yield curve was 6mo ly 18mo 2y 1.525% 1.801% 1.842% 1.880% Part 1: Vasicek Model (5pts) Take a Vasicek model with parameters 7 = 1, 1 = 5%, o = 20%, y* = 1.5, 7* = 10% and suppose that the current repo rate r(0) = 1%. 1. What is the model's 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 a(0,T) and B(0,7). 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. On December 29, 2017 the Treasury semi-annually compounded yield curve was 6mo ly 18mo 2y 1.525% 1.801% 1.842% 1.880% Part 1: Vasicek Model (5pts) Take a Vasicek model with parameters 7 = 1, 1 = 5%, o = 20%, y* = 1.5, 7* = 10% and suppose that the current repo rate r(0) = 1%. 1. What is the model's 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 a(0,T) and B(0,7). 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