1. Extract the term structure of interest rates out to 3 years given the following bond data:
Maturity (yrs) Coupon rate (%) Yield to maturity (%)
0. 5 1. 0 1. 5
1. 0 1. 5 1. 75
1. 5 2. 0 2. 0
2. 0 2. 5 2. 25
2. 5 3. 0 2. 50
3. 0 3. 5 2. 75
2. The time t= 0 continuously compounded term structure of interest rates is given by r(0,T)=0. 05 - 0. 005e^{-0.10T}. Find the price of a Treasury bond with exactly 3 years to maturity and a coupon rate of 4. 0%.
3. Find a formula for the instantaneous forward rates f(0;T) associated with the continuously compounded term structure of interest rates
r(0,T)=0. 05 - 0. 005e^{-0.10T}.
4. At time t an investor shorts a $1 face value zero coupon bond that matures at time T >t and uses the entire proceeds to purchase a zero coupon bond that matures at time S > T.
(a) In what quantity is the zero coupon bond that matures at time S purchased? Your answer should be expressed in terms of the time t prices P(t,T) and P(t,S).
(b) describe why these transactions are equivalent to agreeing to lend over the future period [T, S] at a rate that is determined at time t.
(c) What is the continuously compounded forward rate f(t;T;S) associated with this loan?
5. A bond is said to be at par if its flat price is equal to its face value. The Par Bond Yield Curve out to N years is a plot of their yields to maturity {y_{0}^{(i)}}_{i-1}^{2N} on the vertical axis versus their respective maturities {i/2yrs}^{2N} i-1 on the horizontal axis. Given the following term structure of interest rates
tj (yrs) r_{0}^{(j)} (%)
0.5 2.0
1. 0 2. 5
1. 5 3. 0
2. 0 3. 5
2. 5 4. 0
3. 0 4. 5
find the par bond yields to maturity {y_{0}^{(i)}}_{i=1}^{6}