dstefan
03-22-2008, 01:34 PM
Chapter 8, Problem 7:
(i) Use bootstrapping to obtain a zero rate curve from the following prices of Treasury instruments with semiannual coupon payments:
\begin{array}{rcl} & \mbox{Coupon Rate} & \mbox{Price} \\ 3-\mbox{Month T-bill} & 0 & 98.7 \\ 6-\mbox{Month T-bill} & 0 & 97.5 \\ 2-\mbox{Year T-bond} & 4.875 & 100 \frac{ 5}{32} \\ 3-\mbox{Year T-bond} & 4.875 & 100 \frac{ 5}{32} \\ 5-\mbox{Year T-bond} & 4.625 & 99 \frac{22}{32} \\ 10-\mbox{Year T-bond} & 4.875 & 101 \frac{ 4}{32} \\ \end{array}
Assume that interest is continuously compounded.
(ii) How would the zero rate curves obtained by bootstrapping from the bond prices above, one corresponding to semi-annually compounded interest, and the other one corresponding to continuously computed interest, compare? In other words, will one of the two curves be higher or lower than the other one, and why?
Solution:
a
(i) Use bootstrapping to obtain a zero rate curve from the following prices of Treasury instruments with semiannual coupon payments:
\begin{array}{rcl} & \mbox{Coupon Rate} & \mbox{Price} \\ 3-\mbox{Month T-bill} & 0 & 98.7 \\ 6-\mbox{Month T-bill} & 0 & 97.5 \\ 2-\mbox{Year T-bond} & 4.875 & 100 \frac{ 5}{32} \\ 3-\mbox{Year T-bond} & 4.875 & 100 \frac{ 5}{32} \\ 5-\mbox{Year T-bond} & 4.625 & 99 \frac{22}{32} \\ 10-\mbox{Year T-bond} & 4.875 & 101 \frac{ 4}{32} \\ \end{array}
Assume that interest is continuously compounded.
(ii) How would the zero rate curves obtained by bootstrapping from the bond prices above, one corresponding to semi-annually compounded interest, and the other one corresponding to continuously computed interest, compare? In other words, will one of the two curves be higher or lower than the other one, and why?
Solution:
a