dstefan
06-06-2008, 12:15 AM
Chapter 2, Problem 7
The continuously compounded 6-month, 12-month, 18-month, and 24-month zero rates are 5%, 5.25%, 5.35%, and 5.5%, respectively. Find the price of a two year semiannual coupon bond with coupon rate 5%.
Solution:
The value of the semiannual coupon bond is
B = \frac{C}{2} ~100 ~e^{-r(0,0.5) 0.5} ~+~ \frac{C}{2} ~100 ~e^{-r(0,1 ) } ~+~ \frac{C}{2} ~100 ~e^{-r(0,1.5) 1.5} ~+~ \left( 100 ~+~ \frac{C}{2} ~100 \right) ~e^{-r(0,2) 2}
where C = 0.05, and r(0,0.5) = 0.05, r(0,1 ) = 0.0525, r(0,1.5) = 0.0535, r(0,2 ) = 0.055.
The input for the bond pricing codes is n = 4; t_cash_flow = [ 0.5 1 1.5 2 ]; v_cash_flow = [ 2.5 2.5 2.5 102.5 ].
The discount factors are disc = [ 0.97530991 0.94885432 0.92288560 0.89583414 ], and the price of the bond is
B = 98.940623.
The continuously compounded 6-month, 12-month, 18-month, and 24-month zero rates are 5%, 5.25%, 5.35%, and 5.5%, respectively. Find the price of a two year semiannual coupon bond with coupon rate 5%.
Solution:
The value of the semiannual coupon bond is
B = \frac{C}{2} ~100 ~e^{-r(0,0.5) 0.5} ~+~ \frac{C}{2} ~100 ~e^{-r(0,1 ) } ~+~ \frac{C}{2} ~100 ~e^{-r(0,1.5) 1.5} ~+~ \left( 100 ~+~ \frac{C}{2} ~100 \right) ~e^{-r(0,2) 2}
where C = 0.05, and r(0,0.5) = 0.05, r(0,1 ) = 0.0525, r(0,1.5) = 0.0535, r(0,2 ) = 0.055.
The input for the bond pricing codes is n = 4; t_cash_flow = [ 0.5 1 1.5 2 ]; v_cash_flow = [ 2.5 2.5 2.5 102.5 ].
The discount factors are disc = [ 0.97530991 0.94885432 0.92288560 0.89583414 ], and the price of the bond is
B = 98.940623.