dstefan
03-22-2008, 01:28 PM
Chapter 8, Problem 3:
Use Newton's method to find the yield of a five year semiannual coupon bond with 3.375% coupon rate and price 100 \frac{1}{32}. What are the duration and convexity of the bond?
Solution:
The bond makes ten coupon payments equal to 1.6875 every six months, and it also pays back the face value at maturity. The cash flow dates and corresponding cash flows are
t_cash_flow = [ 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 ] and v_cash_flow = [ 1.6875 1.6875 ... 101.6875].
With initial guess x0 = 0.1, Newton's method converges in four iterations:
x1 = 0.021397014741596;
x2 = 0.033057328860338;
x3 = 0.033400811402235;
x4 = 0.033401098538031.
The yield of the bond is 3.3401%.
The duration of the bond is 4.642735 and the convexity of the bond is 22.573118.
Use Newton's method to find the yield of a five year semiannual coupon bond with 3.375% coupon rate and price 100 \frac{1}{32}. What are the duration and convexity of the bond?
Solution:
The bond makes ten coupon payments equal to 1.6875 every six months, and it also pays back the face value at maturity. The cash flow dates and corresponding cash flows are
t_cash_flow = [ 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 ] and v_cash_flow = [ 1.6875 1.6875 ... 101.6875].
With initial guess x0 = 0.1, Newton's method converges in four iterations:
x1 = 0.021397014741596;
x2 = 0.033057328860338;
x3 = 0.033400811402235;
x4 = 0.033401098538031.
The yield of the bond is 3.3401%.
The duration of the bond is 4.642735 and the convexity of the bond is 22.573118.