题目
A $100 bond with 7.0 years to maturity has a 4.0% per annum coupon rate that is paid semi-annually. What is the effective convexity of the bond when the yield is 4.0% such that the bond's price is $100 (if coupon rate equals yield, bond prices at par)?
选项
A.42.60
B.98.77
C.214.30
D.856.80
答案
A
解析
If we use a shock of 10 bps (per example, we can also use 1 bps, but the answer only differs by 0.000222, and is still 42.60):P[@ 3.9%] is given by: 14 = N, 1.95 = I/Y, 2 = PMT, 100 = FV; CPT PV, /- = 100.607448 (STO 1 for retrieval)P[@ 4.1%] is given by: 14 = N, 2.05 = I/Y, 2 = PMT, 100 = FV; CPT PV, /- = 99.396812 (STO 2 for retrieval)Please note that after your price the bond at 3.9%, you only need to re-enter "2.05 = I/Y" and re-compute as the other inputs are unchanged!Dollar convexity = (99.396812＋100.607448 - 2 × 100) / 0.001^2 = 4,260.And convexity (C) = (P[yield @ 4.1%] ＋P[yield @ 3.9%] - 2×$100)/(10 bps)^2 × 1/P = dollar convexity×1/P = 4,260/$100 = 42.60如果我们使用10 bps的变动（例如，我们也可以使用1 bps，但答案仅相差0.000222，但仍为42.60）：P[@ 3.9%] 价格为: 14 = N, 1.95 = I/Y, 2 = PMT, 100 = FV; CPT PV, /- = 100.607448 (STO 1 for retrieval)P[@ 4.1%]价格为: 14 = N, 2.05 = I/Y, 2 = PMT, 100 = FV; CPT PV, /- = 99.396812请注意，在将债券价格定为3.9％之后，您只需重新输入“ 2.05 = I / Y”并重新计算，因为其他输入不变！Dollar convexity = (99.396812 100.607448 - 2 × 100) / 0.001^2 = 4,260.convexity (C) = (P[yield @ 4.1%] P[yield @ 3.9%] - 2×$100)/(10 bps)^2 × 1/P = dollar convexity×1/P = 4,260/$100 = 42.60