题目
A speculative (aka, junk) bond has 15.0 years to maturity and pays a semi-annual 6 1/8 coupon; i.e., its coupon rate is 6.125% payable semi-annually. Its yield is 11.00%. If we assume a reasonable shock value (i.e., less than 100 basis points), which of the following is nearest to the bond's effective convexity?
选项
A.12.4 years^2
B.98.0 years^2
C.124.3 years^2
D.Cannot answer because face value is not given
答案
B
解析
In this case, the initial price = -PV(0.1100/2,15×2,100×0.06125/2,100) = $64.574, and if the yield shock is ＋/- 50 bps, then:Price(yield 0.0050) = -PV(0.1150/2,15×2,100×0.06125/2,100) = $61.996, andPrice(yield - 0.0050) = -PV(0.1050/2,15×2,100×0.06125/2,100) = $67.310.In regard to false (D), please note that the convexity will be unchanged if we (consistently) change the face value to any amount. Further, while the convexity will vary very slightly as we alter the shock value, it is approximately 98.0 years for shock values below 1.0%. 在这种情况下，初始价格-PV(0.1100/2,15×2, 100×0.06125/2, 100) = $64.574 Price(yield 0.0050) = -PV(0.1150/2, 15×2, 100×0.06125/2, 100) = $61.996, and Price(yield- 0.0050) = -PV(0.1050/2, 15×2, 100×0.06125/2, 100) = $67.310. 关于（D）是错误的，请注意，如果我们（一致地）将面值更改为任意值，则曲度将保持不变。此外，虽然随着我们更改冲击值，曲度会非常微小地变化，但是对于低于1.0％的冲击值，大约需要98.0年。