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A 30-year 4.0% semi-annual coupon bond h...

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题目

A 30-year 4.0% semi-annual coupon bond has a price of $100.00 at a yield of 4.00%. At this 4.00% yield the bond has a modified duration of 17.380 years. If the yield drops by one basis point, to 3.99%, the price increases to $100.1740 and the duration increases to 17.3920 years. Which is nearest to the bond's convexity at a 4.0% yield? (significantly more difficult than an exam question)

选项

A.95

B.422

C.1,646

D.4,333

答案

B

解析

C = d^2P/dy^2 × 1/P = [change in dollar duration/change in rate] × 1/P.In this case, without regard to the sign ( +/-), the change in dollar duration is given by Duration[at 3.99%]×Price[at 3.99%] - Duration[at 4.00%]×Price[at 4.00%], such that:Convexity (C) = [(100.1740×17.3920 - 100×17.380)/0.0001] × 1/100 = 421.89.Note the exact (analytical) convexity is equal to 420.8130 (very close!)C = d ^ 2P / dy ^ 2×1 / P = [美元持续时间/汇率变化]×1 / P。在这种情况下,不考虑符号(+ /-),美元持续时间的变化由Duration [at 3.99%]×Price [at 3.99%]-Duration [at 4.00%]×Price [at 4.00%]给出 ,这样:曲度(C)= [(100.1740×17.3920-100×17.380)/0.0001]×1/100 = 421.89。请注意,精确的(分析性)曲度等于420.8130(非常接近!)