老师可以使用计算器进行计算吗

问题如下：

An investor buys a three-year bond with a 5% coupon rate paid annually. The bond, with a yield-to-maturity of 3%, is purchased at a price of 105.657223 per 100 of par value. Assuming a 5-basis point change in yield-to-maturity, the bond’s approximate modified duration is closest to:

选项：

2.78.

2.86.

5.56.

解释：

A is correct.

The bond’s approximate modified duration is closest to 2.78. Approximate modified duration is calculated as:

ApproxModDur= [(PV−) − (PV+)] / [2×(ΔYield)×(PV0)]

Lower yield-to-maturity by 5 bps to 2.95%: PV-=105.804232

PV−= 5 / (1+0.0295) + 5/(1+0.0295)^2 + 105/ (1+0.0295)^3 =105.804232

Increase yield-to-maturity by 5 bps to 3.05%: PV+=105.510494

PV+= 5/ (1+0.0305) + 5/ (1+0.0305)^2 + 105/ (1+0.0305)^3 =105.510494

PV₀ = 105.657223, ΔYield = 0.0005

modified duration = (105.804232 − 105.510494)/(2×0.0005×105.657223) = 2.78

$ApproxModDur=\frac{105.804232-105.510494}{2\times0.0005\times105.657223}=2.78$

考点：approximate modified duration

解析：分别算出利率上升5bps后的PV+(105.510494)和利率下降5bps后的PV-(105.804232)，代入approximate modified duration公式即可，故选项A正确。