V哥_品职助教 · 2018年11月08日
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
