一是tenor，参考price-maturity曲线，随着到期日接近，平价溢价折价债券都会趋于par value；二是yield，参照...
最为精准的衡量利率风险的指标确实是modified duration,但是由于modified durtaion也是从Macaulay duration转换得来的,所以两个都可以作为衡量利率风险的指标。这两个duration多数情况下是可以结合起来一起看的。 这道题考察的其实是下面这幅图,零息债券,折价债券,溢价债券和永续债券的Macaulay durtaion的变化特点。所以我们...
Macaulay duration, a weighted average of the time until cash flows are received, forms the basis for understanding the sensitivity of fixed-income products to interest rate changes. Here, weights correspond to the present value of the cash flows. Modified duration, on the other hand,...
The Macaulay duration and the modified duration are chiefly used to calculate the duration of bonds. The Macaulay duration calculates the weighted average time before a bondholder would receive the bond's cash flows. Conversely, the modified duration measures the price sensitivity of a ...
Modified duration = Macaulay duration / (1+y)其中y是债券每期的yield。所以发现，只有现金流确定的...
那么很明显,修正久期等于麦考利久期除以()(1+r),即DModified=DMacaulay1+r。 接下来,式(1)同时乘以PV,以得到美元久期(dollar duraion or money duration), dPVdr=−PV1+rDMacaulay=−PV×DModified=−Ddollar(2) 也就是美元久期等于修正久期乘以债券现值,Ddollar=PV×DModified。
即PVBP（基点价值，通常记作PV01或DV01）。总结来说，麦考利久期、修正久期和美元久期都是衡量债券价格对利率变动反应的工具，其中美元久期更侧重于反映实际价值变化，而PVBP则是这一变化的量化单位。在后续的免疫策略讨论中，这些概念将起到核心作用，特别是在单一负债和多负债免疫策略的构建中。
BPV=-MD*1bp*P,所以用到的是modified duration,而不再是mac duration了。 总之,虽然single liability与multiple liabiliies都叫免疫,但两类免疫的目标是不一样的,前者的目标是追求realized return,后者的目标是追求资产与负债的value变化相同,因此,前者要用mac duration,后者要用modified duration。 ---虽然现在很...
This bond duration tool can calculate the Macaulay duration and modified duration based oneitherthe market price of the bond or the yield to maturity (or the market interest rate) of the bond. Since you'll have one or the other, choose the easier path to compute the duration. ...
A key assumption to this duration is that the yield curve is flat and that when rate changes, the yield curve shifts in a parallel fashion. [See also Duration and Modified duration ]Springer USEncyclopedia of Finance