嗨,从没放弃的小努力你好: 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 ...
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...
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 ...
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。 从上式不难看出,实际...
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。
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,...
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...
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...
Macaulay duration is the weighted average of the time to receive the cash flows from a bond. It is measured in units of years.
Modified Duration Formula The modified duration formula is: MacaulayDuration1+YTMAnnualPayments\frac{Macaulay\ Duration}{1+\frac{YTM}{Annual\ Payments}}1+AnnualPaymentsYTMMacaulayDuration Where: Macaulay Duration:The duration of the bond as measured in years (see how to compute it above) ...