# Interest rate PV01 for a floating rate bond

I have seen this approach in my work and I would like to understand the theoretical justification behind this approach.

To calculate the interest rate PV01 of a floating rate note. A synthetic bond is created that pays the next coupon (which was fixed already during the previous coupon payment date) and the face value (say 100) at the next coupon payment date. The price of this bond is equated to the price of a hypothetical treasury bond that pays 100 at the next coupon payment date. The yield of this synthetic bond is calculated and the yield based sensitivity (pv01) is termed as the pv01 of the original floater.

I haven’t been able to understand how the two prices are equal. Can anybody help me out here?

## 1 Answer

It's because the FRN is equal to a portfolio of (a) the shorter dated bond you described and (b) a forward bond, purchased on the next coupon payment date, featuring a floating rate coupon and a maturity date the same as the FRN. If the bond in (b) has zero dv01, the result follows. We argue that indeed it has zero dv01, because when interest rates move, both the return on the bond and the discount rate move identically. Like any rule of thumb, it's an approximation. If there is a spread on the FRN over the floating interest rate, this will create a small dv01.

• Thanks for the answer. Is there any book or source from where I can further read about this particular financial engineering for A FRN May 20, 2018 at 6:16
• I am still not able to understand how you engineered the FRN. Can you please explain further on this? May 20, 2018 at 8:05
• If the FRN is engineered using the shorter synthetic bond and a forward bond. How is the price of a zero coupon treasury bond that matures on the next coupon date equal to the price of the FRN for calculating Interest rate pv01 (even though the actual price of the FRN is actually different from the price of the treasury ZCB). May 20, 2018 at 9:34
• Who said anything about a ZCB? The shorter bond pays a coupon and the face value, according to your description.
– dm63
May 20, 2018 at 9:48
• I have mentioned that “The price of the synthetic bond is equated to the price of a hypothetical treasury bond that pays 100 (the face value) at the next coupon date. (Which is indeed a ZCB)”. May 20, 2018 at 10:25