# How to calculate accrued interest for a reverse floater?

I was looking at an example from my lecture notes regarding a reverse floater. We have the following data (We use the Act/365 convention):

• Nominal value: 1000 EUR
• Maturity: 14.04.2026
• Coupon: 4,5% less a 6-month-reference interest rate, but at least 0%
• Clean price (02.03.2023): 97,25
• For the reference interest rate we have:
• 14.04.2022: -0,3%
• 14.10.2022: 2,1%
• 14.04.2023: 3,2%

I tried to calculate the dirty price at 02.03.2023 myself for a nominal value of $$N = 100000$$ EUR, but I am not sure if my calculation are correct:

The next coupon date will be the 14.04.2023. The reference rate was fixed at the 14.10.2023 and is 2,1%. Therefore, the coupon should be $$Coupon = N \cdot 0,5 \cdot (4,5\% - 2,1\%)^+ = 1200.$$ I counted a total of 139 days from 15.10.2022 to 02.03.2023. Since there a total of 182 days between the two coupon dates, the accrued interest is $$139/182 \cdot 1200 = 916,48$$ EUR. And therefore we have a dirty price of $$97,25\% \cdot N + 916,48 = 98166,48$$ EUR.

I am quite new to this and not sure if this is correct. Could somebody verify my calculations?

Furthermore the exercise claims, that we can decompose this product into simpler products using 2 long positions in a coupon bond with nominal value $$N$$ and a coupon of 2,25% each, a short position in a floating rate note with the nominal value $$N$$ and an interest rate cap with a fixed rate of 4,5%, again with nominal value $$N$$.

What is the thought process behind this decomposition, wouldn't it be much easier to just claim that a floating rate note is just an interest rate floor with fixed leg of 4,5%?

• There are >1 variants of Actual/365 daycount convention, although they're similar enough. I suggest you take a look at the Quantlib C++ source code rkapl123.github.io/QLAnnotatedSource/da/d98/… and try to find how this differs from your daycount calculation. Jun 12, 2023 at 12:06
• Thanks, I will have a look at it. Jun 12, 2023 at 19:16