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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%?

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    $\begingroup$ 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. $\endgroup$ Jun 12, 2023 at 12:06
  • $\begingroup$ Thanks, I will have a look at it. $\endgroup$ Jun 12, 2023 at 19:16

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For the coupon calculation, it looks essentially correct. The only caveat is that the day count convention Act/365 usually means the payment would be 139/365 times 2400, rather than 139/182 times 1200. The latter method inherently assumes the coupons in the 2 6 month periods are exactly equal in weight, which I believe is the Act/365 (fixed) convention. However, the bond prospectus would in practice settle the question.

On the decomposition, it is usually easier to decompose using an out of the money option, rather than an in the money option (then the adjustment to be made is smaller). Other than that the decompositions are the same. (Did you mean 4.5% rather than 5%).

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  • $\begingroup$ Thank you very much for clarifying! Yes, I meant 4,5% rather than 5%. $\endgroup$ Jun 12, 2023 at 19:18

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