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Are there errata in the Brigos's text of Interest Rate Models in chapter 16 when it is defined the YYIIS payoff? In formula (16.3) is defined Party A's payoff as:

\begin{align} \\ N\psi_i\left[\frac{I\left(T_i\right)}{I\left(T_{i-1}\right)}-1\right] \\ \end{align}

Where $\psi_i$ is the floating-leg year fraction for the interval $\left[T_{i-1},T_i\right]$

I think that CPI rentability is not annualized so we do not need $\psi_{i}$ factor in order to calculate the period rentability in terms of an annual rentability. Isn't it? I am not sure because these possible errata are in the following pages of the chapter...

Thanks in advance

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  • $\begingroup$ For inflation swaps the payment does not need the DCF. For present valuing you need a discount factor but not the $\psi$ as it is written in your formula. $\endgroup$
    – Attack68
    Commented May 29 at 19:31

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One possible explanation I see is that the natural periodicity of this product is annual and that the fraction of a year is practically 1, so multiplying it by the fraction of a year is motivated by the day count conventions agreements between party A and party B.

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