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Interpreting the Year Fraction in an Inflation Swap Payoff

Article Quant Q&A · Author: Alexis Sánchez Tello
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Summary

The question examines a year-fraction multiplier in a quoted inflation swap payoff, where the period’s CPI ratio change is multiplied by notional and the floating-leg accrual fraction. The author wonders whether the fraction is unnecessary because CPI return over the period is already a period return, rather than an annualized rate.

The response suggests that the product’s natural payment interval may be annual, making the year fraction close to one, and that its inclusion may reflect day-count conventions agreed by the counterparties. This offers a possible interpretation, not a definitive correction to the cited formula. The exchange provides no further derivation, contract terms, or detailed convention evidence, so it does not settle how the payoff should be implemented across different accrual periods. Users should consult the swap documentation and conventions applicable to the specific trade.

Key ideas

  • The cited inflation swap payoff multiplies a CPI ratio change by notional and a year fraction.
  • The question is whether that fraction is needed for a nonannualized period return.
  • The answer proposes that an annual payment period and day-count agreements may explain the factor.
  • The brief exchange does not establish a universal inflation swap convention or confirm an erratum.

Tags

Fixed incomeDerivatives pricing
Full text
# YYIIS Inflation swap chapter 16 of Brigo's text


# YYIIS Inflation swap chapter 16 of Brigo's text












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

## Answer by Alexis Sánchez Tello (score 1)

https://quant.stackexchange.com/a/75452

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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.