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I'm trying to solve for the convexity adjustment for an inflation YoY swap with unconventional payoff, where $I_i$ is CPI at time i:

$Notional * ([I_i/I_{i-1}]^{Day Count Fraction} - 1)$

In the normal case, the payoff is: $Notional * Day Count Fraction * (I_i/I_{i-1} - 1)$ And we can show using the Jarrow-Yildirim model that the PV is as follows:

enter image description here

with convexity adjustment (e^D_i (t) ), where enter image description here

However I am struggling with the payoff raised to the day count fraction instead of multiplied by day count fraction. How can I deal with this raised power in the convexity adjustment derivation?

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  • $\begingroup$ This is unnatural. Are you sure this is the payoff ? $\endgroup$
    – dm63
    Commented Nov 24, 2023 at 3:55
  • $\begingroup$ yes the payoff is accurate. $\endgroup$
    – bphone
    Commented Nov 26, 2023 at 3:01
  • $\begingroup$ What is the date of the payoff ? If the yoy swap is annual pay , then day count fraction is 1, so the convention is the same. $\endgroup$
    – dm63
    Commented Nov 26, 2023 at 3:33
  • $\begingroup$ the coupons pay quarterly, so the day count fraction for each coupon payment T_i will be from [T_i, 3m] $\endgroup$
    – bphone
    Commented Nov 28, 2023 at 1:09

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