Let $M_{t\to t+2}^{\\\$}$ be the pricing kernel (SDF) from period $t$ to $t+2$. Let inflation over period $t$ to $t+1$ be denoted by $\Pi_{t \to t+1}$. Is it possible to observe the following quantity in the market (?): $$\mathbb{E}_t(M_{t\to t+2}^{\\\$} \Pi_{t \to t+1}). $$

That is, the price of a contract which pays out inflation that prevailed from period $t$ to $t+1$, to be delivered in period $t+2$.

I was thinking that perhaps some kind of TIPS bond or inflation swap contract has this type of payoff. For example, a 2 year zero-coupon inflation indexed bond has price $\mathbb{E}_t(M_{t\to t+2}^{\\\$} \Pi_{t \to t+2})$. This looks very similar to the quantity I would like to compute, but unfortunately it delivers inflation over the entire 2 year period, instead of just inflation from period $t$ to $t+1$.

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    $\begingroup$ That's an inflation flow with pay delay $-$ pay delays are very common in Inflation products, at least for GBP. As an example of products, you have zero coupon swaps (which pay as a lump sum the inflation rate between year $y_1$ and $y_2$) or year-on-year swaps (which have yearly flows paying the inflation between $y$ and $y+\text{1 year}$). $\endgroup$ Mar 15 at 17:41
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    $\begingroup$ For zero-coupon swaps. For YoY swaps. See also this link. $\endgroup$ Mar 15 at 17:43
  • $\begingroup$ @DaneelOlivaw thanks so much for your reply! Do you know if one can obtain data on delayed inflation contracts? For example Bloomberg or some other database? $\endgroup$ Mar 15 at 19:16

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