# Is the price of the following inflation derivative observed/traded?

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 $$t+1$$.

• 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 $y+\text{1 year}$). Mar 15 at 17:41