Pricing a Delayed Payout on Recent Inflation

Summary

The document poses a fixed-income pricing question: whether a market instrument reveals the value of a claim that pays at a later date based on inflation realized over an earlier period. It expresses that value as an expectation of the nominal pricing kernel multiplied by the earlier inflation outcome. The central issue is the mismatch between when inflation is measured and when the payoff is delivered.

A two-year zero-coupon inflation-indexed bond is offered as a nearby example, but its payoff reflects cumulative inflation across the full two-year horizon, so it does not directly match the proposed one-period inflation payoff delivered later. The document does not provide a replication, valuation method, or answer about whether the desired price is directly observable or can be inferred from traded instruments. Its contribution is therefore the precise framing of the payoff and the distinction from a standard inflation-linked bond; further analysis would be needed to establish market observability or construct a hedge.

Key ideas

• The proposed claim pays later based on inflation realized over an earlier interval.
• Its value is framed as a pricing-kernel expectation involving that earlier inflation outcome.
• A multi-period zero-coupon inflation-linked bond has a different payoff because it tracks cumulative inflation over its full term.
• The document poses the observability question but does not identify a matching traded instrument or provide a pricing solution.

Tags

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


# 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 $t+1$.

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