Inflation Swap

An inflation swap turns future inflation — unknowable, uninsurable by ordinary means — into a rate you can lock today. One party pays whatever inflation actually turns out to be (measured by a price index like CPI or euro HICP); the other pays a fixed rate agreed upfront.

A pension fund whose payouts rise with inflation is terrified of high inflation: it receives inflation in the swap, so surging prices generate swap gains that fund the higher pensions. A utility whose regulated revenues rise with inflation might take the other side, monetising its natural hedge.

The fixed rate that clears this market — the swap breakeven — is one of the cleanest measures anywhere of what markets expect inflation to be.

The standard contract: zero-coupon

The dominant format exchanges just one payment at maturity: fixed side pays \((1+K)^T - 1\); inflation side pays \(I_T/I_0 - 1\), the index's total growth. Nothing happens until maturity — clean, and easy to strip into a curve of breakevens by tenor.

Variants

• Year-on-year (YoY): annual payments of each year's inflation vs. a fixed rate — matches inflation-linked liabilities paying annually; embeds convexity differences vs. zero-coupon.
• Real-rate swaps and asset swaps on linkers connect the swap and bond markets.
• Caps/floors on inflation: options, e.g. the 0% floors embedded in many linkers, or LPI (limited price indexation) structures capping UK pension indexation.

Swap vs. bond breakevens

Both linker markets and swap markets produce "breakeven inflation"; they differ by balance-sheet and liquidity premia (the linker asset-swap basis). Swaps are often the cleaner expectation gauge — no bond financing noise — and central banks watch measures like the euro 5y5y forward inflation swap as their headline expectations indicator.

Pricing and curve building

Zero-coupon quotes \(K(T)\) directly define the inflation forward curve: \( \mathbb{E}^{\mathbb{Q}}[I_T]/I_0 = (1+K(T))^T \). Seasoned swap value for the inflation receiver:

using today's re-quoted forward inflation. Curve construction must handle the indexation lag (payments reference the index 2–3 months back) and seasonality — monthly CPI patterns are modelled explicitly so short-dated swaps price the right month's print.

Convexity and YoY modelling

YoY legs pay \(\tfrac{I_{t_i}}{I_{t_{i-1}}}-1\), a ratio of two lognormals whose expectation requires a model of inflation-rate volatility and autocorrelation (Jarrow–Yildirim's "foreign currency" analogy — real economy as foreign market, inflation index as exchange rate — or market models on forward inflation). The YoY-vs-ZC convexity correction and inflation smile (from caps/floors) are the quant content of the market.

Risk premia decomposition

Term-structure models with survey anchoring attempt the split; policymakers care because only the first term is "expectations de-anchoring".