Valuation models

Inflation swaps

Zero-coupon and year-on-year CPI swaps off a zero-coupon inflation curve, with the par rate, both legs, the projected index path, cash flows and PV01.

Inputs

SwapCurrencySideNotionalMaturityyFixed rate at parFixed rate%Discount curveDiscount curve: flat rate% ccInflation curveUS CPI-U today1Y zero-coupon inflation%2Y zero-coupon inflation%5Y zero-coupon inflation%10Y zero-coupon inflation%30Y zero-coupon inflation%

Results

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Methodology

Conventions

The index is projected off zero-coupon inflation swap rates: I(t) = I(0) (1 + z(t))^t.
Whole months count as twelfths of a year, as inflation swaps quote them.
Flows are discounted on the nominal curve; year-on-year ratios have no convexity adjustment.

References

Kerkhof (2005), Inflation Derivatives Explained
Brigo and Mercurio, ch. 15

Formulas

Zero-coupon: N (I(T)/I(0) − 1) vs N ((1 + K)^T − 1)
Year-on-year: Σ N τ (I(tᵢ)/I(tᵢ₋₁) − 1) vs Σ N τ K
Par rate: K* = (I(T)/I(0))^(1/T) − 1