Real rate swaps and inflation asset swaps

A fixed real rate on an inflation-indexed notional against floating or fixed nominal, with the par real rate and PV01, and the par asset swap spread of an inflation-linked bond against its z-spread.

Inputs

Currency

Notional

Maturityy

Real rate at par

Real rate%

Index the principal at maturityDiscount curve

Discount curve: flat rate% cc

Inflation curve

US CPI-U today

1Y 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

Real rate swap: a fixed real rate on a notional scaled by I(t)/I(0), with the principal indexed at maturity, against floating or fixed nominal.
Inflation asset swap: the linker's indexed flows swapped for floating plus a spread; the package costs par.

References

Kerkhof (2005), Inflation Derivatives Explained
Deacon, Derry and Mirfendereski, Inflation-Indexed Securities

Formulas

Real leg: Σ N r τᵢ R(tᵢ) D(tᵢ) + N (R(T) − 1) D(T)
Par real rate: r* = (nominal − indexation) / Σ N τᵢ R(tᵢ) D(tᵢ)
ASW spread: s = (P_rf − P_dirty) / (100 A)