Valuation models

Inflation-linked bonds

TIPS, UK linkers and OATi with coupons and principal scaled by the index ratio, real and indexed clean prices, real yield, breakeven inflation, z-spread and the deflation floor.

Inputs

CurrencyFaceMaturityyReal coupon%CouponsBase index (at issue)Deflation floor at parInflation vol (floor)%Priced fromReal clean priceDiscount 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

Real coupons and principal are scaled by the index ratio I(t)/I(base), projected off the inflation curve.
The price is quoted in real terms; the value is the indexed dirty price.
With a deflation floor the principal is repaid at no less than par: intrinsic, or Black with an inflation vol.

References

Deacon, Derry and Mirfendereski, Inflation-Indexed Securities
US Treasury TIPS terms

Formulas

Index ratio: R(t) = I(t) / I(base)
Value: P = Σ (100c/f) R(tₖ) D(tₖ) + 100 max(R(T), 1) D(T)
Real price: P(real) = P / R(0) − AI(real)