Valuation models

Brady bonds

Treasury-collateralized principal and rolling interest guarantee on the collateral curve, sovereign flows at the stripped spread solved from a price, with step-up, floating and amortizing coupons, stripped and blended yields, effective duration, PV01 and CS01.

Inputs

Face valueMaturity inyCoupon%PaidInterest guaranteemonthsClean priceCollateral curve (Treasuries)Collateral curve (Treasuries): flat rate% cc

Coupon steps, one per line: tenor (or date) and the coupon from then onPrincipal collateralized by Treasury zerosSolve the stripped spread from a price

Results

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Methodology

Conventions

The final principal (when collateralized) and the coupons inside the rolling interest guarantee are discounted on the collateral curve.
The rest is sovereign risk, discounted on the collateral curve plus the stripped spread, solved from a price.
Par bonds step their fixed coupon, discount bonds float at the index plus a margin, FLIRBs and DCBs amortize.

References

Fabozzi, The Handbook of Fixed Income Securities

Formulas

Value: V = Σ Cᶜᵢ P(tᵢ) + Σ (CFᵢ − Cᶜᵢ) P(tᵢ) e^(−s tᵢ)
Stripped yield: V − Vᶜ = Σ (CFᵢ − Cᶜᵢ)(1 + y/f)^(−f tᵢ)