Valuation models

Floaters and amortizing bonds

FRNs, capped and floored FRNs and inverse floaters from the forward curve, caps and floors with Black-76 on each fixing, discount margin, plus amortizing bonds with weighted average life.

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Methodology

Conventions

  • Index forwards come off the curve; caps and floors are Black-76 options on each fixing, or intrinsic without a vol.
  • Amortizing bonds pay coupons on the balance outstanding at the start of each period.

References

  • Hull, Options, Futures, and Other Derivatives, ch. 29

Formulas

Forward
F_k = (D(t_k−1)/D(t_k) − 1) / τ_k
Capped coupon
c = ℓF + s − ℓ Call(F, (cap − s)/ℓ) + ℓ Put(F, (floor − s)/ℓ)
Inverse coupon
c = R − ℓF + s + ℓ Call(F, (R + s − floor)/ℓ)