Valuation models

Caps, floors and collars

Caplets on each fixing off the curve, Black-76, shifted Black or Bachelier, flat cap vol or a caplet surface, implied flat vol from a premium, vega and PV01.

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Methodology

Conventions

  • Each caplet is an option on one fixing, paid at the period end; a period fixing today is excluded.
  • Lognormal vols use Black-76, optionally shifted; normal vols use Bachelier.

References

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

Formulas

Caplet
c = N τ D(T) [F N(d1) − K N(d2)]
Parity
Cap(K) − Floor(K) = payer swap at K
Collar
V = Cap(K_cap) − Floor(K_floor)