Valuation models

FSAs, average-rate, participating and quanto swaps

Forwards off the index curves, averaged fixings, Black-76 or Bachelier floorlets and the quanto convexity adjustment, with the par rate, period table and PV01.

Inputs

Results

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Methodology

Conventions

  • Forwards are simple rates off the index curve over each period, discounted on the discount curve.
  • FSA: one period paying the forward of one index less another, less the contract spread.
  • Average rate: each period pays the mean of the daily, weekly or monthly fixings, each projected over its own sub-period.
  • Participating: a payer swap plus a share of a floor at the fixed rate, its floorlets by Black-76 or Bachelier.
  • Quanto: a foreign index paid on the domestic notional, its forwards adjusted for the rate-FX correlation.

References

  • Hull, Options, Futures, and Other Derivatives

Formulas

FSA
V = Nτ(F₁ − F₂ − K)P(T)
Participating
V = V_payer(K) + p Σ Nτᵢ P(tᵢ) Put(Fᵢ, K)
Quanto forward
F̂ = F e^(−ρ σ_F σ_X t)