Valuation models

Basis and cross-currency swaps

Each leg projected and discounted on its own curve, notional exchanges converted at spot, par basis spread, FX delta and PV01.

Inputs

Results

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Methodology

Conventions

  • Each float leg projects off its own curve, or the discount curve; both discount on the discount curve.
  • Cross-currency legs discount on their own currency's curve and convert at spot.

References

  • Hull, Options, Futures, and Other Derivatives, ch. 7

Formulas

Float leg
PV = Σ N τ (F + s) D
Par spread
s* = s ∓ V / Σ N τ D
Cross-currency
V = PV(receive) − S · PV(pay), with notional exchanges