Valuation models

FX volatility products

Forward volatility agreements as forward-start straddles on the forward vol, and FX variance and volatility swaps by replication on the smile, with vega.

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Methodology

Conventions

  • An FVA delivers an ATM-forward straddle on the strike date, paid for at the agreed vol.
  • The forward vol comes from the two ATM vols' total variance.
  • FX variance swaps replicate variance from the smile, with the base currency's rate as the carry.

References

  • Wystup, FX Options and Structured Products
  • Gatheral, The Volatility Surface

Formulas

Forward vol
σ_f = √((σ₂² T₂ − σ₁² T₁) / (T₂ − T₁))
Straddle
Π(σ) = 2 N S D_b(T₂) [2Φ(σ√τ / 2) − 1]