Valuation models
Commodity swaptions
The right to pay or receive a fixed price on a monthly or quarterly commodity swap, valued by moment matching the swap's sum of futures under Black, one-factor Schwartz, Schwartz-Smith or Gabillon, with each month's vol to expiry, delta and vega.
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Methodology
Conventions
- Each period's future is read at the period's mid-point and paid at its end.
- The swap's value at expiry is a sum of correlated lognormal futures, moment-matched to one lognormal.
References
- Schwartz and Smith (2000)
- Gabillon (1991)
Formulas
- Schwartz-Smith
- d ln F = σχ e^{−κ(T−t)} dWχ + σξ dWξ
- Gabillon
- d ln F = σS e^{−κ(T−t)} dWS + σL(1 − e^{−κ(T−t)}) dWL
- Moments
- M₂ = Σᵢⱼ DᵢDⱼFᵢFⱼ e^{Cᵢⱼ}, σ²T = ln(M₂/M₁²)