Valuation models

Swing options

The right to take or deliver volume at a strike on daily, weekly or monthly dates, between a take-or-pay minimum and a maximum number of exercises, valued by dynamic programming over the rights used on a trinomial tree, with forward starting strikes and multiple peakers, against the European and forward strips.

Inputs

Results

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Methodology

Conventions

  • On each exercise date the holder may take the volume at the strike, at least the minimum and at most the maximum number of times.
  • A trinomial tree on the log price (lognormal, rate less convenience yield) with dynamic programming over the rights used.
  • A forward starting swing fixes its strike on the start date as a share of the price then; a multiple peaker has no minimum.

References

  • Hull, Options, Futures, and Other Derivatives
  • Jaillet, Ronn and Tompaidis (2004), Valuation of commodity-based swing options

Formulas

Rights
Vᵢ(x, k) = max(v (S − K) + Cᵢ(x, k + 1), Cᵢ(x, k))
Minimum
wait only if k + (N − i − 1) ≥ n_min