Valuation models

Gas storage

Injection and withdrawal rates, costs, capacity and end inventory, valued by dynamic programming on a one-factor Schwartz spot fitted to the forward curve, split into intrinsic and extrinsic value, with the expected inventory and flows by date, delta and vega.

Inputs

Results

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Methodology

Conventions

  • Log spot is the forward curve plus a mean-reverting factor (one-factor Schwartz), so expected spot equals the forward.
  • Backward induction over decision dates, inventory levels and price nodes; the intrinsic value uses the forward curve alone.
  • The expected schedule simulates the optimal policy forward.

References

  • Boogert and de Jong (2008)
  • Schwartz (1997)

Formulas

Spot
ln Sₜ = g(t) + Xₜ, dX = −κX dt + σ dW
Bellman
Vᵢ(x, v) = max_{v′} { Dᵢ π(Sᵢ, v′ − v) + E[Vᵢ₊₁ | x] }