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Energy & Commodity Risk

Model carbon exposure, hedge payoffs, and correlated or mean-reverting price decks — the way energy prices actually behave

Overview

Four parameter-driven models for commodity price and hedging. No table goes into the visual — you describe each price as a distribution and the simulation produces the range. Two of them model several commodities at once, because Brent, WTI and Henry Hub do not move independently and pretending they do understates the risk.

Answer the question: "What does our carbon bill and hedge book look like next year across the whole range of prices — not just at the one price in the budget?"

The four models on this page

Model What it computes Key inputs
Carbon CostEmissions above the free allowance, priced at an uncertain carbon priceEmissions (tCO2e) · CO₂ price · Free allowance
Hedging PayoffEffective realised price under a swap, put or collarPrice · Structure · Strike · Premium · Floor · Cap
Price Deck (correlated)Three commodities simulated together through a correlation matrixBrent · WTI · Henry Hub · three ρ values
Price Deck (mean-reverting OU)Ornstein-Uhlenbeck paths that pull back toward a long-term meanSpot P0 · Long-term mean L · Half-life · Volatility σ · Horizon

Carbon Cost

Two uncertain quantities multiplied together: how much you emit and what a tonne costs. The free allowance is subtracted first, so the model shows the cliff that appears once an operation grows past its allocation.

Default parameters:

  • ▸Emissions (tCO₂e):PERT(800, 1000, 1300)
  • ▸CO₂ price:Triangular(50, 80, 120)
  • ▸Free allowance:0
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Try this: Set the free allowance to roughly your current emissions, then raise emissions by 20%. Cost does not rise 20% — everything above the allowance is charged at full price, so the increase lands entirely on the exposed tonnes.
Carbon Cost simulation showing the distribution of annual carbon cost and a tornado of drivers

Hedging Payoff

Prices the three structures a producer usually chooses between and reports the effective price each one delivers across the price distribution. Reported side by side, because the interesting question is not what a hedge pays but which shape suits the exposure.

Default parameters:

  • ▸Price:Triangular(40, 60, 90)
  • ▸Structure:swap / put / collar
  • ▸Strike:swap and put
  • ▸Premium:put only
  • ▸Floor / Cap:collar only
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Try this: Compare the swap against the collar on the same price distribution. The swap fixes the outcome; the collar keeps some upside but only pays below the floor. Which is better depends entirely on how wide your price range is.
Hedging Payoff simulation comparing swap, put and collar effective prices

Price Deck (correlated)

Each commodity is drawn from its own normal distribution, then coupled through a correlation matrix so scenarios stay physically plausible. Brent and WTI at ρ 0.9 move almost in lockstep; gas at 0.3 does its own thing much of the time.

Default parameters:

  • ▸Brent:Normal(80, 10)
  • ▸WTI:Normal(76, 10)
  • ▸Henry Hub:Normal(3, 0.5)
  • ▸ρ Brent-WTI / Brent-HH / WTI-HH:0.9 / 0.3 / 0.3
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Try this: Drop ρ Brent-WTI from 0.9 to 0.3 and watch the combined revenue spread widen. That gap is the diversification the correlation was suppressing — and assuming it exists when it does not is how hedge books get surprised.
Correlated Price Deck simulation showing three commodity price distributions

Price Deck (mean-reverting OU)

The model to use over multiple years. A normal draw treats every period as independent, so prices wander off indefinitely; Ornstein-Uhlenbeck pulls them back toward a long-term level at a speed set by the half-life, which is closer to how commodity prices have historically behaved.

Default parameters:

  • ▸Brent (P0 / L / half-life / σ):80 / 70 / 2 / 12
  • ▸WTI (P0 / L / half-life / σ):76 / 66 / 2 / 12
  • ▸Henry Hub (P0 / L / half-life / σ):3 / 3 / 1.5 / 0.5
  • ▸Horizon T:5 periods
  • ▸ρ Brent-WTI / Brent-HH / WTI-HH:0.9 / 0.3 / 0.3
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Try this: Run the correlated deck and this one over the same horizon. Year one looks similar; by year five the OU paths have converged toward the long-term mean while the plain normal ones have fanned out to prices nobody would plan against.
Mean-reverting Price Deck simulation showing Ornstein-Uhlenbeck price paths converging to a long-term mean
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Why correlation is a separate model: Simulating Brent and WTI independently produces scenarios that cannot happen — one at $110 while the other sits at $60. Both Price Deck models take a correlation matrix so the commodities move together, and the difference shows up in the tails, which is exactly where a hedge book is judged.