Vose SoftwareModelRisk example · Oil and gas
Hedging Production with Swaps and Collars
Swap, collar or puts? How four hedging strategies change the range of two years of oil revenue.
From the model’s saved run
Which strategy?
Revenue over 24 months for each strategy, on the same simulated prices and volumes (US$m).
| Strategy | Mean US$m | 5th pct US$m | 95th pct US$m | Worst 5% average | Below budget chance |
|---|---|---|---|---|---|
| Unhedged | 246.3 | 159.2 | 361.7 | 144.9 | 42.3% |
| Swap | 246.2 | 212.0 | 290.0 | 205.4 | 21.5% |
| Costless collar | 246.6 | 192.7 | 318.3 | 185.7 | 38.6% |
| Bought puts | 245.4 | 183.5 | 352.6 | 176.5 | 46.0% |
| Measure | Unit | Value | |||
| Budget revenue (Inputs sheet) | US$m | 227.0 | |||
| Planned revenue at the forward price | US$m | 259.2 |
Worst 5%: average revenue in the worst 5% of outcomes (planned revenue minus VoseSimCVARp of the shortfall).
S-curve (cumulative probability) of Unhedged, Swap, Costless collar, Bought puts from the saved simulation.
The business question
A mid-size producer sells about 150 thousand barrels of oil a month, and its lenders watch its revenue closely. The oil price could fall a long way in two years, but it could also rise.
The treasurer can lock in today's forward price with a swap, buy put options that set a floor while keeping the upside, or combine a bought put with a sold call into a costless collar.
Each strategy reshapes the range of revenue differently, and none of them is free in every sense: a swap gives up the upside, puts cost a premium, a collar caps the price. Production is uncertain too, and an outage leaves the company hedged on oil it does not produce.
The model simulates monthly prices and volumes for two years and applies the four strategies to the same paths, so that their effect on the downside, the upside and the budget can be compared directly.
- Who it is for
- Treasurers, commercial and risk managers, CFOs and boards deciding on a hedging programme.
- Main outputs
- Revenue over 24 months for each strategy: mean, 5th and 95th percentiles, the average of the worst 5% of outcomes (CVaR) · the chance of falling below the budget · the expected payoff of each hedge, i.e. what the protection costs.
How the model works
Three sheets after this one, read from left to right. Each one feeds the next.
Inputs sheet
Planned volume per month, the monthly uptime range, the chance and length of an outage; today's price and its volatility; the hedge ratio and the terms of the swap, the collar and the puts; the budget price.
Hedges sheet
A geometric Brownian motion with zero expected drift (the forward curve is flat) gives 24 monthly prices. Volume is the plan times the month's uptime, or zero during an outage.
Each hedge pays on the hedged volume whatever is produced: the swap pays the swap price minus the market price, the put pays when the price is below its strike, the collar is a bought put and a sold call. A strategy's revenue is the physical revenue plus its hedge's payoff.
Results sheet
For each strategy, the 24-month revenue: mean, 5th and 95th percentiles, the average of the worst 5% of outcomes, and the chance of falling below the budget. Then the expected payoff of each hedge, which is its cost.
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The results in detail
What the protection costs
The mean payoff of each hedge: what it earns or costs on average over all simulated futures.
| Measure | Unit | Value |
|---|---|---|
| Swap | US$m | −0.15 |
| Costless collar | US$m | 0.29 |
| Bought puts, after the premium | US$m | −0.93 |
| Premium paid for the puts | US$m | 9.18 |
| Average price over the 24 months | US$/bbl | 72.07 |
How to read these results
- A swap narrows the range most: it lifts the bad outcomes and gives up the good ones, and halves the chance of missing the budget. It costs nothing on average because the swap price equals the forward price.
- Bought puts keep almost all of the upside and cut the worst outcomes, but the premium is paid in every scenario: their mean payoff is slightly negative (the bank's margin), and because the premium is also paid when prices are moderate, puts slightly raise the chance of missing the budget.
- The costless collar sits in between: the sold call pays for the put, so it costs nothing up front, but it gives away the upside above the call strike.
- None of the strategies changes the expected revenue much. Hedging changes the shape of the range, not its centre. The choice depends on which outcomes the company cannot afford: the worst 5% and the chance of missing the budget measure exactly that.
- Hedges pay on the planned volume. If an outage stops production, the company is still hedged: with a swap it pays out when prices rise on oil it does not have. Keeping the hedge ratio below the expected uptime limits this.
See it move. Open the workbook, change an input on the Inputs sheet and run the simulation: every table and chart on this page updates in Excel.
Inputs and assumptions
Every assumption in the model, with its uncertainty and where it comes from. The figures are illustrative.
Production 4 inputs
What the company expects to sell, and what can go wrong.
| Assumption | Unit | Uncertainty | Low | Most likely | High |
|---|---|---|---|---|---|
| Planned productionAbout 4,900 barrels a day. | kbbl per month | Fixed | 150 | ||
| Uptime in a monthShort shutdowns and weather. The value shown is the mean; a new uptime is drawn for every month on the Hedges sheet. | of plan | PERT · drawn elsewhere | 85% | 97% | 100% |
| Chance of a major outage in the two yearsCompressor failure or pipeline damage: one such event in the last 20 field-years. | probability | Fixed | 5% | ||
| Length of an outageNo production at all while it lasts. | months | Fixed | 3 | ||
Oil price 2 inputs
A geometric Brownian motion whose expected value in every month equals today's forward price.
| Assumption | Unit | Value |
|---|---|---|
| Forward price (flat curve)Today's quote for the next 24 months. | US$/bbl | 72.00 |
| Annual price volatilityImplied volatility of 12-month options. | 30% |
Hedges 6 inputs
All hedges cover the same share of the planned volume in every month.
| Assumption | Unit | Value |
|---|---|---|
| First year hedgedThe 24 months hedged start in January of this year. | year | 2027 |
| Hedge ratioBoard policy: between 40% and 70% of planned volume. | of planned volume | 60% |
| Swap priceThe company receives this and pays the market price. | US$/bbl | 72.00 |
| Put strike (collar floor and bought puts)The floor. | US$/bbl | 62.00 |
| Call strike (collar cap)Chosen so that the sold call pays for the bought put: the collar costs nothing up front. | US$/bbl | 87.00 |
| Put premiumBank quote for 62 puts, about 10% above their fair value. | US$/bbl | 4.25 |
Budget 2 inputs
The revenue the company has promised its lenders.
| Assumption | Unit | Value | Uncertainty |
|---|---|---|---|
| Budget oil priceConservative planning price. | US$/bbl | 65.00 | Fixed |
| Budget uptimeThe most likely uptime above. | of plan | 97% | Calculated |
Units and conventions
- Money
- US$ million (US$m); prices in US$ per barrel.
- Volumes
- kbbl = thousand barrels per month.
- Percentiles
- 5th percentile: a 5% chance of less revenue. CVaR 5%: the average shortfall in the worst 5% of outcomes.
- Hedge ratio
- Share of the planned (not the actual) volume that is hedged, in every month.
Key assumptions and limitations
- Price
- Geometric Brownian motion with constant volatility and a flat forward curve: the expected price in every month equals today's forward price. No jumps or mean reversion over two years.
- Hedges
- Monthly settlement against the month's average price; no credit risk, margin calls or basis risk. The put premium is paid with the hedge, undiscounted.
- Production
- Uptime varies month by month; an outage stops production for three months. Prices and volumes are independent.
- Data
- Volumes, prices and quotes are invented for this example.
How to use it
- Enter your production plan, price and volatility on the Inputs sheet, and the quotes you have for the swap, the collar and the puts.
- Press F9 on the Hedges sheet to see a price path and how each hedge pays out.
- Run a simulation from the ModelRisk ribbon (10,000 samples with a fixed seed are set).
- Try other hedge ratios and strikes and simulate again: the Results sheet shows the trade-off between downside and upside.
ModelRisk functions used
- VoseTimeGBM
- 24 monthly prices from a geometric Brownian motion, as one array formula.
- VosePERT, VoseBernoulli, VoseStepUniform
- Monthly uptime, whether an outage happens, and the month it starts.
- VoseInput, VoseOutput
- Name the uncertain inputs and the revenue and payoff outputs.
- VoseSimMean, VoseSimPercentile, VoseSimProbability, VoseSimCVARp
- Statistics of the simulation for the tables and charts on the Results sheet; VoseSimCVARp averages the worst 5% of shortfalls.
Further reading
- Monte Carlo simulation explained (Vose guide)
- Hull, J. C. (2022). Options, Futures, and Other Derivatives, 11th edition. Pearson — chapters on hedging strategies.
- Vose, D. (2008). Risk Analysis: A Quantitative Guide, 3rd edition. Wiley — chapter on financial risk and value at risk.
Download the workbook and run it yourself. It opens in Excel with ModelRisk. The free trial runs every example model.
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An illustrative example: the figures are invented for teaching and do not describe a real company, project or asset. Last updated 9 October 2026.