Hedging Programme Chosen by the Optimizer

The business question

OG-09 compared hedges on 60% of a producer's oil sales. Hedging has a price: the bank's swap price is US$1 below the forward, and its puts cost a little more than fair value. The board wants the cheapest programme that keeps the chance of missing the budget to 1 in 10, within a 70% hedging cap.

Here the ModelRisk Optimizer chooses the swap share, put share and put strike together.

Who it is for

Treasurers, commercial and risk managers, CFOs and boards deciding on a hedging programme.

Main outputs

The Optimizer's swap share, put share and put strike against a starting plan (OG-09's swap on 60% of planned volume) · for both plans and with no hedge: the mean, 5th and 95th percentiles of two years' revenue and the chance of missing the budget · the expected cost of the hedges · the distributions of revenue and of the hedges' payoff.

How the model works

Four sheets after this one, read from left to right. Each one feeds the next.

1. 1

   Inputs sheet

   Planned volume, the monthly uptime range and the chance and length of an outage. Today's forward price and its volatility; the bank's swap price and its premiums for puts at four strikes; the hedging cap; the budget price and the largest chance of missing the budget that the board accepts.

2. 2

   Decisions sheet

   The three cells the Optimizer changes — the share of planned volume swapped, the share protected by bought puts, and the put strike — with their bounds, the starting plan they are compared with, the goal (the most revenue after hedging, on average) and the limits (the budget, and the hedging cap).

3. 3

   Hedges sheet

   A geometric Brownian motion with no expected drift gives 24 monthly prices. Volume is the plan times the month's uptime, or nothing during an outage. Each plan's swap pays the swap price minus the market price, and its puts pay when the price is below the strike, less the premium. Revenue and a below-budget flag for each plan are outputs.

4. 4

   Results sheet

   Both plans, and no hedge, on the same simulated prices and volumes: the mean and the 5th and 95th percentiles of two years' revenue, the chance of missing the budget, the expected cost of the hedges, and the distributions of revenue and of the hedges' payoff.

ModelRisk techniques

• ModelRisk Optimizer: two hedge shares and a strike from a list
• Chance of missing the budget as a probability limit
• Hedging cap as a formula limit
• Monthly GBM price VoseTimeGBM
• Both programmes on the same paths

Find similar models

Product

• ModelRisk
• Optimizer

Type

• Simulation
• Optimisation

Application

• Pricing and hedging
• Choosing a strategy

Uses

• PERT
• Bernoulli
• Step uniform
• Time series
• Geometric Brownian motion

Inputs and assumptions

Every assumption in the model, with its uncertainty and where it comes from. The figures are illustrative.

Units and conventions

Money

US$ million (US$m); prices in US$ per barrel.

Volumes

kbbl = thousand barrels per month.

Shares

The swap share and the put share are shares of the planned (not the actual) volume, in every month.

Expected cost

Of the hedges: minus their mean payoff, premiums included. What the bank's margins cost on average over the two years.

Below budget

Revenue over the 24 months less than the budget revenue: budget price × planned volume × the most likely uptime.

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. Premiums are paid with the hedge, undiscounted. The bank's quotes hold whatever volume is hedged.

Production

Uptime varies month by month; an outage stops production for three months. Prices and volumes are independent.

Optimizer

Each plan the Optimizer tries is judged on the same 10,000 simulated price and volume paths (common random numbers, seed 1) as the simulation on the Results sheet, so plans are compared fairly and the limit the Optimizer met holds on the Results sheet too.

Data

Volumes, prices and quotes are invented for this example.

How to use it

1. Enter your production plan, price and volatility, the bank's quotes, your budget and the chance of missing it that you accept on the Inputs sheet.
2. On the ModelRisk ribbon, open the Optimizer: the task is saved in this workbook. Press Start. When it finishes, apply the best solution: the swap share, put share and put strike on the Decisions sheet change.
3. Run a simulation from the ModelRisk ribbon (10,000 samples with a fixed seed are set) to compare the new plan with the starting plan on the Results sheet.
4. To watch the search from the beginning, copy the starting plan onto the Optimizer’s plan first.

ModelRisk functions used

ModelRisk Optimizer

Chooses the swap share, the put share and the put strike: the most mean revenue after hedging, the chance of missing the budget at most the limit, the two shares within the hedging cap.

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.

VoseSimMean, VoseSimPercentile

The mean and percentiles of revenue, and the cost of the hedges, for both plans and with no hedge.

VoseSimProbability

The chance of missing the budget, for both plans and with no hedge.

Further reading

• Monte Carlo simulation explained (Vose guide)
• Hull, J. C. (2022). Options, Futures, and Other Derivatives, 11th edition. Pearson — chapters on hedging strategies.
• OG-09 Hedging production with swaps and collars: the same producer, with a swap, a costless collar and bought puts on 60% of planned volume compared side by side.