Chapter 35: Energy and Commodity Derivatives

Agricultural Commodities

Futures on agricultural products (corn, wheat, soybeans, live cattle, pork bellies, coffee, sugar, cocoa, orange juice) have traded for over 150 years. Key features:

• Seasonality: Prices and volatility vary with the growing/harvest cycle
• Storage costs: Physical storage is required, creating contango markets
• Weather dependence: Supply shocks from droughts, floods, freezes
• Government intervention: Subsidies, price supports, import/export restrictions

The convenience yield is often significant for agricultural commodities — having the physical commodity available for processing creates value beyond the price.

Metals

Precious Metals (Gold, Silver, Platinum)

• Investment assets: Held primarily for investment, not consumption
• Gold priced by arbitrage: $F_0=S_0{e}^{(r+u)T}$ where $u$ is storage cost
• Gold leasing market: central banks lease gold to earn a return (gold lease rate)
• Gold futures typically in contango

Base Metals (Copper, Aluminum, Zinc, Lead, Nickel, Tin)

• Consumption assets with industrial uses
• Traded on the London Metal Exchange (LME) and COMEX
• Prices driven by industrial demand, especially from China (the world's largest consumer)

Energy Products

Crude Oil

The most actively traded commodity. Key benchmarks:

• WTI (West Texas Intermediate): CME/NYMEX, delivered in Cushing, Oklahoma
• Brent: ICE Futures Europe, North Sea benchmark

Oil futures exhibit:

• Strong seasonality in products (gasoline demand peaks in summer, heating oil in winter)
• Geopolitical risk premiums
• OPEC+ production decisions as major price drivers
• The convenience yield is critical — holding physical oil provides strategic value during supply disruptions

Natural Gas

• Highly seasonal demand (heating in winter, cooling in summer)
• Storage constraints: limited storage capacity causes extreme price volatility
• Transportation constraints: pipeline capacity limits
• Much higher volatility than oil (can spike 5-10x)
• Regional pricing (unlike oil which is globally priced)

Electricity

The most unusual commodity:

• Non-storable (except via pumped hydro or batteries, which are limited)
• Extreme intraday price variation (peak vs. off-peak can differ 10x)
• Must balance supply and demand instantaneously
• Price spikes (up to price caps of $1,000-$9,000/MWh) during shortages
• Seasonality: summer peak in warm regions (air conditioning), winter peak in cold regions (heating)

Modeling Commodity Prices

Commodities often exhibit mean reversion: prices tend to pull back toward the marginal cost of production. A commonly used model:

$d\ln S=[\theta (t)-a\ln S]dt+\sigma dz$

where $a$ governs the speed of mean reversion. This prevents prices from drifting indefinitely upward.

Seasonality

Seasonal patterns are incorporated with deterministic seasonal functions added to the drift or the long-run mean.

Jumps

Commodity prices exhibit jumps (weather events, supply disruptions, geopolitical shocks). Jump-diffusion models are more appropriate than pure diffusion.

Weather Derivatives

Payoffs depend on weather variables: temperature (HDD, CDD), rainfall, snowfall, wind speed.

• HDD (Heating Degree Days): $\max (65°F-\text{avg daily temp},0)$ — measures heating demand
• CDD (Cooling Degree Days): $\max (\text{avg daily temp}-65°F,0)$ — measures cooling demand

Typical structures:

• Call option on cumulative HDD: Pays if the winter is colder than expected
• Put option on cumulative CDD: Pays if the summer is cooler than expected

Uses: Energy companies hedge revenue against warm winters (lower heating demand); farmers hedge against drought; amusement parks hedge against rainy summers.

Insurance Derivatives

Catastrophe (CAT) Bonds

A bond where the principal is partially or fully forgiven if a specified catastrophic event occurs (hurricane, earthquake). Investors receive above-market coupons but risk loss of principal.

Industry Loss Warranties (ILWs)

Pays out if the total insurance industry loss from a specified event exceeds a threshold. Based on an objective industry index, not the individual insurer's losses.

Pricing Challenges

• No traded underlying asset (weather and insurance events are not traded)
• Historical data is limited (catastrophes are rare)
• Actuarial models rather than no-arbitrage models
• The market price of risk is significant (investors demand high risk premiums for CAT bonds)

Hedging for Energy Producers

An integrated energy producer faces multiple risks:

• Price risk: Spot prices of oil, gas, electricity
• Volume risk: Production can be affected by weather, equipment failure
• Basis risk: Local prices may deviate from benchmark prices
• Timing risk: Production and hedging dates may not align

A comprehensive hedging program typically uses a combination of:

• Futures and swaps for base price exposure
• Options to retain upside while protecting downside
• Weather derivatives to hedge volumetric demand risk
• Structured products (swaptions, extendable swaps) for flexibility