Trading calendar spread options on energy futures

Sponsored feature: CME Group


What is a CSO?
CSOs are options on the spread between two different futures expirations. The energy futures term structure represents the time value of energy market variables such as storage costs, seasonality and supply/demand conditions. CSOs provide a leveraged means of hedging against, or speculating on, a change in the shape of the futures term structure.

CME Group has a diverse product offering that includes crude oil, natural gas and refined product CSOs. This article illustrates the main characteristics of CSOs and some of their applications in the energy markets.

A CSO is an option to enter into two separate futures positions: one long and one short. A call option can be exercised into a long futures position that is closest to expiration and a short futures position in a more distant month. The put option can be exercised into a short futures position that is closest to expiration and a long futures position in a more distant month. The strike price is the price differential between the long and short futures positions.

A call option with a $0.50 strike price, for example, represents a long futures position priced $0.50 higher than a short futures position of a more distant maturity. A put option with a $0.50 strike price, by contrast, represents a short futures position priced $0.50 higher than a long futures position of a more distant maturity.

The payoff for a long CSO call or put position at maturity T is:

C(T) = Max. (0, (FT1(T) – FT2 (T))-K)

P(T) = Max. (0, K – (FT1(T) – FT2 (T)))

T: Option expiration
FT1(T) – FT2(T): Calendar spread
K: Strike price

If the futures spread settles higher than $0.50 on the day of the CSO expiration, the owner of the $0.50 call profits on the difference.

Natural gas CSOs
The natural gas term structure is defined by seasonality. The withdrawal season (‘winter’) is from November to March and is noted for its volatility. The injection season (‘summer’) runs from April to October and is generally less volatile.

During the winter season, gas consumption peaks as a result of increased heating demand from residential, commercial and industrial end-users. During the summer season, gas demand decreases while production continues, resulting in excess natural gas that can be stored. As a result of unpredictable winter demand, the winter natural gas futures trade at a premium to the summer futures (figure 1). The winter term structure is in backwardation – defined by the scenario when near-month futures are priced higher than back-month futures – versus the summer term structure in contango, characterised by near-month futures trading at a discount to back-month futures.


Commercial firms typically produce or purchase natural gas at a lower price during the summer season and inject that natural gas into storage. Those firms then sell the stored natural gas in the winter season at a higher price to profit from the demand premium. The ability to purchase, store and sell natural gas across the winter and summer seasons creates implicit optionality.

Crude oil CSOs
The crude oil futures and options markets are global and are the most liquid and actively traded commodities contracts in the world. The forward-term structure in crude oil is largely influenced by supply/demand, storage costs and production estimates. This results in the market’s expectation of a more continuous price evolution. This is in contrast to the natural gas market, where seasonality dictates the shape of the forward futures curve.

In crude oil, a backwardated market generally reflects potential supply constraints or shortages – distant futures prices are cheaper than near term because demand for oil adds a premium to the nearest delivery contract. Conversely, a higher price on the more distant futures contracts generally reflects plentiful supply or inventory levels. This is often referred to as a contango market, as illustrated in figure 2, where the West Texas Intermediate (WTI) term structure on May 1, 2015 is in steep contango.


The shape of the forward curve has important implications for inventory management. For example, if the market is backwardated, the current value of inventory is greater than the deferred future price. Holding inventory in this situation could result in selling at a lower price. Conversely, in a contango market, holding inventory and selling at a deferred date is expected to yield extra revenue net of storage costs.

This convenience yield can be viewed as the embedded optionality attached to holding a physical commodity. It is defined as the difference between the positive gain of holding a commodity minus the cost of storage. Therefore, the convenience yield can be positive or negative depending on the time period and the level of oil inventory.

Pricing option models and hedging tools that are traditionally utilised for standard vanilla options should not be applied to spread options for a variety of reasons, most notably the possibility of negative strike prices. Spread option pricing varies, but can be classified into two main approaches: numerical models and analytical models. Numerical models include Monte Carlo simulation, fast Fourier transform and numerical integration. The primary analytical model is a closed-form solution, known as the Bachelier model. The Bachelier model relies on the assumption that the underlying spread follows a symmetrically normal price distribution. Since the price follows a normal distribution, volatility also needs to be treated differently. Figure 3 presents a price versus volatility example. These models are commonly used across the CSO trader community.


Oil and gas prices are highly elastic with respect to various fundamental factors including weather, geopolitical risk and unanticipated supply/demand. Unpredictable changes from any of these factors can have an impact on forward-curve prices and the correlation between the calendar months. CSOs are flexible products that are sensitive to the slope of the forward-term curve and will rise or fall in value as the shape of that term curve changes with time. A move from contango to flat to backwardation will change the values of term differences along the curve, and CSOs can be leveraged to realise those steepening or flattening changes. CME Group has a diverse product offering of CSOs across crude oil, natural gas and refined products. Additionally, CME offers intercommodity spread options such as WTI-Brent and crack spreads.

For specific examples of how to use CME Group’s CSOs on energy futures, view the full white paper, Trading calendar spread options on energy futures, here.

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