Multi-factor forward curve models for energy risk management

In the second article of this series, Carlos Blanco and Michael Pierce introduce the most common multi-factor models of the forward curve used for energy derivatives pricing and risk measurement

In energy markets, forward price changes over time are largely determined by new information regarding the expected average spot price during a future delivery window, and therefore their behaviour is substantially different from that exhibited by spot prices, which immediately react to short-term changes in the physical market.

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Forward curve behaviour

Some of the key features of energy forward price behaviour are the following:
• Time-to-maturity effect: when a forward contract approaches its delivery period, its volatility and correlation with other forward contracts changes. As a general rule, as we get closer to the maturity of the contract, the volatility tends to increase (see figure 2.1), while correlations with other contracts often break down. This effect can be observed in the options markets by observing the term structure of implied volatilities from options on forward contracts.

• Complex forward curve dynamics: As we can see in figure 1, within any given period, the forward curve experiences simultaneous changes in levels, slope and inter-month spreads. Simplistic models of the evolution of the forward curve often fail to capture these dynamics.

• Seasonality: the level and variability of many energy futures contracts is highly seasonal. For example, the price levels and fluctuations of the national balancing point gas contract in the UK for January and July delivery have very specific characteristics. In addition, the volatility of those contracts also changes by season, and when spot prices are most volatile, the full forward curve exhibits larger changes.

• Limited time series of contract behaviour: many futures contracts start trading just a few months prior to their delivery period and expire only a few days before the delivery period starts. In order to build a continuous time series of forward prices or returns to derive volatility, correlations and other model parameters, the price history of several contracts needs to be combined.