# Market Models

The deregulation of energy markets gave rise to the need for mathematical modelling of electricity and gas prices. Only if commodity prices reflect a realistic behaviour, risk indicators such as Value-at-Risk or Profit-and-Loss yield probable risk prognoses. Since electricity and gas are bad or non-storable commodities, their prices have certain characteristics which cannot be depicted appropriately in many classical financial mathematical models.

#### Typical Characteristics

• Seasonality
• Mean-Reversion
• Weather and temperature dependent fluctuation
• Spikes
• Correlation between commodities
• Negative electricity prices

Fraunhofer ITWM has developed a 3-Factor Model for the modelling of spot and futures prices in commodity markets such as energy and gas.

#### Three-Factor Model

The model is mainly based on the following components:

• Non-stochastic seasonality
• Long-term trends
• Mean-reverting, short-living price fluctuations
• Spikes

The three random processes are also called factors and they determine the behaviour of the commodity prices. With the interaction of these components all important characteristics of the spot and futures prices can be depicted in the model.

The mean-reverting price fluctuations and spikes are mainly relevant for the spot prices. The futures prices are driven by the trend component (except shortly before the delivery period). Spikes, positive as well as negative ones, occur rarely but are short-lived, irregular jumps upward or downward, relatively, followed by a quick return to the regular level. In the model, weather dependent fluctuations are depicted by short-lasting fluctuations.

With the help of the correlation between single factors, the correlation between the different commodities is simulated. In practice this means, that the energy prices will increase in long-term when the gas prices will do the same.

#### Random-Sampling for hourly Spot Prices

In order to also simulate hourly spot prices, we apply a so-called Random-Sampling method. A day type and seasonal correct profile from the historical spot prices is randomly chosen and applied on the simulated base-spot price.

By the help of this method hourly spot prices, and therefore peak and off-peak prices, can be simulated realistically and risks in the spot price can be evaluated with the right market solution.