The aim of this paper is to price certain contracts in the electricity market in analogy to interest rate products. Such contracts are delivery contracts with retail or institutional customers. In fact, many features of electricity products exist almost identically in structured Libor products and some models have already been adapted to the world of commodities. However, there have been no attempts to apply these techniques to value such structures in the retail market. Though the market under consideration is far from being driven by only rational participants, we show how to quantify features such as call rights for customers and hedge analysis for utilities.

We use the case of a two-factor forward model that has been proven to be useful for electricity markets, capturing volatility term-structure effects and the influence of delivery periods on the contract’s volatility. This model will be calibrated to option data.

The main task consists of the valuation of multiple call rights that are incorporated into retail contracts. When deciding whether or not to quit the contract, the residual value of the contract should be known. However, this value is unknown due to the multiple call rights. Thus, deciding whether or not to give away the contract and all future cancel rights is a non-trivial task. The Longstaff-Schwartz algorithm has proven to be useful in pricing multicallable products. We extend this algorithm and make it suitable for our purposes.

It is our aim to illustrate the tools and procedures that are provided by academic literature within this field of research. We aim to outline how transparancy can be gained by such methods. It is not our intention to compare and judge about one or another retail structure. Though many of the assumptions behind the models used can be challenged, we show that our results are reasonable, helpful and that the assumptions are supported by our model results. The tools used in the text give support to any
structuring team, even in the retail business.

---

Valuation models for energy derivatives need to adequately account for the characteristics of energy markets such as extreme price fluctuations and stochastic seasonal patterns. Further, futures contracts on stocks stipulate delivery of the underlying asset on a fixed delivery date whereas futures contracts in the energy market stipulate continuous delivery over a certain period of time which complicates the endogenous derivation of the price dynamics of these contracts.
In this paper we combine a low-dimensional Markovian Heath-Jarrow-Morton (HJM) process with an additional Lévy process to model the behaviour of energy spot prices. We apply the HJM process to directly address the dynamics of an entire seasonal term structure of futures prices. This allows us to capture the particularities of the delivery provisions and also is consistent with option-implied volatilities. Given that futures prices represent the risk-neutral market expectation of future spot prices, a stochastic seasonal pattern of the spot price process is modelled. The Lévy component accounts for the statistical characteristics of the historical time series with respect to extreme spikes. Based on this model, real options in the energy market can be valued.
We calibrate the model to historical U.S. natural gas prices and to current prices of respective options. Furthermore, we determine numerically the value of a storage contract and discuss hedging strategies in the futures market. Finally, historical time series are used to validate results.