Modeling and valuing make-up clauses in gas swing contracts

In the last 10 years, thanks to the worldwide energy liberalization process, the birth of competitive gas markets and the recent financial crisis, traditional long term swing contracts in Europe have been supplemented in a significant way by make-up clauses which allow postponing the withdrawal of gas to future years when it could be more profitable. This introduces more complexity in the pricing and optimal management of swing contracts. This paper is devoted to a proper quantitative modelization of one type of make-up clause in a gas swing contract. More in detail, we succeed in building an algorithm to price and optimally manage the make-up gas allocation among the years and the gas taking in the swing subperiods within the years: we prove that this problem has a quadratic complexity with respect to the number of years. The algorithm can be adapted to different instances of make-up clauses as well as to some forms of carry-forward clauses. Then, as an example, we show the algorithm at work on a 3-year contract and we present a sensitivity analysis of the price and of the make-up policy with respect to various parameters relative both to the price dynamics and to the swing contract. To the authors' knowledge, this is the first time that such a quantitative treatment of make-up clauses appears in literature.