Analysis of a multiple year gas sales agreement with make-up, carry-forward and indexation

Abstract

A typical gas sales agreement, also called a gas swing contract, is an agreement between a supplier and a purchaser for the delivery of variable daily quantities of gas, between specified minimum and maximum daily limits, over a certain number of years at a strike price. The main constraint of such an agreement that makes them difficult to value is that there is a minimum volume of gas (termed the take-or-pay or minimum bill) for which the buyer will be charged at the end of the year (or penalty date), regardless of the actual quantity of gas taken. We propose a framework for pricing such swing contracts where both the gas price and strike price (an index) are stochastic processes. With the help of a two-dimensional trinomial tree, we are able to price such swing contracts with both so-called make-up and carry-forward provisions; find optimal daily decisions and optimal yearly usage of both the make-up bank and the carry-forward bank. With the help of a number of numerical examples, we also provide a detailed analysis, not only of the different features these contracts have, but also how different model parameters will affect both the optimal value and the optimal decisions

Moving average options: Machine Learning and Gauss-Hermite quadrature for a double non-Markovian problem

“…Table (13) reports the results for the tests with fixed computational time. GPR-GHQ is very often the best method, in particular for M = 20 and M = 30, as well as when the computational target time is 2 minutes.…”

“…Finally, it is worth mentioning the works of Dong and Kang [13,14] who study a particular type of swing contracts that include a moving average feature, by means of a two-dimensional trinomial tree and least squares Monte Carlo methods. To conclude this review, we also mention the research on the dynamic hedging of moving average options of Warin [27].…”