Swing Contracts Research Articles

A Linked Swing Contract Market Design With High Renewable Penetration and Battery Firming

As renewable generation and energy storage systems become increasingly cost-effective, modern power systems are increasingly reliant on variable energy resources (VERs) to meet demand. However, the variability and uncertainty of VERs' generation require additional flexibility to mitigate their impacts. Unfortunately, the current power market designs rigidly define different power and reserve products, making it difficult to fully recognize and compensate for this flexibility. Furthermore, since the marginal operating costs of the system quickly approach zero, current marginal cost-based market mechanisms struggle to provide price signals that allow independent power producers to make informed decisions about constructing, operating, and retiring plants. To address these issues, this paper proposes a new linked electricity market design based on swing contracts for operating power systems with high penetration of VERs and energy storage resources. The feasibility of the proposed approach is demonstrated through study results on the modified IEEE 118-bus test system.

Swing contract pricing: With and without neural networks

Swing contract pricing: With and without neural networks

A New Look at the Swing Contract: From Linear Programming to Particle Swarm Optimization

As the energy market has grown in importance in recent decades, researchers have paid increasing attention to swing option contracts. Early studies evaluated the swing contract as if it were a financial derivative contract, by ignoring its storage constraints. Aided by recent advances in artificial intelligence (AI) and machine learning (ML) technologies, recent studies were able to incorporate storage limitations. We make two discoveries in this paper. First, we contribute to the literature by proposing an AI methodology—particle swarm optimization (PSO)—for the evaluation of the swing contract. Compared to the other ML methodologies in the literature, PSO has an advantage by expanding to include more features. Secondly, we study the relative impact of the price process (exogenously given) that underlies the swing contract and the storage constraints that affect a quantity decision process (endogenously decided), and discover that the latter has a much greater impact than the former, indicating the limitation of the earlier literature that focused only on price dynamics.

Markets for Flexibility: It Don’t Mean a Thing If It Ain’t Got That Swing [Book Review

This book proposes a new wholesale electricity market design paradigm, with a focus on North America, for centrally managed electricity markets that are based on the novel concept of swing contracts. The author, a professor at Iowa State University, has been working on electricity market design and agent-based computational economics for many years. Her extensive academic, research, and industry experiences, as well as her training in both economics and mathematics, make her highly qualified to provide fresh thinking in this important area. The book proposes the adoption of swing contracts between the system operator and relevant resources to provide flexibility. This flexibility is represented in the form of future availability of dispatchable power paths (“reserve”) with prespecified physical attributes and economic attributes (for pricing purposes). The book contains rigorous mathematical descriptions of the proposed mechanism and implementations.

New class of optimal multiple stopping times problems

This paper is devoted to study a new discounted nonlinear optimal multiple stopping times problem with discounted factor β > 0 and infinite horizon. Under the right continuity of the underlying process, we show that the problem can be reduced to a sequence of ordinary optimal stopping problems. Next in the Markovian case, we characterise the value function of the problem in terms of β-excessive functions. Finally, in the special case of a diffusion process, we give explicit expressions for the value function of the problem as well as the optimal stopping strategy. As an explicit example in finance, we apply our theoretical results to manage a new generalised swing contract which gives its holder n rights to mark the price X of a stock, where the payment is only allowed at the final exercise time rather than at each exercise time as in the classical swing contact.

Evaluation of gas sales agreements with indexation using tree and least-squares Monte Carlo methods on graphics processing units

A typical gas sales agreement, also called a gas swing contract, is an agreement between a supplier and purchaser for the delivery of variable daily quantities of gas between specified minimum and maximum daily limits. The primary constraint of such agreements that makes them difficult to value is that the strike price is set based on the indexation principle, under which the strike price is called the index. Each month, the value of the index is determined by the weighted average price of certain energy products (e.g. crude oil) in the previous month. We propose a lattice-based method (trinomial trees) and a simulation-based method (least-squares Monte Carlo simulations) for pricing such swing contracts with indexation. With the help of graphics processing unit (GPU) technology, we can efficiently evaluate the algorithms. We also provide a detailed analysis using several numerical examples of the indexation and how different model parameters will affect both the optimal value and optimal decisions.

Optimal multiple stopping under catastrophic event

In this paper, we introduce a new optimal multiple stopping times problem, where we assume each exercise right happens before the date of release of a catastrophic event modelled by a random variable and this catastrophe can be natural (e.g., earthquake, tsunami) or technological (e.g., nuclear event). Since a sudden catastrophe will have a direct influence on prices variation, especially those of underlying as well as option's prime, eventual catastrophic event will be modelled by the first time the underlying's price exceeds some large barrier. The originality of this paper comes from a mathematical model taking account of a nonlinear criteria of sum of the underlying stopped at stopping times of the holder's filtration information as well as a random number of exercise rights at sopping times involving prior to a catastrophic event. This will generalises the concept of swing contracts, where the exercise rights number is only deterministic and finite.

Volatility Uncertainty Quantification in a Stochastic Control Problem Applied to Energy

This work designs a methodology to quantify the uncertainty of a volatility parameter in a stochastic control problem arising in energy management. The difficulty lies in the non-linearity of the underlying scalar Hamilton-Jacobi-Bellman equation. We proceed by decomposing the unknown solution on a Hermite polynomial basis (of the unknown volatility), whose different coefficients are solution to a system of non-linear PDEs of the same kind. Numerical tests show that computing the first basis elements may be enough to get an accurate approximation with respect to the uncertain volatility parameter. We experiment the methodology in the context of swing contract (energy contract with flexibility in purchasing energy power), this allows to introduce the concept of Uncertainty Value Adjustment (UVA), whose aim is to value the risk of misspecification of the volatility model.

Pricing and risk of swing contracts in natural gas markets

Motivated by the growing importance of swing contracts in natural gas markets, this article extends the literature on commodity price modelling as well as valuation methods and sensitivity analysis for swing options. While most previous studies focused on simple price models, we face the challenge of deriving option properties under more realistic commodity price dynamics. We begin by formulating a multi-factor price forward curve model with parametric volatility functions, which can capture uncertainty in both yearly seasonality and time-to-maturity effects, and propose a two-step calibration procedure to fit such models to empirical data. We then show how results from the literature can be combined to obtain swing option values and sensitivities in such a general framework. In this context, we also provide new theoretical results and a first numerical approach to efficiently estimate swing options’ gammas. For options’ deltas, we expand upon existing studies by including a larger variety of contract specifications and by focusing on a multidimensional variant of the Longstaff–Schwartz algorithm as an alternative option valuation method. With these contributions, we supply important tools for swing option sellers and buyers relying on accurate option value and risk estimates to maintain their business models, hedge option-related risks and adequately represent swing options in financial reporting.

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

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.

Semianalytical pricing and hedging of fixed and indexed energy swing contracts

Semianalytical pricing and hedging of fixed and indexed energy swing contracts

Swing Contracts With Dynamic Reserves for Flexible Service Management

The increasing penetration of variable energy resources in modern electric power systems requires additional flexibility in reserve provision to maintain reliable and efficient grid operations. However, full recognition and appropriate compensation of this flexibility is difficult to ensure within current power market designs due to rigidity in reserve definitions and requirements. This paper proposes a new mixed-integer linear programming formulation for the optimal clearing of a day-ahead market based on swing contracts with dynamically updated regulation reserve zones. Five-bus and 30-bus test cases are used to illustrate the effectiveness of the proposed new market design.

External VS. Internal Audit in the Accounting of Complex Contractual Instruments: A Survey on EU Firms

<p>This article aims at ascertain if external and independent audit can improve the reliability of IAS/IFRS financial statements with regard to the accounting of complex contractual instruments such as swing contracts for the sale and purchase of energy commodities. To this end, first of all the standard contents of the contracts at stake will be identified, based on those usually recurring in corporate practice. Then, it will be ascertained whether such contracts subtend an industrial usage only, so that the pertinent arrangement has to be accounted as a standard purchase/sale transaction, or whether the counterparts are pursuing financial intendments, since in such assumption the swing contract must be accounted as a financial instrument in accordance with IFRS 9/IAS 39. Conclusively, the modalities will be analysed which are used by a number of European companies whose typical activity is the purchase/sale of energy commodities, to account such kind of contracts. The survey aims at verify if the accounting modalities chosen by companies whose financial statements are subject to an external and independent audit (voluntarily or mandatorily pursuant to the applicable laws) are more compliant with the principle of faithful representation than those which are not subject to an external and independent audit.</p>

THE EVALUATION OF MULTIPLE YEAR GAS SALES AGREEMENT WITH REGIME SWITCHING

A typical gas sales agreement (GSA), 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 specified set of contract prices. The main constraint of such an agreement that makes them difficult to value is that in each gas year there is a minimum volume of gas (termed 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 for an underlying gas forward price curve that follows a regime switching process in order to better capture the volatility behavior in such markets. With the help of a recombining pentanomial tree, we are able to efficiently evaluate the prices of the swing contracts, find optimal daily decisions and optimal yearly use of both the make-up bank and the carry forward bank at different regimes. We also show how the change of regime will affect the decisions.

Modelling and Numerical Valuation of Power Derivatives in Energy Markets

In this work we investigate the pricing of swing options in a model where the underlying asset follows a jump diffusion process. We focus on the derivation of the partial integro-differential equation (PIDE) which will be applied to swing contracts and construct a novel pay-off function from a tree-based pay-off matrix that can be used as initial condition in the PIDE formulation. For valuing swing type derivatives we develop a theta implicit-explicit finite difference scheme to discretize the PIDE using a Gaussian quadrature method for the integral part. Based on known results for the classical theta-method the existence and uniqueness of solution to the new implicit-explicit finite difference method is proven. Various numerical examples illustrate the usability of the proposed method and allow us to analyse the sensitivity of swing options with respect to model parameters. In particular the effects of number of exercise rights, jump intensities and dividend yields will be investigated in depth. AMS subject classifications: 65M10, 91B25

Explicit approximations of multi-asset option prices including Greeks

In this article, we give a lower bound approximation to a stochastic programme that is typical for many complex financial derivatives, e.g., Bermudan options, Rainbow options and swing contracts. The approximation is based on an algorithm that does not require any simulation but uses a well-known spread option pricing formula. Since the method explicitly computes lower bounds for the claim’s value, sensitivities such as deltas and gammas are available as well as derivatives with respect to correlations and other inputs. Our resulting procedure is a powerful and practical tool for the pricing and risk analysis of exotic payoff structures. As such, it is useful in the day-to-day environment of financial institutions.

Optimal Exercise of Swing Contracts in Energy Markets: An Integral Constrained Stochastic Optimal Control Problem

We characterize the value of swing contracts in continuous time as the unique viscosity solution of a Hamilton--Jacobi--Bellman (HJB) equation with suitable boundary conditions. The case of contracts with penalties is straightforward, and in that case only a terminal condition is needed. Conversely, the case of contracts with strict constraints gives rise to a stochastic control problem with a nonstandard state constraint. We approach this problem by a penalty method: we consider a general constrained problem and approximate the value function with a sequence of value functions of appropriate unconstrained problems with a penalization term in the objective functional. Coming back to the case of swing contracts with strict constraints, we finally characterize the value function as the unique viscosity solution with polynomial growth of the HJB equation subject to appropriate boundary conditions.

Modelling and Numerical Valuation of Power Derivatives in Energy Markets

AbstractIn this work we investigate the pricing of swing options in a model where the underlying asset follows a jump diffusion process. We focus on the derivation of the partial integro-differential equation (PIDE) which will be applied to swing contracts and construct a novel pay-off function from a tree-based pay-off matrix that can be used as initial condition in the PIDE formulation. For valuing swing type derivatives we develop a theta implicit-explicit finite difference scheme to discretize the PIDE using a Gaussian quadrature method for the integral part. Based on known results for the classical theta-method the existence and uniqueness of solution to the new implicit-explicit finite difference method is proven. Various numerical examples illustrate the usability of the proposed method and allow us to analyse the sensitivity of swing options with respect to model parameters. In particular the effects of number of exercise rights, jump intensities and dividend yields will be investigated in depth.

Modeling and valuing make-up clauses in gas swing contracts

In the last 10years, 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.

Valuation of Swing Contracts by Least-Squares Monte Carlo Simulation

Summary Natural gas and electricity are commonly traded through swing contracts that enable the buyer to exploit changes in market price or market demand by varying the quantity they receive from the producer (seller). The producer is assured of selling a minimum quantity at a fixed price, but must be able to meet the variable demand from the buyer. The flexibility of such contracts enables both parties to mitigate the risks and exploit the opportunities that arise from uncertainty in production, demand, price, and so on. But how valuable are they? Traditional net present value (NPV), based on expected values, cannot value this flexibility, and the traditional options/valuation techniques could not model the complexity of the terms of such contracts. Taking gas contracts as an example, this paper seeks to (a) raise awareness of how flexibility creates value for both parties and (b) show how least-squares Monte Carlo (LSM) simulation can be used to quantify its value in dollar terms, from the perspective of both producer and buyer. Because the value of flexibility arises from the ability it gives to respond to fluctuations (e.g., in commodity prices), a useful model of swing contracts needs to reflect the nature of these fluctuations.