Multistage Stochastic Portfolio Optimisation in Deregulated Electricity Markets Using Linear Decision Rules

The deregulation of electricity markets increases the financial risk faced by retailers who procure electric energy on the spot market to meet their customers’ electricity demand. To hedge against this exposure, retailers often hold a portfolio of electricity derivative contracts. In this paper, we propose a multistage stochastic mean-variance optimisation model for the management of such a portfolio. To reduce computational complexity, we perform two approximations: stage-aggregation and linear decision rules (LDR). The LDR approach consists of restricting the set of decision rules to those affine in the history of the random parameters. When applied to mean-variance optimisation models, it leads to convex quadratic programs. Since their size grows typically only polynomially with the number of periods, they can be efficiently solved. Our numerical experiments illustrate the value of adaptivity inherent in the LDR method and its potential for enabling scalability to problems with many periods.OR in energy, electricity portfolio management, stochastic programming, risk management, linear decision rules

Liquidity risks on power exchanges

Financial derivatives are important hedging tool for asset’s manager. Electricity is by its very nature the most volatile commodity, which creates big incentive to share the risk among the market participants through financial contracts. But, even if volume of derivatives contracts traded on Power Exchanges has been growing since the beginning of the restructuring of the sector, electricity markets continue to be considerably less liquid than other commodities. This paper tries to quantify the effect of this insufficient liquidity on power exchange, by introducing a pricing equilibrium model for power derivatives where agents can not hedge up to their desired level. Mathematically, the problem is a two stage stochastic Generalized Nash Equilibrium and its solution is not unique. Computing a large panel of solutions, we show how the risk premium and player’s profit are affected by the illiquidity.illiquidity, electricity, power exchange, artitrage, generalized Nash Equilibrium, equilibrium based model, coherent risk valuation

The valuation of power futures based on optimal dispatch

The pricing of contingent claims in the wholesale power market is a controversial topic. Important challenges come from the non-storability of electricity and the number of parameters that impact the market. We propose an equilibrium model based on the fundamentals of power generation. In a perfect competitive market, spot electricity prices are determined by the marginal cost of producing the last unit of power. Electricity can be viewed as a derivative of demand, fuels prices and carbon emission price. We extend the Pirrong-Jermakayan model such as to incorporate the main factors driving the marginal cost and the non-linearities of electricity prices with respect to fuels prices. As in the Pirrong-Jermakayan framework, any contingent claims on power must satisfy a high dimensional PDE that embeds a market price of risk, as load is not a traded asset. Analyzing the specificity of the marginal cost in power market, we simplify the problem for evaluating power futures so that it becomes computationally tractable. We test our model on the German EEX for "German Month Futures" with maturity of June and September 2008.power contingent claims, PDE valuation of financial derivatives, unit commitment, market price of risk, EEX

Optimisation of electricity energy markets and assessment of CO2 trading on their structure : a stochastic analysis of the greek power sector

Power production was traditionally dominated by monopolies. After a long period of research and organisational advances in international level, electricity markets have been deregulated allowing customers to choose their provider and new producers to compete the former Public Power Companies. Vast changes have been made in the European legal framework but still, the experience gathered is not sufficient to derive safe conclusions regarding the efficiency and reliability of deregulation. Furthermore, emissions' trading progressively becomes a reality in many respects, compliance with Kyoto protocol's targets is a necessity, and stability of the national grid's operation is a constraint of vital importance. Consequently, the production of electricity should not rely solely in conventional energy sources neither in renewable ones but on a mixed structure. Finding this optimal mix is the primary objective of the study. A computational tool has been created, that simulates and optimises the future electricity generation structure based on existing as well as on emerging technologies. The results focus on the Greek Power Sector and indicate a gradual decreasing of anticipated CO2 emissions while the socioeconomic constraints and reliability requirements of the system are met. Policy interventions are pointed out based on the numerical results of the model. (C) 2010 Elsevier Ltd. All rights reserved

A stochastic predictive control approach to project risk management

This work shows a control policy based on MPC and applied to project risk management. MPC has been applied due the properties that presents such as the easy constraint treatment or the extension to multivariable case. The control actions are the mitigation actions to execute in order to reduce the risk exposure. Stochastic variables have been introduced to model the uncertainties of risk impacts. Integer variables are involved in the optimization problem modelling the mitigation actions

Utility indifference pricing and hedging for structured contracts in energy markets

In this paper we study the pricing and hedging of structured products in energy markets, such as swing and virtual gas storage, using the exponential utility indifference pricing approach in a general incomplete multivariate market model driven by finitely many stochastic factors. The buyer of such contracts is allowed to trade in the forward market in order to hedge the risk of his position. We fully characterize the buyer's utility indifference price of a given product in terms of continuous viscosity solutions of suitable nonlinear PDEs. This gives a way to identify reasonable candidates for the optimal exercise strategy for the structured product as well as for the corresponding hedging strategy. Moreover, in a model with two correlated assets, one traded and one nontraded, we obtain a representation of the price as the value function of an auxiliary simpler optimization problem under a risk neutral probability, that can be viewed as a perturbation of the minimal entropy martingale measure. Finally, numerical results are provided.Comment: 32 pages, 5 figure

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 are 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 behaviour in such markets. With the help of a recombing pentanonial tree, we are able to efficiently evaluate the prices of the swing contracts, find optimal daily decisions and optimaly early 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.gas sales agreement; swing contract; take-or-pay; make-up; carry forward; forward price curve; regime switching volatility; recombing pentanomial tree

Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008