Optimization Methods for Gas and Power Markets

Enrico Edoli is Founder and CEO of Phinergy, a consulting firm which produces analytics and quantitative tools for energy trading and risk management. He has published several technical articles and a book related to quantitative energy finance. He is also Lecturer of a course in Mathematical Finance at the University of Padova. Enrico has a degree in Mathematics from the University of Padova, Italy and a PhD in Applied Mathematics from the same university.Stefano Fiorenzani is a recognized expert in Energy Trading and Risk Management, with a career spanning numerous top European energy companies and financial institutions. He has published several scientific and business articles and three books on advanced methods in the energy finance area. Stefano is Founder and Chairman of Phinergy. He holds a degree in Economic Science, a Master of Science in Financial Economics and a PhD in Mathematical Finance.Tiziano Vargiolu is Associate Professor of Probability and Statistics at the Department of Mathematics of the University of Padua, Italy, since 1998. There, he has taught courses on Probability, Statistics and Quantitative Finance at undergraduate, master's and PhD level, and directed PhD and master's theses in Financial Mathematics. His research interests span a wide range of topics including stochastic optimal control, pricing of contingent claims, portfolio optimization, interest rates models, credit risk and energy markets.

Energy markets are extremely competitive markets. Optimization of business decisions is fundamental for performance maximization. This book represents an excellent synthesis of optimization theory and practice applied to a wide and significant range of cutting-edge business problems characterizing power and natural gas markets.' - Domenico De Luca, CEO, Axpo Trading and Member of Executive Board Axpo Group 'Optimization methods play an important role when making decisions and managing risk in today's liberalized energy markets. When planning a power plant or entering a structured gas contract, stochastic control is the key mathematical tool to assess the inherent risk. The authors of this book present an excellent account of the problems and methods for optimization in energy and power markets. The scope ranges from a rigorous theoretical analysis of the control problems, through numerical methods and to in-depth discussions of relevant practical case studies. This book is unique in providing a solid mathematical analysis of various optimization problems, yet never losing the market practice out of sight. It will be an invaluable reference for both academics and practitioners in power and gas markets.' - Fred Espen Benth, Professor of Mathematical Finance at the University of Oslo, Department of Mathematics and Deputy Manager

• 1. Optimization in Energy Markets 1.1 Classification of optimization problems1.1.1 Linear versus Nonlinear Problems 1.1.2 Deterministic versus Stochastic Problems 1.1.3 Static versus Dynamic Problems1.2 Optimal portfolio selection among different investment alternatives1.3 Energy Asset Optimization 1.3.1 Generation Asset Investment Valuation with Real Option Methodology 1.3.2 Generation, Transportation and Storage Asset Operational Optimization and Valuation 1.4 Energy Trading and Optimization 1.4.1 Asset allocation with Capital Constraints 1.4.2 Intraday trading 2. Optimization Methods2.1 Linear Optimization2.1.1 LP problems2.2 Nonlinear Optimization2.2.1 Unconstrained problem2.2.2 Constrained Problems with Equality Constraints2.2.3 Constrained Problems with Inequalities Constraints2.3 Pricing financial assets2.3.1 Pricing in energy markets2.3.2 Pricing in incomplete markets2.3.3 A motivating example: utility indifference pricing2.4 Deterministic Dynamic Programming2.5 Stochastic Dynamic Programming, discrete time2.5.1 A motivating example2.5.2 The general case2.5.3 Tree methods2.5.4 Least Square Monte Carlo methods2.5.5 Naïve Monte Carlo with Linear Programming2.6 Stochastic Dynamic Programming, continuous time2.6.1 The Hamilton-Jacobi-Bellman equation2.7 Deterministic numerical methods2.7.1 Finite Difference Method for HJB equation2.7.2Boundary conditions2.8 Probabilistic numerical methods2.8.1 Tree methods, continuous time2.8.2 Computationally simple trees in dimension 12.8.3 Lattice of trees2.8.4 Monte Carlo methods3. Cases on Static Optimization3.1 Case A: investment alternatives3.2 Case B: Optimal generation mix for an electricity producer: a mean-variance approach3.3 Conclusions 4. Valuing project's exibilities using the diagrammatic approach4.1 Introduction4.2 Description of the Investment Problem4.3 Traditional evaluation Methods4.4 Modelling Electricity Price Dynamics4.5 Valuing Investment Flexibilities By Means Of The Lattice Approach4.5.1 Investment alternative A4.5.2 Investment alternative B4.5.3 Investment alternative C4.6 Conclusions5. Virtual Power Plant Contracts5.1 Introduction5.2 Valuation Problem5.2.1 Example6. Algorithms comparisonThe Swing Case6.1 Introduction6.2 Swing contracts6.2.1 Indexed strike price modelling for gas swing contracts6.2.2 The stochastic control problem6.2.3 Dynamic Programming6.3 Finite difference algorithm6.3.1 Boundary conditions6.3.2 The algorithm6.4 Least Square Monte Carlo algorithm6.4.1 The algorithm, and a reduction to one dimension6.5 Naïve Monte Carlo with Linear Programming6.6 Numerical Experiments6.6.1 Finite differences6.6.2 Least Square Monte Carlo6.6.3 One year contract6.7 Conclusions7.Storage contracts7.1 The contract7.2 The evaluation problem7.3 The optimal strategy (in the case of a physical gas storage)7.4 The implementation7.4.1 The gas cave7.4.2 The gas spot price7.4.3 The boundary conditions7.4.4 Numerical experiment, no-penalty case7.4.5 Numerical experiment, penalty case8. Optimal Trading Strategies in Intraday Power Markets8.1 Intraday power markets8.1.1 Intraday power price features8.1.2 Conclusions8.2 Optimal Algorithmic Trading in Auction-Based Intraday Power Markets8.2.1 The optimization problem8.2.2 Example: Italian intra-day market8.3 Optimal Algorithmic Trading in Continuous Time Power Markets8.3.1 The optimization problem8.3.2 Example: EPEX Spot market