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.

1. Optimization in Energy Markets
1.1 Classification of optimization problems
1.1.1 Linear versus Nonlinear Problems
1.1.2 Deterministic versus Stochastic Problems
1.1.3 Static versus Dynamic Problems
1.2 Optimal portfolio selection among different investment alternatives
1.3 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 Methods
2.1 Linear Optimization
2.1.1 LP problems
2.2 Nonlinear Optimization
2.2.1 Unconstrained problem
2.2.2 Constrained Problems with Equality Constraints
2.2.3 Constrained Problems with Inequalities Constraints
2.3 Pricing financial assets
2.3.1 Pricing in energy markets
2.3.2 Pricing in incomplete markets
2.3.3 A motivating example: utility indifference pricing
2.4 Deterministic Dynamic Programming
2.5 Stochastic Dynamic Programming, discrete time
2.5.1 A motivating example
2.5.2 The general case
2.5.3 Tree methods
2.5.4 Least Square Monte Carlo methods
2.5.5 Naïve Monte Carlo with Linear Programming
2.6 Stochastic Dynamic Programming, continuous time
2.6.1 The Hamilton-Jacobi-Bellman equation
2.7 Deterministic numerical methods
2.7.1 Finite Difference Method for HJB equation
2.7.2Boundary conditions
2.8 Probabilistic numerical methods
2.8.1 Tree methods, continuous time
2.8.2 Computationally simple trees in dimension 1
2.8.3 Lattice of trees
2.8.4 Monte Carlo methods
3. Cases on Static Optimization
3.1 Case A: investment alternatives
3.2 Case B: Optimal generation mix for an electricity producer: a mean-variance approach
3.3 Conclusions
4. Valuing project's exibilities using the diagrammatic approach
4.1 Introduction
4.2 Description of the Investment Problem
4.3 Traditional evaluation Methods
4.4 Modelling Electricity Price Dynamics
4.5 Valuing Investment Flexibilities By Means Of The Lattice Approach
4.5.1 Investment alternative A
4.5.2 Investment alternative B
4.5.3 Investment alternative C
4.6 Conclusions
5. Virtual Power Plant Contracts
5.1 Introduction
5.2 Valuation Problem
5.2.1 Example
6. Algorithms comparison
The Swing Case
6.1 Introduction
6.2 Swing contracts
6.2.1 Indexed strike price modelling for gas swing contracts
6.2.2 The stochastic control problem
6.2.3 Dynamic Programming
6.3 Finite difference algorithm
6.3.1 Boundary conditions
6.3.2 The algorithm
6.4 Least Square Monte Carlo algorithm
6.4.1 The algorithm, and a reduction to one dimension
6.5 Naïve Monte Carlo with Linear Programming
6.6 Numerical Experiments
6.6.1 Finite differences
6.6.2 Least Square Monte Carlo
6.6.3 One year contract
6.7 Conclusions
7.Storage contracts
7.1 The contract
7.2 The evaluation problem
7.3 The optimal strategy (in the case of a physical gas storage)
7.4 The implementation
7.4.1 The gas cave
7.4.2 The gas spot price
7.4.3 The boundary conditions
7.4.4 Numerical experiment, no-penalty case
7.4.5 Numerical experiment, penalty case
8. Optimal Trading Strategies in Intraday Power Markets
8.1 Intraday power markets
8.1.1 Intraday power price features
8.1.2 Conclusions
8.2 Optimal Algorithmic Trading in Auction-Based Intraday Power Markets
8.2.1 The optimization problem
8.2.2 Example: Italian intra-day market
8.3 Optimal Algorithmic Trading in Continuous Time Power Markets
8.3.1 The optimization problem
8.3.2 Example: EPEX Spot market