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Managing Energy Risk: An Integrated View on Power and Other Energy Markets


Managing energy risk is a practical guide to using modern techniques in financial mathematics for trading energy.

Taking a multi-commodity view on the energy markets, addressing electricity, oil, gas, coal and CO2 emissions and explaining their fundamental relations, this book is a comprehensive overview of the energy markets and their products explaining models for pricing, portfolio optimization, risk measurement and market analysis.

By integrating energy economics approaches, including fundamental market models, with financial engineering approaches commonly used in banks and other trading companies, Managing Energy Risk is valuable resource, relevant for risk management, structuring, pricing, market analysis, and model development.

Markus Burger is Head of Risk Control at EnBW Trading GmbH, the trading unit of the third largest energy supply company in Germany. He leads the market risk measurement ream with responsibility for valuation and stochastic modelling as well as credit risk management. Previously, he was a analyst for interest rate derivatives at Landesbank Baden-Wurttemberg (LBBW). He holds a Masters degree and a PhD in mathematics from the University of Karlsruhe, Germany. His practical involvement and research includes stochastic modeling, risk measurement and valuation in the energy sector.

Bernhard Graeber is Head of Methodology and Models at EnBW Trading GmbH. His department is responsible for the development of load forecasting algorithms, of power plant dispatch models and of fundamental market models for electricity, CO2 certificates and fuels. He studies mechanical engineering and physics at the University of Stuttgart, Germany and at the University of Auckland, New Zealand and holds a PhD in energy economics from the University of Stuttgart. he has more that 10 years of experience in electricity market analysis and modeling.

Gero Schindlmayr is Head of Market Risk and Valuation Models at EnBW Trading GmbH. before joining EnBW he worked as a quantitative analyst for equity derivatives at Deutsche Bank A.G. He holds a PhD in mathematics and a Master's degree in operations research from the RWTH Aachen, Germany and an M.Sc degree in mathematics from Warwick University, UK. He is co-author of a book titled Equity Derivatives: Theory and Applications and of several papers in the area of energy derivatives and energy risk. His main field of work includes stochastic pricing models for electricity and gas, commodity forward curve modeling, value-at-risk models and multi-commodity risk.



1 Energy Markets.

1.1 The oil market.

1.1.1 Consumption, production and reserves.

1.1.2 Crude oil trading.

1.1.3 Refined oil products.

1.2 The natural gas market.

1.2.1 Consumption, production and reserves.

1.2.2 Natural gas trading.

1.2.3 Price formulas with oil indexation.

1.2.4 Liquefied natural gas.

1.3 The coal market.

1.3.1 Consumption, production and reserves.

1.3.2 Coal trading.

1.3.3 Freight.

1.3.4 Coal subsidies in Germany: BAFA-indexed prices.

1.4 The electricity market.

1.4.1 Consumption and production.

1.4.2 Electricity trading.

1.4.3 Products in the electricity markets.

1.4.4 Energy exchanges.

1.5 The emissions market.

1.5.1 Kyoto Protocol.

1.5.2 EU emissions trading scheme.

1.5.3 Flexible mechanisms.

1.5.4 Products and market places.

1.5.5 Emissions trading in North America.

2 Energy Derivatives.

2.1 Forwards, futures and swaps.

2.1.1 Forward contracts.

2.1.2 Futures contracts.

2.1.3 Swaps.

2.2 “Plain vanilla” options.

2.2.1 The put–call parity and option strategies.

2.2.2 Black’s futures price model.

2.2.3 Option pricing formulas.

2.2.4 Hedging options: the “Greeks”.

2.2.5 Implied volatilities and the “volatility smile”.

2.2.6 Swaptions.

2.3 American and Asian options.

2.3.1 American options.

2.3.2 Asian options.

2.4 Commodity bonds and loans.

2.5 Multi-underlying options.

2.5.1 Basket options.

2.5.2 Spread options.

2.5.3 Quanto and composite options.

2.6 Spot price options.

2.6.1 Pricing spot price options.

2.6.2 Caps and floors.

2.6.3 Swing options.

2.6.4 Virtual storage.

3 Commodity Price Models.

3.1 Forward curves and the market price of risk.

3.1.1 Investment assets.

3.1.2 Consumption assets and convenience yield.

3.1.3 Contango, backwardation and seasonality.

3.1.4 The market price of risk.

3.1.5 Derivatives pricing and the risk-neutral measure.

3.2 Commodity spot price models.

3.2.1 Geometric Brownian motion.

3.2.2 The one-factor Schwartz model.

3.2.3 The Schwartz–Smith model.

3.3 Stochastic forward curve models.

3.3.1 One-factor forward curve models.

3.3.2 A two-factor forward curve model.

3.3.3 A multi-factor exponential model.

3.4 Electricity price models.

3.4.1 The hourly forward curve.

3.4.2 The SMaPS model.

3.4.3 Regime-switching model.

3.5 Multi-commodity models.

3.5.1 Regression analysis.

3.5.2 Correlation analysis.

3.5.3 Cointegration.

3.5.4 Model building.

4 Fundamental Market Models.

4.1 Fundamental price drivers in electricity markets.

4.1.1 Demand side.

4.1.2 Supply side.

4.1.3 Interconnections.

4.2 Economic power plant dispatch.

4.2.1 Thermal power plants.

4.2.2 Hydro power plants.

4.2.3 Optimisation methods.

4.3 Methodological approaches.

4.3.1 Merit order curve.

4.3.2 Optimisation models.

4.3.3 System dynamics.

4.3.4 Game theory.

4.4 Relevant system information for electricity market modelling.

4.4.1 Demand side.

4.4.2 Supply side.

4.4.3 Transmission system.

4.4.4 Historical data for backtesting.

4.4.5 Information sources.

4.5 Application of electricity market models.

4.6 Gas market models.

4.6.1 Demand side.

4.6.2 Supply side.

4.6.3 Transport.

4.6.4 Storage.

4.6.5 Portfolio optimisation.

4.6.6 Formulation of the market model.

4.6.7 Application of gas market models.

4.7 Market models for oil, coal, and CO2 markets.

5 Electricity Retail Products.

5.1 Interaction of wholesale and retail markets.

5.2 Retail products.

5.2.1 Common full service contracts.

5.2.2 Indexed contracts.

5.2.3 Partial delivery contracts.

5.2.4 Portfolio management.

5.2.5 Supplementary products.

5.3 Sourcing.

5.3.1 Business-to-business (B2B).

5.3.2 Business-to-consumer (B2C).

5.3.3 Small accounts.

5.3.4 Municipalities and reseller.

5.4 Load forecasting.

5.5 Risk premium.

5.5.1 Price validity period.

5.5.2 Balancing power.

5.5.3 Credit risk.

5.5.4 Price–volume correlation.

5.5.5 Strict risk premiums.

5.5.6 Hourly price profile risk.

5.5.7 Volume risk.

5.5.8 Operational risk.

5.5.9 Risk premium summary.

6 Risk Management.

6.1 Market price exposure.

6.1.1 Delta position.

6.1.2 Variance minimising hedging.

6.2 Value-at-Risk and further risk measures.

6.2.1 Definition of Value-at-Risk.

6.2.2 Parameters of the Value-at-Risk measure.

6.2.3 Computation methods.

6.2.4 Liquidity-adjusted Value-at-Risk.

6.2.5 Estimating volatilities and correlations.

6.2.6 Backtesting.

6.2.7 Further risk measures.

6.3 Credit risk.

6.3.1 Legal risk.

6.3.2 Quantifying credit risk.

6.3.3 Credit rating.


A Mathematical background.

A.1 Econometric methods.

A.1.1 Linear regression.

A.1.2 Stationary time series and unit root tests.

A.1.3 Principal component analysis.

A.1.4 Kalman filtering method.

A.1.5 Regime-switching models.

A.2 Stochastic processes.

A.2.1 Conditional expectation and martingales.

A.2.2 Brownian motion.

A.2.3 Stochastic integration and Itô’s lemma.

A.2.4 The Feynman–Kac theorem.

A.2.5 Monte Carlo simulation.