Energy and Power Risk
Modelling approaches in energy markets and the clean dark/spark spread
Master Thesis in "Mathematical Finance", Oxford (2011)
In this thesis, we give a review of different elements of modelling approaches in energy markets. On the basis of a clean dark and clean spark spread, we look in detail on the underlyings electricity, natural gas, coal and emission allowances. For each commodity, we present general aspects such as demand and supply structure, markets and financial instruments. With the knowledge of the fundamental particularities of each market, we provide a survey of the existing literature on different modelling approaches of commodities and discuss a suitable price process for each underlying with respect to clean dark/spark spread simulation. In case of emission allowances, we conduct a small empirical analysis, in order to find a suitable model for the second trading period. The processes are calibrated to market data and we examine the modelling framework by conducting a forecasting analysis for clean dark/spark spread and by comparing the results to alternative approaches. Our findings stress the importance of a well suited seasonal component and mean-reversion, but also show the difficulties arising by calibration complex models.
Valuation of Power Plants and Abatement Costs in Carbon Markets
Master Thesis in "Mathematical Finance", Oxford (2011)
Carbon markets are relatively new markets, which have been created by the introduction of tradable allowance certificates. A company must own a sufficient number of them in order to avoid being charged a penalty for its carbon dioxide emissions. This is meant to encourage companies to reduce carbon emissions, for example by investing in new technologies or by switching to different fuel sorts. The emission certificates will obviously also have an influence on the value of power plants, as electricity producers will not only have to buy the fuel but also emission certificates to cover the produced emissions.
The aim of the thesis will be to give a short introduction into the field of carbon markets and to model the allowance price by considering it as a derivative on the demand and on the total emissions to date. This will lead to a nonlinear PDE for the allowance price, the properties of which will be investigated. The gained knowledge will be used for a real options approach for the valuation of a power plant which takes into account the costs for the allowance certificates. The difference in value to the case, when no emission certificates are involved can be interpreted as the abatement costs for the emissions.
Modelling seasonal dependent jumps and pricing swing options in electricity markets
Master Thesis in "Mathematical Finance", Oxford (2010)
Since the deregulation of power markets, electricity is a tradable product. The electricity time series have special properties like seasonality, high volatility, mean-reversion and occurrence of spikes because power is a non storable good. Due to the uncertainty and volatility of electricity time series, there is a substantial need for risk management, and it is the forward and option market that is used for the risk transformation. The models describing the forward and option market are becoming more and more sophisticated but so far seasonal dependent spikes were not examined intensively. In this thesis, it is found that the probability of spikes in the Nordic market is higher in spring and summer and that the probability of spikes in the Dutch, German and UK markets is higher in summer and autumn. Furthermore, a model based on a nonhomogenous Poisson-process is proposed to model the seasonal dependent spikes and it is shown how the parameters can be estimated using maximum likelihood. The estimation errors are discussed. As an example of option pricing, the thesis finishes with results for a swing option under the assumption of the Ornstein-Uhlenbeck process.
Valuing power plants under emission reduction regulations and investing in new technologies: An exchange option on real options
Master Thesis in "Mathematical Finance", Oxford (2010)
In this dissertation we model the value of a power generation asset through a real option approach. With electricity, fuel and emission allowances we express every essential uncertainty on the energy market by an own stochastic process and derive an optimal clean spark spread. Typical operational constraints of a power plant are taken into account. Beside analysing the behaviour of the generation asset under different constraints, we want to evaluate the option to invest in new technologies to improve these constraints. In this dissertation, we do not set up the standard American option with strike equal to the investment as usual, but set up an exchange option on two real options with different constraints. We show that this approach handles an option on new technology much more sensitive to the individual price uncertainties and considers all possible employments. If the intrinsic value of the exchange option exceeds the realization costs, it is time to invest. We also state an explicit Monte Carlo algorithm and present numerical results for the option to install a Carbon Capture and Storage unit.
Market Dynamics and Derivative Instruments in the EU Emissions Trading Scheme
Master Thesis in "Mathematical Finance", Oxford (2009)
In January 2005, the European Emissions Trading System (EU-ETS) has formally entered into operation. Within the new trading system, the right to emit a particular amount ofCO2 - called EU Allowances (EUAs) - becomes a tradable commodity.
This thesis studies the development of markets for EU Allowances and illustrates the price development of EUAs in the spot and the futures market. The analysis show that the market suffered from regulatory restrictions in the early years, but from 2008 on emission certificates are traded with increasing liquidity and the market develops towards a mature state. The price development of EUAs is also analysed in comparison to other energy assets in order to examine dependencies and causalities. The results of statistic analysis prove that EUAs drive and are driven by the price development of other energy assets. Due to growing liquidity of EUAs and the impact on and from other energy assets, it becomes increasingly important for CO2 emitting companies as well as traders of the EUAs to have a valid spot and futures price models. Therefore, I discussed typical approaches of commodity spot and futures models regarding the adequacy for EUAs and studied the relationship between spot and futures prices in the EU-ETS in the the second phase of the EU-ETS.
Swing Options on Electricity Prices in a Jump-Diffusion Regime
Master Thesis in "Mathematical Finance", Oxford (2005)
Electricity trade at spot markets is a quite new subject of interest both for traders and research. As electricity is not storable such as other assets or commodities the underlying stochastic processes are more challenging to study and model. Furthermore, the valuation of derivatives on electricity prices is not as straightforward as in the case of assets. Still there is the need of the market participants for different types of derivatives hedging price and volume risk arising from sudden changes in the electricity prices. In this thesis two different stochastic price models are discussed in detail. The first one is the mean-reversion model of logarithmic prices and the other one is mean-reversion jump-diffusion model which is able to reproduce the price spikes often observed in electricity spot price data. For both models a parameter estimation is done based on the spot price data (2000-2004) from the European Energy Exchange (EEX). A statistical analysis of the EEX data is done and especially the sensitivity of the parameter estimation to periodicity, considered time range and sampling is discussed. For the jump-diffusion parameters which are more difficult to be retrieved two different methods are used: Recursive Filtering and Maximum Likelihood Estimation. Both methods are tested with the path generation routine which will be used later in the option valuation method.
Using these two different stochastic models swing options of different types (American call option, swing option with arbitrary number of up-swings and down-swings) are valuated using Monte Carlo simulations based on the Longstaff-Schwartz least-squares algorithm. The impact of both models in comparison to standard geometric Brownian motion is investigated in detail. In addition, different penalty functions and their impact on the resulting option price are tested for the different price models. Furthermore, simple test runs with Markov-switching jump-diffusion are performed and the resulting option prices discussed. Finally the early exercise boundaries for different up-swings are discussed shortly considering the impact of jumps.
Modeling and Risk Measuring of Electricity Spot Prices
Master Thesis in "Mathematical Finance", Oxford (2004)
Valuation of Energy Derivatives with Monte Carlo Methods
Master Thesis in "Mathematical Finance", Oxford (2004)
In this thesis two pricing models for energy derivatives are discussed. One is a standard mean reverting process of the logarithmic prices. The other is a model proposed by Barlow which exhibits the feature of price spikes. Both models are fitted to spot price data from the European Energy Exchange (EEX) in Leipzig, Germany.
Non-Gaussian Price Dynamics in Energy Markets
Master Thesis in "Mathematical Finance", Oxford (2004)
In standard finance theory it is often assumed that random changes of the value of a risky asset are independent of each other and normally distributed (Gaussian). However, empirical evidence reveals that particularly the tails of the distribution of returns are significantly non-Gaussian. Furthermore, correlations between returns exist. Both findings have strong implications for derivative pricing, hedging strategies and other applications of the theory. In this study, statistical analysis techniques probing the validity of the Gaussian assumption have been applied to electricity markets, in particular prices from the Nordic Power Exchange, one of the longest running power markets, have been studied. Electricity is a non-storable flow-commodity and transmission between distant areas is expensive. Therefore, the evolution of its price depends much on the regional balance between demand and supply leading to predictable patterns on different time scales. In order to extract the random component of the price, the seasonality component has been quantified and separated from the available time series first. The existence of mean reversion around the predictable pattern has been confirmed and accounted for. It turns out that the residual non-deterministic component is significantly non-Gaussian. The second part of the thesis deals with the pricing of derivatives tradable at the Nordpool financial markets. As a consequence of the non-Gaussian nature of the electricity prices the approach of Bouchaud and Sornette to the pricing and hedging of derivative securities has been chosen because it does not assume a particular underlying distribution or price model. After extending the method to incorporate seasonality and mean reversion it has been applied to calculate the prices of electricity power derivatives. In particular, a seasonal forward contract and European power options have been considered and good agreement to quoted prices has been found. Therefore, the applicability of the extended Bouchaud and Sornette approach to the electricity markets has been confirmed.
Valuation of Swing Options and Examination of Exercise Strategies by Monte Carlo Techniques
Master Thesis in "Mathematical Finance", Oxford (2003)
Monte–Carlo simulation techniques are used to investigate (standardized)
Swing options. In a first approach, this is done by an algorithm which
is based on the Longstaff Schwartz method for American and Bermudan
options. This algorithm yields the value of the Swing option under the
assumption that the optimal exercise strategy is applied. Furthermore the
optimal strategy can be extracted from the algorithm. Various examples
including Swing options with upswings, downswings and penalties are
valued numerically, and an upper boundary for Swing options is found
in the computer experiment. In a second approach, the exercise strategy
is used as input parameter and the expected payoff with respect to this
strategy is calculated by strictly forward evolving Monte Carlo. For these
simualtions, a one factor log–normal mean–reverting process is used to
desribe the behaviour of the underlying spot price. The success of several
sample strategies is discussed in terms of process properties like mean–
reversion speed and volatility.
Swing Options in Electricity Markets
Master Thesis in "Mathematical Finance", Oxford (2003)
Usual retail contracts permit consumers to vary the quantity of power they can receive.
This thesis deals with the question if and under what circumstances power
can be sold cheaper in case consumers dispense with this volumetric (or swing) optionality.
After introducing the mathematical framework we investigate the optimal
exercise behavior for a particular swing option. Then we introduce a mean reverting
stochastic process for the electricity spot price and calibrate it to market data. A
contract, where the customer cannot decide when to turn on his electronic device, is
by far not suitable in all circumstances. Therefore we present two situations where
such a contract is feasible: the case of an owner of an electric car who is indifferent
when his car is charged and the heating of water during the day. The situations are
modeled and the resulting fixed electricity price is compared to the price the distributor
could offer if the relevant electronic device would always be turned on at the
same time.
Swing Options and Seasonality of Power Prices
Master Thesis in "Mathematical Finance", Oxford (2002)
A log-normal mean-reverting diffusion model with time-dependent parameters,
i. e. equilibrium level as well as volatility, is used to describe the stochastic
process followed by electricity prices. One focus of the thesis is the effects
of seasonality in the electricity market. These effects are an immediate consequence
of the fact that electricity is hard to store. The model parameters are
calibrated to market data from the European Electricity Exchange in Leipzig
(Germany).
The resulting process is then used as the starting point for a Black-Scholes-like
derivation of a valuation model to price derivative securities. The model will
then be applied to swing contracts. These contracts represent a very flexible
kind of options that can even be endowed with contractual penalties. Here,
different penalty functions are studied within a finite-difference approximation
scheme
Risk Measurement in the Electricity Market
Diploma Thesis in "Mathematical Finance", Oxford (2000)
Electricity trading has been rapidly growing in Europe since more and more markets are being deregulated. As it has been accepted in the financial markets for a long time, the risks of these trading activities have to be managed appropriately. However, it is difficult to transfer methods from the financial sector to the energy industry. Though, spectacular million dollar losses in the US electricity trading market have shown the necessity for a thorough controlling of risks. Risks in electricity trading are very complex and multi-dimensional: market risks, credit risks, and operational risks. This study concentrates on one dimension: the market risk of electricity spot prices. Mainly, daily data from 1996 to 2000 from the largest exchange in Europe, the Scandinavian Nord Pool, is used. The project consists of two parts: In the first part, the time series are analysed graphically and the properties of power prices are determined. These properties can be very different from financial time series: Prices are much more volatile, exhibit frequent spikes, are strongly mean-reverting, and show predictable patterns. These properties are explained by the non-storability of electricity and by the characteristics of demand and supply. In the second part of this project, different measurement methods that are known from the financial sector are applied to electricity time series. We show that this transfer is difficult and only partially successful. Because of the special properties of power prices, the price returns have fat tails and are not independently and identically distributed. Therefore, the model of normally distributed returns as applied in the financial markets, e.g., in the RiskMetrics„· market risk methodology, fails to give a satisfactory risk estimation. Furthermore, a jump diffusion model and historical simulations are studied. Their ability to describe the distribution of returns is better than for the ¡§normal¡¨ model, but their backtesting results for high quantiles are still insufficient. Finally, the last method studied is the Extreme Value Theory that models only the tails of the return distribution. This method provides the best results in out-of-sample tests.
