Seasonally Modulated Regime Switching Models and their Application to Electricity Spot Prices and Wind Power Generation

Master Thesis in "Mathematical Finance", Oxford (2017)


In this work we investigate the application of regime switching models to electricity spot prices and wind power generation. Our modelling approach incorporates seasonally modulated transition probabilities for the regime switch. We investigate four sub-processes as candidates for the respective regimes: a normal, a log-normal, a generalized CIR, and a Weibull processes. To fit model parameters we use the Expectation Maximisation algorithm. We present benchmark analyses of the fitting algorithm to underscore its performance. Application of the modelling approach and fitting algorithm to electricity spot price data shows small significance of seasonality, while we observe strong signs of cyclical behaviour in wind power generation.



A Monte Carlo Analysis of Financial Contracts for Renewable Trading

Master Thesis in "Mathematical Finance", Oxford (2017)



Wavelet-based time series filtering and smoothing in electricity markets

Master Thesis in "Mathematical Finance", Oxford (2016)



In this thesis, we discuss two applications for wavelet techniques in the analysis of price time series in electricity markets:

The first one is a technique based on the continuous wavelet transformation (CWT) for identifying and eliminating fluctuations at certain scales from price time series. With our method, which we apply to price time series of Australian electricity markets, we are able to identify a number of activities at certain scales, reaching from intraday fluctuations up to patterns of one week. Using our technique, we successfully remove one of these fluctuations by eliminating the corresponding wavelet coefficients. We also compare our technique with standard fitting methods for eliminating periodicities and show that our approach is superior. It allows for a much better elimination of the fluctuations and even makes it possible to remove oscillations only locally in certain regions of the time series.

As a second topic, we apply wavelet methods in order to construct smooth, continuous forward curves from market data. By combining two central ingredients, the multi-resolution analysis (MRA) and the so-called Besov norm, we are able to develop an expression for forward curves in terms of wavelet coefficients and formulate a quadratic programming problem in order to obtain a forward curve that is as smooth as possible. The great advantage of this approach in comparison to other spline techniques is, that with the help of the MRA, the obtained wavelet coefficients become smaller and smaller when going to finer scales and thus become negligible at a certain point. Some of these coefficients are even exactly equal to zero, leading to a sparse representation of the forward curve. We investigate this technique using different types of wavelets and explore a number of possible improvement schemes.


Modelling of electricity future prices by use of a Levy Multifactor Market Model and Independent Component Analysis

Master Thesis in "Mathematical Finance", Oxford (2015)


Valuation in Incomplete Energy Markets - A closer look on the optimization and hedging of physical assets and trading strategies

Master Thesis in "Quantitative Finance", Frankfurt School of Finance & Management (2014)


Valuation and Hedging of Gas Storage Facilities 

Master Thesis in "Mathematical Finance", Oxford (2012)


Natural gas storage facilities allow their operators to profit from seasonal price spreads. Furthermore, the option to store natural gas can be monetised by actively trading in the spot and futures markets if profitable opportunities arise. Gas storage facilities are priced as a real options using risk neutral valuation techniques. The valuation of a storage facility is a challenging task due to the complex dynamics driving the price processes of natural gas futures. Practitioners therefore revert to heuristics to solve the dynamic stochastic programming problem in order to derive optimal trading strategies. The Monte Carlo simulation based rolling intrinsic valuation is a heuristic known to produce near-optimal valuation results. It captures the static intrinsic value as well as the majority of the extrinsic value stemming from the inherent optionality of the storage facility. Merchant traders operating a storage facility are exposed to the high volatilities of natural gas markets. In order to implement efficient risk mitigation strategies, accurate sensitivities with respect to the main risk drivers have to be computed. In this thesis we propose two methods for calculating these so-called Greeks—pathwise differentiation and the likelihood ratio method. Both approaches are commonly used for the calculation of sensitivities in a simulation based framework for financial derivatives, but they can also be applied to compute hedge parameters for the real option embedded in a storage facility.


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.