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University of Oxford Kellogg College Master of Science in Mathematical Finance Valuing power plants under emission reduction regulations and investing in new technologies: An exchange option on real options d-fine GmbH1 Supervisor: Professor Sam Howison2 April 2010 1d-fine GmbH, Opernplatz 2, 60313 Frankfurt, Germany (info@d-fine.de) 2University of Oxford, Mathematical Institute, [email protected] Abstract 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. 1 Contents 1 Introduction 2 2 Modelling power plants 5 2.1 The clean spark spread . 5 2.2 Energy markets . 6 2.2.1 Electricity prices . 6 2.2.2 Fuel prices . 8 2.2.3 Emission allowance prices . 11 2.2.4 Correlations . 14 2.3 Operational constraints . 14 2.3.1 Heat rate, emission rate and optimal generation level . 15 2.3.2 Ramp rates and start up costs . 16 2.3.3 Minimum up time, minimum down time and cold time . 17 2.3.4 Variable operational and maintenance costs . 18 2.3.5 Forced and scheduled outages . 18 3 A Real option approach for valuing power plants 20 3.1 The real option approach . 20 3.2 Real option valuation using dynamic programming . 20 3.2.1 Backward induction . 20 3.2.2 Least squares Monte Carlo . 22 4 Implementation aspects 26 4.1 Monte Carlo simulation . 26 4.2 Parameter calibration . 27 4.2.1 Electricity prices . 27 4.2.2 Fuel prices . 27 4.2.3 Emission allowance prices . 29 4.2.4 Correlations . 30 4.3 The algorithm . 32 4.4 Example valuations . 33 5 Investing in new technologies 37 5.1 An American style exchange option on real options . 37 5.2 Analytical valuation of American options . 38 5.3 Numeric valuation . 39 5.4 Examples . 40 6 Conclusions 44 2 1 Introduction The world demand for energy is constantly rising. Nowadays, especially for new emerging economies like India, China and Brazil, energy is the basis for economic growth and wealth. In contrast, it is well known that the fossil energy sources on earth are limited and the accessible coal stocks, oil and gas sources will last for few more decades only. Additionally, pollution and global climate change becomes a big issue around the world with the power industry as the biggest pol- luter. Do these aspects put fuel-fired power plants to the stack of old technologies? A first argument against this hypothesis is, that by 2015 a generation of nuclear power plants in European nations will have to be shut down because they are becoming old and unsafe3 and no new ones could be build well-timed for years after that4. Secondly, alternative resources like Uranium will last for 83 years at the current rate of consumption5. This is shorter than other fossil energy resource like coal with its current reserves-to-production ratio of 137 years according to IEO20096. Thirdly, renewables are not reliable and even the latest technology im- provements are far away from generating the needed huge amount of electricity. And last but not least, there are several technology improvements in efficiency, flexibility and emission reduction for coal and gas power plants. Thus, the major part of electricity produced worldwide currently comes and will come from fuel- driven power plants for the next decades, which makes them a desirable object for investors. For example, in the IEO2009 reference case, world coal consumption increases by 49% from 2006 to 2030. For an investment in existing or new physical assets it is necessary to evaluate the proper value of the object. In this thesis we want to estimate the value of fuel driven power plants as electricity generation assets which consuming fuel and producing emissions. We do this by simulating electricity, fuel and emission al- lowances as uncertainties on the energy market, each through a selected stochastic process and derive the so called clean spark spread, the margin between these three commodities. For valuation we use a real option approach. An alternative and common method is called Discounted Cash Flows (DCF) which sums the expected, discounted future cash flows to estimate the present value. There are three mainly disadvan- 3ARD, www.tagesschau.de/inland/meldung1516.html Standorte und Laufzeiten deutscher Atomkraftwerke, 2004 4The Economist, How long till the lights go out?, Aug 6th 2009 5International Atomic Energy Agency, Nuclear Technology Report 2009, 2009 6Energy Information Administration, International Energy Outlook 2009, May 2009 3 tages of the DCF method. Firstly, the estimated value of the cash flows may be difficult to assess for distant years. Secondly, it is difficult to assess right discount factors including the risk aversion of investors and thirdly, it does not include technical properties of the facility or operational irregularity. For more details on DCF and its merits and limits see for example [Geman05]. Differently to DCF, the real option approach can captures typical operational constraints of a power plant. Also the operational, irreversible decisions a plant operator will have made are considered by setting the asset to different states. One more advantage of a real option approach is, that it captures the impact of price volatility to the value of a power plant more realistically. Keeping in mind that a modern peaker - a very flexible generation unit - has very high ramp rates, the operator has the option to adjust production over very short time periods to face price movements in a volatile market. Surely, a real option approach also has its difficulties. An appropriate stochastic process can be measured only if there are liquid markets. We will come back to this issue in section 4.2. One special goal in this dissertation is to introduce the additional uncertainty emission allowance prices into the clean spark spread by a separate stochastic process and observe its affect to power plant values. Our motivation is that cli- mate change due to industry emission has become a severe political issue because it affects the environment of the whole planet and is thought to be responsible for natural disasters. There are new regulations from advisors to meet their promises to reduce emission made in the Kyoto Protocol. The Kyoto protocol takes care of six different greenhouse gases: carbon dioxide CO2, methane CH4, nitrous ox- ide N2O, sulphur hexafluoride SF6, hydrofluorocarbons H − F KW=HF Cs and perfluorocarbons F KW=P F Cs. On the one hand, emissions of most of these gases are allowed under restrictions and taxation and the costs per emitted unit is rather deterministic. Thus we will capture these costs in the deterministic op- erational and maintaining costs. One the other hand, CO2 is part of the Kyoto emissions trading flexible mechanism and thus emission allowance prices depend on supply and demand. In the European Union, a very important instrument is the European Union Emission Trading Scheme (EU-ETS) where CO2 emission allowances can be traded between emission producers and emission reducers or other counterparties. Here we focus on this market. A short introduction to the EU-ETS is given in the Appendix. Furthermore, we want to evaluate the option to invest into emission reduction technologies like a Carbon Capture and Storage (CCS) unit. Small pilot plants have been built with these new technologies but nobody knows whether or when it will be needed to install CCS in big projects. To handle this issue we do not 4 follow former articles on this topic which go from the costs point of view and try to identify building costs and average savings and model an American option. We come from the profit point of view and use our real option model to value the actual returns including the new technology. This approach handles a new technology much more sensitive and consider all its possible employments than standard American options. In fact, a technology investment is originally nothing else than an exchange of operational parameters and thus can be modelled as an exchange option on two real options with different constraints. The thesis is organised as follows: we start by setting up the model to value a general fuel-driven generation asset. The clean spark spread is defined and for all uncertainties proper stochastic processes are identified. Then, in section 2.3 we introduce the treatment of a number of general constraints on generation assets, which leads us to a complex multi-state problem. In section 3 we explain the real option approach to model this multi-state problem. To solve it the dynamic programming technique is introduced in section 3.2 Then, we use Least Square Monte Carlo methods firstly introduced by Longstaff and Schwartz to find a so- lution.

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