Abstract
Investment decisions in power plants and other assets are typically made under evolving uncertainties. Power companies often have managerial discretion over the timing of the investment as well as flexibility regarding the type of technology. By abstracting from some real-world details, the real options approach provides an elegant mathematical framework in which to assess the value of such flexibilities to provide both managerial and policy insights. In this chapter, we introduce the real options approach and contrast it with the now-or-never net present value perspective. Besides dealing with the issue of optimal timing , the real options approach also enables a power company to value operational flexibility , e.g., in the form of faster ramping, as compound options . Other flexibilities, such as modularized investment and endogenous capacity choice , are also amenable to analysis via this approach. Finally, the impact of risk aversion is explored, and the chapter concludes with extensions and exercises for further analysis.
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- 1.
Of course, there may be other streams of revenue, e.g., from feed-in tariffs (FITs) or renewable energy certificates (RECs) , and the possibility to sell the power in various types of markets, e.g., futures, day-ahead, and balancing. We neglect these possibilities for the sake of exposition.
- 2.
Because of nonconvexities in power plant operations such as startup costs and minimum uptimes, electricity prices may actually become negative during certain hours. For example, it may be cheaper for a power plant with high startup costs to remain online even during off-peak periods when demand is low. Thus, the power plant effectively pays to continue generation [22]. Nevertheless, we assume in this chapter for the sake of clarity that prices are nonnegative.
- 3.
There is considerable debate over whether energy prices follow BMs or mean-reverting processes. For example, Pindyck [32] analyzes 127 years of coal, natural gas, and oil prices to test for mean reversion. He finds that while such energy prices are indeed mean reverting, the rate of mean reversion is so low that using a GBM assumption for the purposes of investment analysis is “unlikely to lead to large errors.” Combined with the fact that real options models in the BM family typically lead to closed-form solutions, we retain the GBM assumption for modeling long-term energy prices. However, this may not be valid for short-term operational analyses in which the electricity price is marked by stronger mean reversion and spikes [8].
- 4.
Depending on the type of facility, this may not be a reasonable assumption. For example, wind farms, solar plants, and run-of-river hydro plants can be constructed relatively quickly because they use standardized components. Nuclear power plants, however, are notorious for time and cost overruns because of the complexity of the task and the lack of suitable sites. Lead times for fossil-fueled installations are somewhere in the middle, e.g., taking up to two years for gas-fired plants and five years for coal plants. For how to handle this “time-to-build” problem , see [28].
- 5.
To see this, note that \(\frac{\beta _1}{\beta _1-1}=\frac{1}{1-\frac{1}{\beta _1}}\). Since \(\beta _1>1\), the denominator of the latter expression is strictly less than one.
- 6.
Although it may be appealing to think of a higher investment threshold price as “delaying” the investment timing, in fact, as the volatility increases, so does the conditional probability that the threshold price will be reached from a given initial price. Intuitively, the higher volatility also increases the likelihood of extremely high (as well as extremely low) prices. Therefore, the overall impact on timing is ambiguous. For a rigorous analysis, see [27].
- 7.
The formal proof of this is left as an exercise at the end of this chapter.
- 8.
Instead of two discrete on–off states, it may also be possible to have several operating states ranging from zero to full capacity. Alternatively, continuous adjustment of the plant’s output may be handled by specifying a production function as in Chap. 6 of [12].
- 9.
In the limit as these fixed transition costs go to zero, the problem collapses to one of costless switching, e.g., as in [30]. The optimal switching thresholds then converge to the operating cost of the plant, i.e., HF. Intuitively, it is optimal to shut down (restart) the plant when the electricity price drops below (increases above) the operating cost.
- 10.
The CRRA utility function is itself a special case of the hyperbolic absolute risk aversion (HARA) class employed in studies of investor behavior.
- 11.
These effectively imply that price values after \(\tau \) are independent of the values before \(\tau \) and depend only on the value of the process at \(\tau \).
References
Adkins, R., Paxson, D.: Renewing assets with uncertain revenues and operating costs. J. Financ. Quant. Anal. 46, 785–813 (2011)
Bøckman, T., Fleten, S.-E., Juliussen, E., Langhammer, H., Revdal, I.: Investment timing and optimal capacity choice for small hydropower projects. Eur. J. Oper. Res. 190, 255–267 (2008)
Chronopoulos, M., Bunn, D., Siddiqui, A.: Optionality and policymaking in re-transforming the British power market. Econ. Energy Environ. Policy 3, 79–100 (2014)
Chronopoulos, M., De Reyck, B., Siddiqui, A.: Optimal investment under operational flexibility, risk aversion, and uncertainty. Eur. J. Oper. Res. 213, 221–237 (2011)
Copeland, T.E., Antikarov, V.: Real Options: A Practitioner’s Guide. Texere, Cheshire (2003)
Dangl, T.: Investment and capacity choice under uncertain demand. Eur. J. Oper. Res. 117, 1–14 (1999)
Décamps, J.-P., Mariotti, T., Villeneuve, S.: Irreversible investment in alternative projects. Econ. Theory 28, 425–448 (2006)
Deng, S.-J.: Valuation of investment and the opportunity to invest in power generation assets with spikes in power prices. Manag. Financ. 31, 94–114 (2005)
Deng, S.-J., Johnson, B., Sogomonian, A.: Exotic electricity options and the valuation of electricity generation and transmission assets. Decis. Support Syst. 30, 383–392 (2001)
Dixit, A.K.: Investment and hysteresis. J. Econ. Perspect. 6, 107–132 (1992)
Dixit, A.K.: Choosing among alternative lumpy investment projects under uncertainty. Econ. Lett. 43, 281–285 (1993)
Dixit, A.K., Pindyck, R.S.: Investment Under Uncertainty. Princeton University Press, Princeton (1994)
Fleten, S.-E., Heggedal, A.M., Siddiqui, A.: Transmission capacity between Norway and Germany—a real options analysis. J. Energy Markets 4, 121–147 (2011)
Fleten, S.-E., Maribu, K., Wangensteen, I.: Optimal investment strategies in decentralized renewable power generation under uncertainty. Energy 32, 803–813 (2007)
Fudenberg, D., Tirole, J.: Preemption and rent equalization in the adoption of new technology. Rev. Econ. Stud. 52, 383–401 (1985)
Gollier, C., Proult, D., Thais, F., Walgenwitz, G.: Choice of nuclear power investments under price uncertainty: valuing modularity. Energy Econ. 27, 667–685 (2005)
Heydari, S., Ovenden, N.C., Siddiqui, A.: Real options analysis of investment in carbon capture and sequestration technology. Comput. Manag. Sci. 9, 109–138 (2012)
Hogan, W.W.: Contract networks for electric power transmission. J. Reg. Econ. 4, 211–242 (1992)
Hugonnier, J., Morellec, E.: Real options and risk aversion. Working paper, HEC Lausanne, Switzerland (2007)
Hull, J.C.: Options, Futures, and Other Derivatives. Prentice Hall, Upper Saddle River (2014)
Huisman, K.J.M., Kort, P.M.: Effects of strategic interactions on the option value of waiting. Center Discussion Paper 1999-92, Tilburg University, The Netherlands (1999)
Huppmann, D., Gabriel, S.A., Leuthold, F.U.: A note on allowing negative energy prices in a discretely constrained MPEC. Energy Econ. 40, 1023–1025 (2013)
Joskow, P., Tirole, J.: Merchant transmission investment. J. Ind. Econ. 53, 233–264 (2005)
Karatzas, I., Shreve, S.: Methods of Mathematical Finance. Springer, New York (1999)
Kort, P., Murto, P., Pawlina, G.: Uncertainty and stepwise investment. Eur. J. Oper. Res. 202, 196–203 (2010)
Linnerud, K., Andersson, A.-M., Fleten, S.-E.: Investment timing under uncertain renewable energy policy: an empirical study of small hydropower projects. Energy, (2014)
Lund, D.: How to analyze the investment-uncertainty relationship in real option models? Rev. Financ. Econ. 14, 311–322 (2005)
Majd, S., Pindyck, R.S.: Time to build, option value, and investment decisions. J. Financ. Econ. 18, 7–27 (1987)
Marnay, C., Venkatarmanan, G., Stadler, M., Siddiqui, A., Firestone, R., Chandran, B.: Optimal technology selection and operation of commercial-building microgrids. IEEE Trans. Power Syst. 23, 975–982 (2008)
McDonald, R., Siegel, D.: Investment and the valuation of firms when there is an option to shut down. Int. Econ. Rev. 26, 331–349 (1985)
Näsäkkälä, E., Fleten, S.-E.: Flexibility and technology choice in gas fired power plant investments. Rev. Financ. Econ. 14, 371–393 (2005)
Pindyck, R.S.: The long-run evolution of energy prices. Energy J. 20, 1–27 (1999)
Pratt, J.W.: Risk aversion in the small and in the large. Econometrica 32, 122–136 (1964)
Rohlfs, W., Madlener, R.: Valuation of CCS-ready coal-fired power plants: a multi-dimensional real options approach. Ener. Syst. 2, 243–261 (2011)
Ross, S.M.: Stochastic Processes. Wiley, Hoboken (1995)
Saphores, J.-D., Gravel, E., Bernard, J.-T.: Regulation and investment under uncertainty—an application to power grid interconnection. J. Reg. Econ. 25, 169–186 (2004)
Siddiqui, A., Fleten, S.-E.: How to proceed with competing alternative energy technologies: a real options analysis. Energy Econ. 32, 817–830 (2010)
Siddiqui, A., Maribu, K.: Investment and upgrade in distributed generation under uncertainty. Energy Econ. 31, 25–37 (2009)
Siddiqui, A., Marnay, C.: Distributed generation investment by a microgrid under uncertainty. Energy 33, 1729–1737 (2008)
Siddiqui, A., Takashima, R.: Capacity switching options under rivalry and uncertainty. Eur. J. Oper. Res. 222, 583–595 (2012)
Šumbera, J.: Application of optimisation methods to electricity production problems. Ph.D. thesis, Department of Operational Research, Faculty of Informatics and Statistics, University of Economics, Prague, Czech Republic (2013)
Takashima, R., Goto, M., Kimura, H., Madarame, H.: Entry into the electricity market: uncertainty, competition, and mothballing options. Energy Econ. 30, 1809–1830 (2008)
Wickart, M., Madlener, R.: Optimal technology choice and investment timing: a stochastic model of industrial cogeneration versus heat-only production. Energy Econ. 29, 934–952 (2007)
World Nuclear Association: Small Nuclear Reactors. Available at http://www.world-nuclear.org/info/Nuclear-Fuel-Cycle/Power-Reactors (2014)
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Conejo, A.J., Baringo, L., Kazempour, S.J., Siddiqui, A.S. (2016). Deciding on Alternative Investments: A Real Options Approach. In: Investment in Electricity Generation and Transmission. Springer, Cham. https://doi.org/10.1007/978-3-319-29501-5_7
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