An optimal multiple stopping approach to infrastructure investment decisions. (English) Zbl 1401.91575
Summary: The energy and material processing industries are traditionally characterized by very large-scale physical capital that is custom-built with long lead times and long lifetimes. However, recent technological advancement in low-cost automation has made possible the parallel operation of large numbers of small-scale and modular production units. Amenable to mass-production, these units can be more rapidly deployed but they are also likely to have a much quicker turnover. Such a paradigm shift motivates the analysis of the combined effect of lead time and lifetime on infrastructure investment decisions. In order to value the underlying real option, we introduce an optimal multiple stopping approach that accounts for operational flexibility, delay induced by lead time, and multiple (finite/infinite) future investment opportunities. We provide an analytical characterization of the firms value function and optimal stopping rule. This leads us to develop an iterative numerical scheme, and examine how the investment decisions depend on lead time and lifetime, as well as other parameters. Furthermore, our model can be used to analyze the critical investment cost that makes small-scale (short lead time, short lifetime) alternatives competitive with traditional large-scale infrastructure.
MSC:
| 91G80 | Financial applications of other theories |
| 60G40 | Stopping times; optimal stopping problems; gambling theory |
Keywords:
optimal multiple stopping; real option; infrastructure investments; lead time; operational flexibilityReferences:
| [1] | Bender, C., Dual pricing of multi-exercise options under volume constraints, Finance and Stochast., 15, 1-26, (2011) · Zbl 1303.91167 |
| [2] | Carelli, M.; Garrone, P.; Locatelli, G.; Mancini, M.; Mycoff, C.; Trucco, P.; Ricotti, M., Economic features of integral, modular, small-to-medium size reactors, Prog. Nucl. Energy, 52, 4, 403-414, (2010) |
| [3] | Carmona, R.; Dayanik, S., Optimal multiple stopping of linear diffusions, Math. Oper. Res., 33, 2, 446-460, (2008) · Zbl 1221.60061 |
| [4] | Carmona, R.; Touzi, N., Optimal multiple stopping and valuation of swing options, Math. Finance, 18, 2, 239-268, (2008) · Zbl 1133.91499 |
| [5] | Chiara, N.; Garvin, M.; Vecer, J., Valuing simple multiple-exercise real options in infrastructure projects, J. Infrastruct. Syst., 13, 2, 97-104, (2007) |
| [6] | Dahlgren, E.; Göçmen, C.; Lackner, K. S.; van Ryzin, G., Small modular infrastructure, Eng. Econ., 58, 4, 231, (2013) |
| [7] | Deng, S.; Oren, S., Electricity derivatives and risk management, Energy, 31, 6-7, 940-953, (2006), (Electricity Market Reform and Deregulation) |
| [8] | Dixit, A.; Pindyck, R., Investment under uncertainty, (1994), Princeton University Press Princeton, NJ, USA |
| [9] | Frayer, J.; Uludere, N., What is it worth? application of real options theory to the valuation of generation assets, Electr. J., 14, 8, 40-51, (2001) |
| [10] | Geman, H.; Ohana, S., Forward curves, scarcity and price volatility in oil and natural gas markets, Energy Econ., 31, 4, 576-585, (2009) |
| [11] | Grasselli, M.; Henderson, V., Risk aversion and block exercise of executive stock options, J. Econ. Dyn. Control, 33, 1, 109-127, (2009) · Zbl 1170.91413 |
| [12] | Henderson, V., Valuing the option to invest in an incomplete market, Math. Financ. Econ., 1, 2, 103-128, (2007) · Zbl 1268.91167 |
| [13] | Jaillet, P.; Ronn, E. I.; Tompaidis, S., Valuation of commodity-based swing options, Manag. Sci., 50, 7, 909-921, (2004) · Zbl 1232.90340 |
| [14] | Jaimungal, S., 2011. Irreversible Investments and Ambiguity Aversion. Working Paper, University of Toronto. · Zbl 1415.91305 |
| [15] | Kaslow, T.; Pindyck, R., Valuing flexibility in utility planning, Electr. J., 7, 2, 60-65, (1994) |
| [16] | Larminie, J.; Dick, A., Fuel cell systems explained, (2003), John Wiley & Sons Ltd Chichester, West Sussex, UK |
| [17] | Leung, T., Li, X., Wang, Z., 2014. Optimal Multiple Trading Times Under the Exponential OU Model with Transaction Costs. Working Paper. · Zbl 1337.60074 |
| [18] | Leung, T.; Sircar, R., Accounting for risk aversion, vesting, job termination risk and multiple exercises in valuation of employee stock options, Math. Finance, 19, 1, 99-128, (2009) · Zbl 1155.91388 |
| [19] | Ludkovski, M., Financial hedging of operational flexibility, Int. J. Theor. Appl. Finance, 11, 8, 799-839, (2008) · Zbl 1180.91305 |
| [20] | Lumley, R.; Zervos, M., A model for investments in the natural resource industry with switching costs, Math. Oper. Res., 26, 4, 637-653, (2001) · Zbl 1082.90537 |
| [21] | McDonald, R.; Siegel, D., Investment and the valuation of firms when there is an option to shut down, Int. Econ. Rev., 26, 2, 331-349, (1985) · Zbl 0576.90008 |
| [22] | Meinshausen, N.; Hambly, B. M., Monte Carlo methods for the valuation of multiple-exercise options, Math. Finance, 14, 4, 557-583, (2004) · Zbl 1169.91372 |
| [23] | Shreve, S., Stochastic calculus for finance II: continuous-time models, (2004), Springer New York, NY · Zbl 1068.91041 |
| [24] | Sick, G.; Gamba, A., Some important issues involving real optionsan overview, Multinatl. Finance J., 14, 1/2, 73-123, (2010) |
| [25] | Westner, G.; Madlener, R., Investment in new power generation under uncertaintybenefits of CHP vs. condensing plants in a copula-based analysis, Energy Econ., 34, 1, 31-44, (2012) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
