Real Options and Mean-Reverting Prices Gregory F. Robel Mathematics & Engineering Analysis July 14, 2001 firstname.lastname@example.org Acknowledgements
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
Gregory F. Robel
Mathematics & Engineering Analysis
July 14, 2001
I would like to thank several colleagues for useful discussions, including Dr. Stuart Anderson, Dr. Mike Epton and Dr. Roman Fresnedo of The Boeing Company; and Dr. Dan Calistrate and Professor Gordon Sick of The University of Calgary. The usual disclaimer applies.
References: [DP], [McDS]
References: [KP], [Si]
References: [DP], [KP], [Pin]
References: [B], [KP], [Pil], [Si]
Maximum error = 0.0347
Maximum error = 0.0142
References: [Co], [Sh], [Si]
References: [L], [SpO]
r = 0.04
x = 1
r = 0.05
r = 0.06
x = 1
x = 1
t1/2 = 2.5
t1/2 = 5
t1/2 = 10
x = 1
--The probability of an “up” step at time i , after j “up” steps, is where and where
[B] S. Bhattacharya, “Project Valuation with Mean-Reverting Cash Flow Streams,” Journal of Finance33, December 1978, pp. 1317-1331.
[BØ] K. Brekke and B. Øksendal, “The High Contact Principle as a Sufficiency Condition for Optimal Stopping.” Stochastic Models and Option Values, D. Lund and B. Øksendal, editors, Elsevier Science Publishers, 1991,
[Ca] D. Calistrate, “Setting Lattice Parameters for Derivatives Valuation”, private communication, 2000.
[Co] G. Constantinides, “Market Risk Adjustment in Project Valuation,” Journal of Finance 33, May 1978, pp. 603-616.
[CoA] T. Copeland and V. Antikarov, Real Options: A Practitioner’s Guide, Texere, 2001.
[DP] A. Dixit and R. Pindyck, Investment under Uncertainty, Princeton University Press, 1994.
[KP] P. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Springer-Verlag, 1992.
[L] Y. Luke, “Algorithms for Rational Approximations for a Confluent Hypergeometric Function,” Utilitas Math.11 (1977), pp. 123-151.
[McDS] R. McDonald and D. Siegel, “The Value of Waiting to Invest,” Quarterly J. Econ.101 (1986), pp. 707-728.
[Pil] D. Pilipovic, Energy Risk, McGraw-Hill, 1998.
[Pin] R. Pindyck, “Irreversibility, Uncertainty, and Investment,” J. Econ. Lit.19 (1991), pp. 1110-1148.
[R] B.L.S. Prakasa Rao, Statistical Inference for Diffusion Type Processes (Kendall’s Library of Statistics 8), Arnold / Oxford University Press, 1999.
[Sh] D. Shimko, Finance in Continuous Time--A Primer, Kolb, 1992.
[Si] G. Sick, “Real Options.” Finance (Handbooks in Operations Research and Management Science, Volume 9), R. Jarrow, V. Maksimovic, and W. Ziemba, editors, pp. 631-691, North-Holland, 1995.
[SO] I. Shoji and T. Ozaki, “Comparative Study of Estimation Methods for Continuous Time Stochastic Processes,” J. Time Series Analysis18 (1997), pp. 485-506.
[SpO] J. Spanier and K. Oldham, An Atlas of Functions, Hemisphere, 1987.
[T] L. Trigeorgis, Real Options, MIT Press, 1996.
[W] P. Wilmott, Paul Wilmott on Quantitative Finance, Wiley, 2000.