Contrasting two approaches in real options valuation: contingent claims versus dynamic programming
This paper compares two well-known approaches for valuing a risky investment using real options theory: contingent claims (CC) with risk neutral valuation and dynamic programming (DP) using a constant risk adjusted discount rate. Both approaches have been used in valuing forest assets. A proof is presented which shows that, except under certain restrictive assumptions; DP using a constant discount rate and CC will not yield the same answers for investment value. A few special cases are considered for which CC and DP with a constant discount rate are consistent with each other. An optimal tree harvesting example is presented to illustrate that the values obtained using the two approaches can differ whcn we depart from these special cases to a more realistic scenariio. Further, the implied risk adjusted discount rate calculated from CC is found to vary with the stochastic state variable and stand age. We conclude that for real options problems the CC approach should be used.
|Date of creation:||Aug 2008|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: (519) 888-4567 ext 33695
Fax: (519) 725-0530
Web page: http://economics.uwaterloo.ca/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
- Gibson, Rajna & Schwartz, Eduardo S, 1990. " Stochastic Convenience Yield and the Pricing of Oil Contingent Claims," Journal of Finance, American Finance Association, vol. 45(3), pages 959-76, July.
- Eduardo S. Schwartz, 1998. "Valuing Long-Term Commodity Assets," Financial Management, Financial Management Association, vol. 27(1), Spring.
- Paddock, James L & Siegel, Daniel R & Smith, James L, 1988. "Option Valuation of Claims on Real Assets: The Case of Offshore Petroleum Leases," The Quarterly Journal of Economics, MIT Press, vol. 103(3), pages 479-508, August.
- Tarek M. Harchaoui & Pierre Lasserre, 1999.
"Testing the Option Value Theory of Irreversible Investment,"
Cahiers de recherche du Département des sciences économiques, UQAM
9905, Université du Québec à Montréal, Département des sciences économiques.
- Harchaoui, Tarek M & Lasserre, Pierre, 2001. "Testing the Option Value Theory of Irreversible Investment," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(1), pages 141-66, February.
- Tarek M. Harchaoui & Pierre Lasserre, 1995. "Testing the Option Value Theory of Irreversible Investment," CIRANO Working Papers 95s-41, CIRANO.
- Harchaoui, T. & Lasserre, P., 1995. "Testing the Option Vakue Theory of Irreversible Investment," G.R.E.Q.A.M. 95b04, Universite Aix-Marseille III.
- Tarek M. Harchaoui & Pierre Lasserre, 1999. "Testing the Option Value Theory of Irreversible Investment," CIRANO Working Papers 99s-35, CIRANO.
- Jean-Daniel M. Saphores, 2000. "The Economic Threshold with a Stochastic Pest Population: A Real Options Approach," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 82(3), pages 541-555.
- McDonald, Robert & Siegel, Daniel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, MIT Press, vol. 101(4), pages 707-27, November.
- Fama, Eugene F., 1977. "Risk-adjusted discount rates and capital budgeting under uncertainty," Journal of Financial Economics, Elsevier, vol. 5(1), pages 3-24, August.
- Brennan, Michael J & Schwartz, Eduardo S, 1985. "Evaluating Natural Resource Investments," The Journal of Business, University of Chicago Press, vol. 58(2), pages 135-57, April.
- Schwartz, Eduardo, 1998. "Valuing long-term commodity assets," Journal of Energy Finance & Development, Elsevier, vol. 3(2), pages 85-99.
- Luis H. R. Alvarez & Erkki Koskela, 2004.
"Taxation and Rotation Age under Stochastic Forest Stand Value,"
CESifo Working Paper Series
1211, CESifo Group Munich.
- Alvarez, Luis H.R. & Koskela, Erkki, 2007. "Taxation and rotation age under stochastic forest stand value," Journal of Environmental Economics and Management, Elsevier, vol. 54(1), pages 113-127, July.
- Schwartz, Eduardo S, 1997. " The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance, American Finance Association, vol. 52(3), pages 923-73, July.
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-84, March.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
- Merton, Robert C., 1971.
"Optimum consumption and portfolio rules in a continuous-time model,"
Journal of Economic Theory,
Elsevier, vol. 3(4), pages 373-413, December.
- R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers 58, Massachusetts Institute of Technology (MIT), Department of Economics.
- Mihail Zervos & Bernhard Meister & Thomas S. Knudsen, 1999. "On the relationship of the dynamic programming approach and the contingent claim approach to asset valuation," Finance and Stochastics, Springer, vol. 3(4), pages 433-449.
- Alvarez, Luis H.R. & Koskela, Erkki, 2006.
"Does risk aversion accelerate optimal forest rotation under uncertainty?,"
Journal of Forest Economics,
Elsevier, vol. 12(3), pages 171-184, December.
- Luis H. R. Alvarez & Erkki Koskela, 2004. "Does Risk Aversion Accelerate Optimal Forest Rotation under Uncertainty?," CESifo Working Paper Series 1285, CESifo Group Munich.
- Eduardo Schwartz & James E. Smith, 2000. "Short-Term Variations and Long-Term Dynamics in Commodity Prices," Management Science, INFORMS, vol. 46(7), pages 893-911, July.
- Slade, Margaret E., 2001. "Valuing Managerial Flexibility: An Application of Real-Option Theory to Mining Investments," Journal of Environmental Economics and Management, Elsevier, vol. 41(2), pages 193-233, March.
- Thomas A. Thomson, 1992. "Optimal Forest Rotation When Stumpage Prices Follow a Diffusion Process," Land Economics, University of Wisconsin Press, vol. 68(3), pages 329-342.
- Graham A. Davis, 1996. "Option Premiums in Mineral Asset Pricing: Are They Important?," Land Economics, University of Wisconsin Press, vol. 72(2), pages 167-186.
- Insley, Margaret, 2002. "A Real Options Approach to the Valuation of a Forestry Investment," Journal of Environmental Economics and Management, Elsevier, vol. 44(3), pages 471-492, November.
- Insley, Margaret & Lei, Manle, 2007. "Hedges and Trees: Incorporating Fire Risk into Optimal Decisions in Forestry Using a No-Arbitrage Approach," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 32(03), December.
- Morck, Randall & Schwartz, Eduardo & Stangeland, David, 1989. "The Valuation of Forestry Resources under Stochastic Prices and Inventories," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(04), pages 473-487, December.
- Margaret Insley & Kimberly Rollins, 2005. "On Solving the Multirotational Timber Harvesting Problem with Stochastic Prices: A Linear Complementarity Formulation," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 87(3), pages 735-755.
When requesting a correction, please mention this item's handle: RePEc:wat:wpaper:08002. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Pat Gruber)
If references are entirely missing, you can add them using this form.