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Contrasting two approaches in real options valuation: contingent claims versus dynamic programming

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Author Info
Margaret Insley (Department of Economics, University of Waterloo)
Tony Wirjanto (Department of Economics, University of Waterloo)

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Abstract

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.

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Paper provided by University of Waterloo, Department of Economics in its series Working Papers with number 08002.

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Date of creation: Aug 2008
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Handle: RePEc:wat:wpaper:08002

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Keywords: optimal tree harvesting; real options; contingent claims; dynamic programming;

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  1. 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. [Downloadable!]
  2. 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. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring. [Downloadable!] (restricted)
  6. Margaret Insley & Kimberly Rollins, 2005. "On Solving the Multirotational Timber Harvesting Problem with Stochastic Prices: A Linear Complementarity Formulation," American Journal of Agricultural Economics, American Agricultural Economics Association, vol. 87(3), pages 735-755, 08. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
  8. Eduardo S. Schwartz, 1998. "Valuing Long-Term Commodity Assets," Financial Management, Financial Management Association, vol. 27(1), Spring.
  9. Schwartz, Eduardo, 1998. "Valuing long-term commodity assets," Journal of Energy Finance & Development, Elsevier, vol. 3(2), pages 85-99. [Downloadable!] (restricted)
  10. 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. [Downloadable!] (restricted)
  11. 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.
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  12. 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. [Downloadable!] (restricted)
  13. 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. [Downloadable!] (restricted)
  14. 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. [Downloadable!]
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  1. Graeme Guthrie & Dinesh Kumareswaran, 2009. "Carbon Subsidies, Taxes and Optimal Forest Management," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 43(2), pages 275-293, June. [Downloadable!] (restricted)
  2. Shan Chen & Margaret Insley, 2008. "Regime switching in stochastic models of commodity prices: An application to an optimal tree harvesting problem," Working Papers 08003, University of Waterloo, Department of Economics. [Downloadable!]
  3. 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. [Downloadable!]
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