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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)

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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Bibliographic Info

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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References

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  1. 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.
  2. Luis H. R. Alvarez & Erkki Koskela, 2004. "Does Risk Aversion Accelerate Optimal Forest Rotation under Uncertainty?," CESifo Working Paper Series 1285, CESifo Group Munich.
  3. Luis H. R. Alvarez & Erkki Koskela, 2004. "Taxation and Rotation Age under Stochastic Forest Stand Value," CESifo Working Paper Series 1211, CESifo Group Munich.
  4. 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, Agricultural and Applied Economics Association, vol. 87(3), pages 735-755.
  5. Tarek M. Harchaoui & Pierre Lasserre, 1999. "Testing the Option Value Theory of Irreversible Investment," CIRANO Working Papers, CIRANO 99s-35, CIRANO.
  6. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, Econometric Society, vol. 53(2), pages 363-84, March.
  7. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
  8. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  9. 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, MIT Press, vol. 103(3), pages 479-508, August.
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  12. 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.
  13. 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, Western Agricultural Economics Association, vol. 32(03), December.
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  15. 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, Cambridge University Press, vol. 24(04), pages 473-487, December.
  16. Gibson, Rajna & Schwartz, Eduardo S, 1990. " Stochastic Convenience Yield and the Pricing of Oil Contingent Claims," Journal of Finance, American Finance Association, American Finance Association, vol. 45(3), pages 959-76, July.
  17. 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, Springer, vol. 3(4), pages 433-449.
  18. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, Elsevier, vol. 3(4), pages 373-413, December.
  19. 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, Agricultural and Applied Economics Association, vol. 82(3), pages 541-555.
  20. Fama, Eugene F., 1977. "Risk-adjusted discount rates and capital budgeting under uncertainty," Journal of Financial Economics, Elsevier, Elsevier, vol. 5(1), pages 3-24, August.
  21. Schwartz, Eduardo, 1998. "Valuing long-term commodity assets," Journal of Energy Finance & Development, Elsevier, Elsevier, vol. 3(2), pages 85-99.
  22. Brennan, Michael J & Schwartz, Eduardo S, 1985. "Evaluating Natural Resource Investments," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 58(2), pages 135-57, April.
  23. Eduardo S. Schwartz, 1998. "Valuing Long-Term Commodity Assets," Financial Management, Financial Management Association, Financial Management Association, vol. 27(1), Spring.
  24. 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.
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Cited by:
  1. Di Corato, Luca & Gazheli, Ardjan & Lagerkvist, Carl-Johan, 2013. "Investing in energy forestry under uncertainty," Forest Policy and Economics, Elsevier, Elsevier, vol. 34(C), pages 56-64.
  2. Chen, Shan & Insley, Margaret, 2012. "Regime switching in stochastic models of commodity prices: An application to an optimal tree harvesting problem," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 36(2), pages 201-219.
  3. Davis, Graham A. & Cairns, Robert D., 2012. "Good timing: The economics of optimal stopping," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 36(2), pages 255-265.
  4. Graeme Guthrie & Dinesh Kumareswaran, 2009. "Carbon Subsidies, Taxes and Optimal Forest Management," Environmental & Resource Economics, European Association of Environmental and Resource Economists, European Association of Environmental and Resource Economists, vol. 43(2), pages 275-293, June.
  5. 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, Western Agricultural Economics Association, vol. 32(03), December.

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