On the Tree-Cutting Problem under Interest Rate and Forest Value Uncertainty
The current literature on optimal forest rotation makes the unrealistic assumption of constant interest rate though harvesting decisions of forest stands are typically subject to long time horizons. We apply the Wicksellian single rotation framework to cover the unexplored case of variable and stochastic interest rate. By modelling the stochastic interest rate according to the Cox-Ingersoll-Ross model and the forest value as a geometric Brownian motion we provide an explicit solution for the Wicksellian single rotation problem and show that increased interest rate volatility increases the optimal exercise threshold of the irreversible harvesting opportunity and thereby prolongs the optimal rotation period. Numerical illustration indicates that the optimal threshold becomes higher at an increasing rate.
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- Samuelson, Paul A, 1976. "Economics of Forestry in an Evolving Society," Economic Inquiry, Western Economic Association International, vol. 14(4), pages 466-92, December.
- Reed, William J & Clarke, Harry R, 1990. "Harvest Decisions and Asset Valuation for Biological Resources Exhibiting Size-Dependent Stochastic Growth," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(1), pages 147-69, February.
- 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.
- Willassen, Yngve, 1998. "The stochastic rotation problem: A generalization of Faustmann's formula to stochastic forest growth," Journal of Economic Dynamics and Control, Elsevier, vol. 22(4), pages 573-596, April.
- Reed, William J., 1984. "The effects of the risk of fire on the optimal rotation of a forest," Journal of Environmental Economics and Management, Elsevier, vol. 11(2), pages 180-190, June.
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