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Regime switching in stochastic models of commodity prices: An application to an optimal tree harvesting problem

  • Shan Chen

    (Department of Economics, University of Waterloo)

  • Margaret Insley

    (Department of Economics, University of Waterloo)

This paper investigates a regime switching model of stochastic lumber prices in the context of an optimal tree harvesting problem. Using lumber derivatives prices, two lumber price models are calibrated: a regime switching model and a single regime model. In the regime switching model, the lumber price can be in one of two regimes in which different mean reverting price processes prevail. An optimal tree harvesting problem is specified in terms of a linear complementarity problem which is solved using a fully implicit finite difference, fully-coupled, numerical approach. The land value and critical harvesting prices are found to be significantly different depending on which price model is used. The regime switching model shows promise as a parsimonious model of timber prices that can be incorporated into forestry investment problems.

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Paper provided by University of Waterloo, Department of Economics in its series Working Papers with number 08003.

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Date of creation: Aug 2008
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Handle: RePEc:wat:wpaper:08003
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  1. Schwert, G.W., 1994. "Mark-up Pricing in Mergers and Acquisitions," Papers 95-01, Rochester, Business - Financial Research and Policy Studies.
  2. Malcolm P. Baker & E. Scott Mayfield & John E. Parsons, 1998. "Alternative Models of Uncertain Commodity Prices for Use with Modern Asset Pricing Methods," The Energy Journal, International Association for Energy Economics, vol. 0(Number 1), pages 115-148.
  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. Jean-Daniel Saphores & Lynda Khalaf & Denis Pelletier, 2002. "On Jumps and ARCH Effects in Natural Resource Prices: An Application to Pacific Northwest Stumpage Prices," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 84(2), pages 387-400.
  5. 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.
  6. Alvarez, Luis H. R. & Koskela, Erkki, 2005. "Wicksellian theory of forest rotation under interest rate variability," Journal of Economic Dynamics and Control, Elsevier, vol. 29(3), pages 529-545, March.
  7. Naik, Vasanttilak, 1993. " Option Valuation and Hedging Strategies with Jumps in the Volatility of Asset Returns," Journal of Finance, American Finance Association, vol. 48(5), pages 1969-84, December.
  8. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
  9. 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.
  10. 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.
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  12. Margaret Insley & Tony Wirjanto, 2008. "Contrasting two approaches in real options valuation: contingent claims versus dynamic programming," Working Papers 08002, University of Waterloo, Department of Economics.
  13. repec:spr:compst:v:50:y:1999:i:3:p:493-518 is not listed on IDEAS
  14. Raymond, Jennie E & Rich, Robert W, 1997. "Oil and the Macroeconomy: A Markov State-Switching Approach," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(2), pages 193-213, May.
  15. Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, vol. 89(2), pages 484-489, June.
  16. 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.
  17. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
  18. 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.
  19. 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.
  20. de Jong, C.M., 2005. "The Nature of Power Spikes: a regime-switch approach," ERIM Report Series Research in Management ERS-2005-052-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
  21. Bessembinder, Hendrik, et al, 1995. " Mean Reversion in Equilibrium Asset Prices: Evidence from the Futures Term Structure," Journal of Finance, American Finance Association, vol. 50(1), pages 361-75, March.
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