Regime Switching in Stochastic Models of Commodity Prices: An Application to an Optimal Tree Harvesting Problem
AbstractThis paper investigates whether a regime switching model of stochastic lumber prices is better for the analysis of optimal harvesting problems in forestry than a more traditional single regime model. Prices of lumber derivatives are used to calibrate a regime switching model, with each of two regimes characterized by a different mean reverting process. A single regime, mean reverting process is also calibrated. The value of a representative stand of trees and optimal harvesting prices are determined by specifying a Hamilton-Jacobi-Bellman Variational Inequality, which is solved for both pricing models using a fully implicit finite difference approach. The regime switching model is found to more closely match the behaviour of futures prices than the single regime model. In addition, analysis of a tree harvesting problem indicates significant differences in terms of land value and optimal harvest thresholds between the regime switching and single regime models.
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Bibliographic InfoPaper provided by University of Waterloo, Department of Economics in its series Working Papers with number 1016.
Length: 52 pages
Date of creation: Jul 2010
Date of revision: Jul 2010
Other versions of this item:
- 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, vol. 36(2), pages 201-219.
- 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.
- C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- Q23 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Forestry
- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-02-05 (All new papers)
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- 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.
- 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.
- Merton, Robert C., 1975.
"Option pricing when underlying stock returns are discontinuous,"
787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
- 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.
- 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.
- 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.
- 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.
- G. William Schwert, 1996.
"Mark-Up Pricing in Mergers and Acquisitions,"
NBER Working Papers
4863, National Bureau of Economic Research, Inc.
- 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.
- 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.
- 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.
- 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.
- Luis H. R. Alvarez & Erkki Koskela, 2001. "Wicksellian Theory of Forest Rotation under Interest Rate Variability," CESifo Working Paper Series 606, CESifo Group Munich.
- 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.
- 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.
- 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.
- 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.
- Insley, M.C. & Wirjanto, T.S., 2010.
"Contrasting two approaches in real options valuation: Contingent claims versus dynamic programming,"
Journal of Forest Economics,
Elsevier, vol. 16(2), pages 157-176, April.
- 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.
- 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.
- 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.
- Martzoukos, Spiros H & Zacharias, Eleftherios, 2008.
"Real Option Games with R&D and Learning Spillovers,"
12686, University Library of Munich, Germany.
- Martzoukos, Spiros H. & Zacharias, Eleftherios, 2013. "Real option games with R&D and learning spillovers," Omega, Elsevier, vol. 41(2), pages 236-249.
- Margaret Insley, 2013. "On the timing of non-renewable resource extraction with regime switching prices: an optimal stochastic control approach," Working Papers 1302, University of Waterloo, Department of Economics, revised Aug 2013.
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