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Regime Switching in Stochastic Models of Commodity Prices: An Application to an Optimal Tree Harvesting Problem

Author

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  • Shan chen

    (Department of Economics, University of Waterloo)

  • Margaret Insley

    (Department of Economics, University of Waterloo)

Abstract

This 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.

Suggested Citation

  • Shan chen & Margaret Insley, 2010. "Regime Switching in Stochastic Models of Commodity Prices: An Application to an Optimal Tree Harvesting Problem," Working Papers 1016, University of Waterloo, Department of Economics, revised Jul 2010.
  • Handle: RePEc:wat:wpaper:1016
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    1. repec:spr:compst:v:50:y:1999:i:3:p:493-518 is not listed on IDEAS
    2. Eduardo Schwartz & James E. Smith, 2000. "Short-Term Variations and Long-Term Dynamics in Commodity Prices," Management Science, INFORMS, pages 893-911.
    3. Schwert, G. William, 1996. "Markup pricing in mergers and acquisitions," Journal of Financial Economics, Elsevier, pages 153-192.
    4. 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 361-375, March.
    5. 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.
    6. 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 1969-1984, December.
    7. 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.
    8. 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.
    9. 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 923-973, July.
    10. 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.
    11. 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 357-384, March.
    12. Alvarez, Luis H. R. & Koskela, Erkki, 2005. "Wicksellian theory of forest rotation under interest rate variability," Journal of Economic Dynamics and Control, Elsevier, pages 529-545.
    13. 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.
    14. 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 147-169, February.
    15. 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.
    16. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    17. 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.
    18. Insley, M.C. & Wirjanto, T.S., 2010. "Contrasting two approaches in real options valuation: Contingent claims versus dynamic programming," Journal of Forest Economics, Elsevier, pages 157-176.
    19. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    20. 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.
    21. 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.
    22. 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.
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    Cited by:

    1. Forand, Jean Guillaume, 2015. "Keeping your options open," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 47-68.
    2. Chevallier Julien & Goutte Stéphane, 2017. "On the estimation of regime-switching Lévy models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, pages 3-29.
    3. Pless, Jacquelyn & Arent, Douglas J. & Logan, Jeffrey & Cochran, Jaquelin & Zinaman, Owen, 2016. "Quantifying the value of investing in distributed natural gas and renewable electricity systems as complements: Applications of discounted cash flow and real options analysis with stochastic inputs," Energy Policy, Elsevier, vol. 97(C), pages 378-390.
    4. Adriana Piazza & Bernardo Pagnoncelli, 2015. "The stochastic Mitra–Wan forestry model: risk neutral and risk averse cases," Journal of Economics, Springer, pages 175-194.
    5. repec:eee:eneeco:v:67:y:2017:i:c:p:1-16 is not listed on IDEAS
    6. Martzoukos, Spiros H. & Zacharias, Eleftherios, 2013. "Real option games with R&D and learning spillovers," Omega, Elsevier, vol. 41(2), pages 236-249.
    7. Fan, Kun & Shen, Yang & Siu, Tak Kuen & Wang, Rongming, 2015. "Valuing commodity options and futures options with changing economic conditions," Economic Modelling, Elsevier, vol. 51(C), pages 524-533.
    8. Ballestra, Luca Vincenzo & Pacelli, Graziella, 2013. "Pricing European and American options with two stochastic factors: A highly efficient radial basis function approach," Journal of Economic Dynamics and Control, Elsevier, vol. 37(6), pages 1142-1167.

    More about this item

    JEL classification:

    • 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

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