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

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 implicit finite difference approach. The regime switching model is found to more closely match the behavior 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.