On the Tree-Cutting Problem under Interest Rate and Timber Value Uncertainty

The current literature on optimal forest rotation makes the unrealistic assumption of constant interest rate even though harvesting decisions of forest stands are typically subject to long time horizons under which interest rates fluctuate and are subject to shocks. We apply the Wicksellian single rotation framework to cover the unexplored case of variable and stochastic interest rate. By modelling the stochastic interest rate as a parametrized mean-reverting model a lá Cox-Ingersoll-Ross and the timber value as a geometric Brownian motion we provide an explicit solution for the two-dimensional path-dependent rotation problem. We show that increased interest rate volatility prolongs the optimal rotation period. Numerical illustration indicates that higher interest rate volatility lengthens the optimal rotation period at an increasing rate.