Robust valuation and optimal harvesting of forestry resources in the presence of catastrophe risk and parameter uncertainty

TL;DR

This paper develops a stochastic bio-economic model to evaluate forest lease values and harvesting strategies considering catastrophe risk and parameter uncertainty, using real data and advanced numerical methods.

Contribution

It introduces a novel framework combining catastrophe risk, parameter uncertainty, and convenience yield modeling for forest resource valuation and harvesting optimization.

Findings

Parameter uncertainty reduces lease value estimates.

Conservative strategies are preferable under high uncertainty.

Convenience yield significantly influences harvesting decisions.

Abstract

We determine forest lease value and optimal harvesting strategies under model parameter uncertainty within stochastic bio-economic models that account for catastrophe risk. Catastrophic events are modeled as a Poisson point process, with a two-factor stochastic convenience yield model capturing the lumber spot price dynamics. Using lumber futures and US wildfire data, we estimate model parameters through a Kalman filter and maximum likelihood estimation and define the model parameter uncertainty set as the 95% confidence region. We numerically determine the forest lease value under catastrophe risk and parameter uncertainty using reflected backward stochastic differential equations (RBSDEs) and establish conservative and optimistic bounds for lease values and optimal stopping boundaries for harvesting, facilitating Monte Carlo simulations. Numerical experiments further explore how parameter uncertainty, catastrophe intensity, and carbon sequestration impact the lease valuation and harvesting decision. In particular, we explore the costs arising from this form of uncertainty in the form of a reduction of the lease value. These are implicit costs that can be attributed to climate risk and will be emphasized through the importance of forestry resources in the energy transition process. We conclude that in the presence of parameter uncertainty, it is better to lean toward a conservative strategy reflecting, to some extent, the worst case than being overly optimistic. Our results also highlight the critical role of convenience yield in determining optimal harvesting strategies.