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

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 Kalman filtering and maximum likelihood estimation and specify 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. 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 which can be attributed to climate risk, and are likely to become more significant as forestry resources play a larger role in the energy transition. 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. Moreover, our results suggest that convenience yield plays a substantial role in determining optimal harvesting strategies within the two-factor model adopted in this study.