Outsourcing stumpage price uncertainty with American put option for active timber management1

Stumpage price fluctuates all the time, creating price uncertainty for timberland owners and managers in making harvest decisions. As Chang and Zhang (2023) suggested, this price uncertainty could be outsourced with a rolling put option method, i.e., purchasing American put options needed every year to partially cover the stumpage price uncertainty. However, implementing rolling put options every year would be challenging in practice. In this paper, we devise a partial put option method to outsource such uncertainty with just one transaction. Specifically, we outsource stumpage price uncertainty with a partial American put option to determine the option values at different stand ages and calculate the corresponding reservation prices. As soon as the spot price exceeds the reservation price, the high stumpage price triggers an immediate timber harvest. The resulting harvest value and stand age are then incorporated into the generalized Faustmann formula to determine the corresponding land expectation value. Our simulations indicate that, compared to being passive stumpage price takers who ignore the price uncertainty, timberland owners could realize better financial performance with our method. In addition, they could choose the coverage level of partial American put option which suits their own risk preferences to balance uncertainty and return. Once timberland owners start actively selecting the strike price, the overall length of the option, and the level of partial option coverage, they are no longer price takers. Instead, they become price setters. That would bring about a sea change in the stumpage market with profound implications for timber supply and social welfare.