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.

中文翻译：

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将立木价格的不确定性外包给美国看跌期权，以实现积极的木材管理


立木价格一直在波动，这给林地所有者和管理者在做出采伐决策时带来了价格不确定性。正如 Chang 和 Zhang （2023） 所建议的那样，这种价格不确定性可以通过滚动看跌期权方法外包，即每年购买所需的美国看跌期权，以部分弥补立木价格的不确定性。然而，每年实施滚动看跌期权在实践中将具有挑战性。在本文中，我们设计了一种部分看跌期权方法，将这种不确定性外包给一笔交易。具体来说，我们将立木价格的不确定性外包给部分美式看跌期权，以确定不同林龄的期权价值并计算相应的预留价格。一旦现货价格超过预留价格，高立木价格就会立即触发木材采伐。然后将得到的收获值和林龄纳入广义 Faustmann 公式中，以确定相应的土地期望值。我们的模拟表明，与忽视价格不确定性的被动立木价格接受者相比，林地所有者可以通过我们的方法实现更好的财务业绩。此外，他们可选择适合自身风险取向的部分美式认沽期权的覆盖水平，以平衡不确定性和回报。一旦林地所有者开始积极选择执行价格、期权的总长度和部分期权覆盖的水平，他们就不再是价格接受者。相反，他们成为价格制定者。这将给立木市场带来翻天覆地的变化，对木材供应和社会福利产生深远影响。