VALUING A TIMBER HARVEST CONTRACT AS A HIGH‐DIMENSIONAL AMERICAN CALL OPTION VIA LEAST‐SQUARES MONTE CARLO SIMULATION

Abstract Industrial timberland ownership in the United States has shifted substantially in the last 20 years. Having sold their fee‐owned timberlands, forest products companies relied heavily on the open market for raw timber. To reduce their exposure to market risks, however, forest products companies have been using a number of supply chain instruments, such as timber harvest contracts. As these vehicles become increasingly important to the forest industry, it is necessary and important to determine their economic values. In this study, we treated a 3‐year timber harvest contract on a 30‐year‐old loblolly pine plantation as a high‐dimensional American call option and calculated its value by the least‐squares Monte Carlo simulation technique. The estimated values of such a contract ranged from $1,693/ac to $1,984/ac under two timber price assumptions. With reasonable starting timber prices and strike price in the simulation, random timber prices led to higher contract values. Results from this study can help private landowners, timber brokers, and forest products companies better manage their business risks.     

Timber harvest scheduling with price uncertainty using Markowitz portfolio optimization

Harvest scheduling models need to account for uncertain revenue predictions when minimizing risk of financial loss is an important management objective. In this paper, we present methods for estimating the means and covariances of stumpage prices and incorporating them in harvest scheduling models. We approached the estimation problem by fitting time-series models to loblolly pine sawtimber and pulpwood stumpage prices in Georgia, USA, and deriving formulas for means and covariances of price predictions. Statistical evidence supported integrated autoregressive models, which caused covariances of price predictions to increase with time. The means and covariances of price predictions were combined with timber yield and land value predictions to give exact formulas for the revenue means and covariances of timber management activities. Sawtimber regimes dominated pulpwood regimes by providing higher mean revenues across a wide range of revenue variances. Harvest scheduling results for a hypothetical forest of pine plantations showed that the forest plan that maximized mean income without concern for risk (expressed as the standard deviation of income) involved sawtimber production with a 35-year rotation age. Risk was reduced 30% with little effect on mean income by using shorter-rotation sawtimber regimes. Risk was reduced 80% by using a mix of short-rotation sawtimber and pulpwood regimes because pulpwood price was only weakly correlated with sawtimber price. The latter risk-reduction came at the expense of mean income, which was reduced by as much as 50%. The risks and compositions of optimal forest plans were extremely sensitive to assumptions about the range of future prices that were inherent in different prediction models. This sensitivity emphasizes the importance of carefully determining the decision makers beliefs about stumpage price behavior.     

STOCHASTIC PRICE MODELS AND OPTIMAL TREE CUTTING: RESULTS FOR LOBLOLLY PINE

An empirical investigation of stumpage price models and optimal harvest policies is conducted for loblolly pine plantations in the southeastern United States. The stationarity of monthly and quarterly series of sawtimber prices is analyzed using a unit root test. The statistical evidence supports stationary autoregressive models for the monthly series and for the quarterly series of opening month prices. In contrast, the evidence supports a non-stationary random walk model for the quarterly series of average prices. This conflicting result is likely an artifact of price averaging. The properties of these series significantly affect the forms of optimal price-dependent harvest rules and expected returns. Further, the results have implications for conclusions about market efficiency and the performance of a fixed rotation age.     

Optimal harvest strategy for even‐aged stands with price uncertainty and risk of natural disturbances

We present a reservation price model to examine the joint impacts of natural disturbances and stumpage price uncertainty on the optimal harvesting decision for even‐aged forest stands. We consider a landowner who manages a loblolly pine stand to produce timber and amenities, under age‐dependent risk of wildfires and uncertainty in future timber prices. We show that the incorporation of risk of wildfires decreases the optimal reservation prices. The inclusion of risk of wildfires leads to lower land values and reduces the mean harvest age compared with the case of no‐risk of wildfires. Higher economic gains are obtained with the reservation price strategy compared with the deterministic rotation age model—a difference in the land value of $2,326 ha^?1 (21%) between the two approaches. Recommendations for Resource Managers

• Our adaptive harvest strategy shows that the incorporation of risk of wildfires decreases the optimal reservation prices compared with the case of no‐risk of wildfires.
• Low reservation prices—a price that makes the landowner indifferent between harvesting or waiting longer—result in lower economic benefits for landowners and potential conversions of lands to nonforest use.
• Forest management practices oriented to reduce the effects of catastrophic disturbances, for example, creating a more complex forest structure with different stand densities, become imperative to ensure the sustainability of forestlands in the US South.
• Our analysis also suggests that the valuation of forestry investments should consider not only the risk of catastrophic events but also uncertainty in future timber prices. Higher appraisals of land value are obtained when timber price uncertainty is explicitly recognized, providing financial incentives for landowners to invest in forestry.

     

Local non-stationarity test in mean for Markov switching GARCH models: an approximate Bayesian approach

In order to exploit mean-reverting behavior among the price differential between two markets, one can use unit root tests to determine which pairs of assets appear to exhibit mean-reverting behavior. Since nonlinear mean reversion shares the same meaning as local stationarity, this paper proposes a Bayesian hypothesis testing to detect the presence of a local unit root in the mean equation using Markov switching GARCH models. This model incorporates a fat-tailed error distribution to analyze asymmetric effects on both the conditional mean and conditional volatility of financial time series. To implement the test, we propose a numerical approximation of the marginal likelihoods to posterior odds by using an adaptive Markov Chain Monte Carlo scheme. Our simulation study demonstrates that the approximate Bayesian test performs properly. The proposed method utilizes the daily basis between the FTSE 100 Index and Index Futures as an illustration.     

TIMBER SUPPLY UNDER DEMAND UNCERTAINTY: WELFARE GAINS FROM PERFECT COMPETITION WITH RATIONAL EXPECTATIONS

ABSTRACT. This paper presents a noneconometric approach to estimating the short‐run timber supply function based on optimal harvest decisions. Determination of optimal harvest levels and estimation of supply function coefficients are integrated into one step by incorporating a parametric short‐run timber supply function into the harvest decision model. In this manner we convert the original harvest decision model into a new optimization problem with the supply function coefficients functioning as “decision variables.” Optimal solution to the new decision model gives the coefficients of the short‐run supply function and, indirectly, the optimal harvest levels. This approach enables us to develop stochastic models of the timber market that are particularly useful for forest sector analysis involving comparison of alternative institutional regimes or policy proposals and when the timber market is affected by stochastic variables. For demonstration purposes, we apply this method to compare the performances of two timber market regimes (perfect competition and monopoly) under demand uncertainty, using the Swedish data. The results show that the expected timber price is 22 percent lower and the expected annual timber supply is 43 percent higher in the competitive market than in the monopoly market. This confirms the theoretical result that monopoly reduces supply and increases price. The expected social welfare gain from perfect competition over monopoly is about 24 percent.     

IS THERE UNIT ROOT IN THE NITROGEN OXIDES EMISSIONS: A MONTE CARLO INVESTIGATION?

Abstract Use of the time‐series econometric techniques to investigate issues about environmental regulation requires knowing whether air pollution emissions are trend stationary or difference stationary. It has been shown that results regarding trend stationarity of the pollution data are sensitive to the methods used. I conduct a Monte Carlo experiment to study the size and power of two unit root tests that allow for a structural change in the trend at a known time using the data‐generating process calibrated to the actual pollution series. I find that finite sample properties of the Perron test are better than the Park and Sung Phillips‐Perron (PP) type test. Severe size distortions in the Park and Sung PP type test can explain the rejection of a unit root in air pollution emissions reported in some environmental regulation analyses.     

Deep learning for energy markets

Deep Learning (DL) is combined with extreme value theory (EVT) to predict peak loads observed in energy grids. Forecasting energy loads and prices is challenging due to sharp peaks and troughs that arise due to supply and demand fluctuations from intraday system constraints. We propose a deep temporal extreme value model to capture these effects, which predicts the tail behavior of load spikes. Deep long‐short‐term memory architectures with rectified linear unit activation functions capture trends and temporal dependencies, while EVT captures highly volatile load spikes above a prespecified threshold. To illustrate our methodology, we develop forecasting models for hourly price and demand from the PJM interconnection. The goal is to show that DL‐EVT outperforms traditional methods, both in‐ and out‐of‐sample, by capturing the observed nonlinearities in prices and demand spikes. Finally, we conclude with directions for future research.     

Forestry management under uncertainty

The forest harvest and road construction planning problem consists fundamentally of managing land designated for timber production and divided into harvest cells. For each time period the planner must decide which cells to cut and what access roads to build in order to maximize expected net profit. We have previously developed deterministic mixed integer linear programming models for this problem. The main contribution of the present work is the introduction of a multistage Stochastic Integer Programming model. This enables the planner to make more robust decisions based on a range of timber price scenarios over time, maximizing the expected value instead of merely analyzing a single average scenario. We use a specialization of the Branch-and-Fix Coordination algorithmic approach. Different price and associated probability scenarios are considered, allowing us to compare expected profits when uncertainties are taken into account and when only average prices are used. The stochastic approach as formulated in this work generates solutions that were always feasible and better than the average solution, while the latter in many scenarios proved to be infeasible.     

MODELING CATASTROPHIC RISK IN ECONOMIC ANALYSIS OF FOREST CARBON SEQUESTRATION

ABSTRACT. The effect of risk from catastrophic tree mortality, such as fire, insect outbreaks and hurricanes, on selling credits for carbon sequestration from a slash pine plantation is modeled. We achieve this task by developing a modified Hartman model and applying it to a slash pine plantation. It is found that risk decreases the land expectation value and the optimal rotation age on a forest stand producing timber and carbon sequestration benefits. This decrease is greater with higher prices of carbon. Furthermore, risk increases the amount of pulpwood produced from the stand and decreases the amount of sawtimber produced. Since pulpwood has a shorter life span than sawtimber this reduces the amount of carbon sequestered. This effect is greater for higher prices of carbon suggesting that risk dampens the effect that a carbon market would have in inducing landowners to sequester more carbon.     

中国期货市场与现货市场的价格引导与价格发现

长期以来对期货市场与现货市场价格关系的实证研究都是基于时间序列方法的研究.为了克服时间序列方法存在着的不足,将使用面板数据方法,在面板单位根检验以及面板协整检验和协整估计的基础上,构建面板误差修正模型来分析期货价格和现货价格的均衡以及相互引导关系.进一步的,在误差修正模型的基础上我们采用信息份额方法(I-S模型)和共同因子贡献法(P-T模型)分析了期货市场和现货市场的价格发现功能.通过上述研究,发现总体上讲我国大宗商品的期货价格和现货价格之间存在着长期均衡,并且表现出了相互引导互为Granger因果的关系.利用I-S模型和P-T模型测算出来的期货市场对价格形成的贡献度分别为88.17%和79.44%,这说明当前我国的期货市场总体上讲是有效率的市场.     

Asymptotic Null Distributions of Stationarity and Nonstationarity Tests Under Local-to-finite Variance Errors

The purpose of this paper is to investigate the asymptotic null distribution of stationarity and nonstationarity tests when the distribution of the error term belongs to the normal domain of attraction of a stable law in any finite sample but the error term is an i.i.d. process with finite variance as . This local-to-finite variance setup is helpful to highlight the behavior of test statistics under the null hypothesis in the borderline or near borderline cases between finite and infinite variance and to assess the robustness of these test statistics to small departures from the standard finite variance context. From an empirical point of view, our analysis can be useful in settings where the (non)-existence of the (second) moments is not clear-cut, such as, for example, in the analysis of financial time series. A Monte Carlo simulation study is performed to improve our understanding of the practical implications of the limi theory we develop. The main purpose of the simulation experiment is to assess the size distortion of the unit root and stationarity tests under investigation.     

The optimal harvesting problem under price uncertainty

In this paper we study the exploitation of a one species forest plantation when timber price is governed by a stochastic process. The work focuses on providing closed expressions for the optimal harvesting policy in terms of the parameters of the price process and the discount factor, with finite and infinite time horizon. We assume that harvest is restricted to mature trees older than a certain age and that growth and natural mortality after maturity are neglected. We use stochastic dynamic programming techniques to characterize the optimal policy and we model price using a geometric Brownian motion and an Ornstein–Uhlenbeck process. In the first case we completely characterize the optimal policy for all possible choices of the parameters. In the second case we provide sufficient conditions, based on explicit expressions for reservation prices, assuring that harvesting everything available is optimal. In addition, for the Ornstein–Uhlenbeck case we propose a policy based on a reservation price that performs well in numerical simulations. In both cases we solve the problem for every initial condition and the best policy is obtained endogenously, that is, without imposing any ad hoc restrictions such as maximum sustained yield or convergence to a predefined final state.     

Emergent dynamics of the first‐order stochastic Cucker‐Smale model and application to finance

In this paper, we study stochastic aggregation properties of the financial model for the N‐asset price process whose dynamics is modeled by the weakly geometric Brownian motions with stochastic drifts. For the temporal evolution of stochastic components of drift coefficients, we employ a stochastic first‐order Cucker‐Smale model with additive noises. The asset price processes are weakly interacting via the stochastic components of drift coefficients. For the aggregation estimates, we use the macro‐micro decomposition of the fluctuations around the average process and show that the fluctuations around the average value satisfies a practical aggregation estimate over a time‐independent symmetric network topology so that we can control the differences of drift coefficients by tuning the coupling strength. We provide numerical examples and compare them with our analytical results. We also discuss some financial implications of our proposed model.     

Stochastic competitive entries and dynamic pricing

How should firms price new products when they do not know the timing, nor the nature of the next competitive entry? To guide managers’ pricing decisions in such contexts, we propose a dynamic pricing model with two types of randomly timed entry, i.e. imitative and innovative. The characterization of the equilibrium strategies reveals how optimal prices vary with the manager’s knowledge about the timing of future competitive entries. We show that price skimming is not always optimal when entry dates are unknown to managers. Everything else equal, we demonstrate that the randomness of competitive entries make forward looking managers to choose constant prices, even though the characteristics of the market would have justified skimming the demand in the normal course. Moreover, we show that the constant pricing policy remains optimal even when the incumbent’s optimal pricing strategy influences the probability of facing a competitive entry. Finally, we find that uncertainty does not necessarily hurt firms’ profits.     

PUBLIC AND PRIVATE FOREST DISTURBANCE REGIMES IN THE SOUTHERN APPALACHIANS

The choice to harvest timber depends on, among other things, the accessibility and location of the forest. This paper examines observed harvest choices derived from satellite imagery and tests for relationships between harvest probability and location, quality, and ownership attributes of the site. Results indicate that the overall probability of harvesting for public lands is significantly lower than for private lands. Substantially different disturbance patterns relative to location attributes are also established for these groups. Results suggest a way to include spatially explicit information regarding private land management in public land management plans. An example demonstrates how alternative uses of public lands might be considered in the broader context of a multiple ownership landscape.     

A dynamic pricing approach for returned products in integrated forward/reverse logistics network design

During the last decade, the stringent pressures from environmental and social requirements have spurred an interest in designing a reverse logistics network. In this paper, we address the problem of designing and planning a multi-echelon, multi-period, multi-commodity and capacitated integrated forward/reverse logistics network. Returned products are categorized with respect to their quality levels, and a different acquisition price is offered for each return type. Furthermore, the reservation incentive of customers, the expected price of customers for one unit of used product described by uniform distribution, is applied to model the customers’ return willingness. Due to the fact that the remaining worthwhile value in the used products is the corporation’s key motivation for buying them from customers, a dynamic pricing approach is developed to determine the acquisition price for these products and based on it determine the percentage of returned products collected from customer zones. The used products’ acquisition prices at each time period are determined based on the customers’ return willingness by each collection center.     

Dynamic price dispersion in Bertrand–Edgeworth competition

This paper studies a dynamic oligopoly model of price competition under demand uncertainty. Sellers are endowed with one unit of the good and compete by posting prices in every period. Buyers each demand one unit of the good and have a common reservation price. They have full information regarding the prices posted by each firm in the market; hence, search is costless. The number of buyers coming to the market in each period is random. Demand uncertainty is said to be high if there are at least two non-zero demand states that give a seller different option values of waiting to sell. Our model features a unique symmetric Markov perfect equilibrium in which price dispersion prevails if and only if the degree of demand uncertainty is high. Several testable theoretical implications on the distribution of market prices are derived.     

上海燃料油期货市场价格发现功能的实证研究

本文利用协整检验、Granger因果检验、误差修正模型和Garbade-Silber模型对上海燃料油期货的价格发现功能进行了探讨,分析了期货与现货价格之间的相互关系,刻画了期货与现货市场在价格发现功能中作用的大小,并由此说明上海燃料油期货市场的效率。结果表明,燃料油的期货价格与现货价格之间存在协整关系,期货市场具有良好的价格发现功能,这对我国建设完整的石油期货市场具有指导意义。     

A powerful wild bootstrap diagnosis of panel unit roots under linear trends and time-varying volatility

Noting that standard panel unit root tests (PURTs) are not reliable in the presence of time varying volatility, recent papers have suggested a few heteroskedasticity–robust PURTs. These tests do not remain pivotal, however, if they are applied on detrended data. Building on recent asymptotic results for bootstrap approximations (Smeekes and Urbain in A multivariate invariance principle for modified wild bootstrap methods with an application to unit root testing, 2014), we provide simulation evidence that recursive detrending followed by a wild bootstrap correction leads to very good size precision for a variety of PURTs designed for testing against panel stationarity formalized with a cross sectionally homogenous autoregressive parameter. With respect to power, the bootstrap variant of the original nonrobust test of Levin et al. (J Econom 108(1):1–24, 2002) turns out to be the most effective among alternative tests. At the implementation side, performing the wild bootstrap correction using the so-called Rademacher distribution is found to be the most effective for both size and power properties of panel unit root inference by means of wild bootstrap based critical values. The empirical illustration shows that GDP per capita is best characterized as a unit root process.