doi:10.1016/j.jedc.2004.09.003
Copyright © 2004 Elsevier B.V. All rights reserved.
Commodity markets, price limiters and speculative price dynamics
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Xue-Zhong Hea and Frank H. Westerhoffb, 
, 
aSchool of Finance and Economics, University of Technology, Sydney, Australia
bDepartment of Economics, University of Osnabrueck, Rolandstrasse 8, D-49069 Osnabrueck, Germany
Received 18 December 2003;
accepted 16 September 2004.
Available online 17 November 2004.
Abstract
We develop a behavioral commodity market model with consumers, producers and heterogeneous speculators to characterize the nature of commodity price fluctuations and to explore the effectiveness of price stabilization schemes. Within our model, we analyze how nonlinear interactions between market participants can create either bull or bear markets, or irregular price fluctuations between bull and bear markets through a (global) homoclinic bifurcation. Both the imposition of a bottoming price level (to support producers) or a topping price level (to protect consumers) can eliminate such homoclinic bifurcations and hence reduce market price volatility. However, simple policy rules, such as price limiters, may have unexpected consequences in a complex environment: a minimum price level decreases the average price while a maximum price limit increases the average price. In addition, price limiters influence the price dynamics in an intricate way and may cause volatility clustering.
Keywords: Commodity markets; Price stabilization; Simple limiters; Technical and fundamental analysis; Bifurcation analysis; Chaos control
JEL classification: D84; G18; Q11
Fig. 1. Bifurcation diagrams for parameters b and c using different initial conditions. The parameters are increased in 500 steps as indicated on the axis. Log prices are plotted from t=500–600. The other parameters are a=1, b=4.5, c=1.5, d=1, m=1 and F=0.
Fig. 2. Homoclinic bifurcation of the map without price limiter (a)–(c) and with price limiter (d). The other parameters are a=1, c=1.5, d=1, m=1 and F=0. (a) b=4, (b) b=4.36, (c) b=4.5 and (d) b=4.5 and Smin=-1.6.
Fig. 3. Local stability region Y for the log of the fundamental value F and Z for the two non-fundamental steady states S± in parameter space (b, c). In addition, pitchfork, flip and homoclinic bifurcation curves. The other parameters are a=1, d=1, m=1 and F=0.
Fig. 4. The top panel shows the unrestricted evolution of the commodity's log price in the time domain. The bottom panel shows the same, but with a lower price boundary of Smin=−1.6. The other parameters are a=1, b=4.5, c=1.5, d=1, m=1 and F=0.
Fig. 5. The bifurcation diagrams in the first line of panels show how log prices react to more restrictive price boundaries. Log price limits are varied in 500 steps and log prices are plotted from t=500–600. The parameter setting is as in Fig. 4. The second and third lines of panels show the mean and the variance of the price process (buffeted with dynamic noise N(0, 0.1). All statistics are based on 10,000 observations.
Fig. 6. The top panel shows log price dynamics when the central authority switches between log price limiters Smin=−1.3 and Smax=1.3. A change in regime occurs if the buffer stock exceeds a level of about ±15. The bottom panel shows the corresponding evolution of the buffer stock. The other parameters are a=1, b=4.5, c=1.5, d=1, m=1 and F=0.
Fig. 7. Log price dynamics under different regimes. First panel: Smin=−1.25, interrupted every 100 periods. Second panel: Smin=−1.3, buffeted with dynamic noise N(0, 0.3). Third panel: Smin=−1.3 and Smax=1.3, both buffeted with dynamic noise N(0, 0.3). Fourth panel: Log price limiters as first-order auto-regressive processes around ±1.3 with AR coefficients of 0.975 and noise N(0, 0.1). The other parameters are a=1, b=4.5, c=1.5, d=1, m=1 and F=0.
Corresponding author. Tel.: +49 0 541 969 2743; fax: +49 0 541 969 12742.
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