石油市场复杂性及仿真研究
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摘要
石油市场是一个典型的复杂系统，除了受到市场供求关系的影响外，还受到其他众多因素的影响，如经济形势、国际关系、突发事件、投机行为和市场心理等。这些因素的共同作用使得石油市场变化异常复杂，任何一个因素微小变化都有可能造成难以预料的结果。大量实证研究表明，国际石油市场是一个非线性的、具有混沌和分形特征的复杂系统；对于这样的复杂系统，传统的线性研究范式已经失效，基于还原论的研究思路不足以探求国际石油市场的内在动力学机制。为了探索国际石油市场及其价格问题的内在特征，得到相应的定性和定量分析结果，为我国有关石油战略的制定提供实证依据和决策支持，本文在复杂系统与复杂性理论框架内，采用混沌和分形分析方法，对国际石油市场复杂性问题进行了系统的实证分析和仿真研究。本文主要取得了如下创新：
(1)应用相空间重构技术，对Brent和WTI原油价格收益率的时间序列进行相空间重构；应用G-P算法，求得了不大于3的分数维吸引子的关联维度，表明上述系统是具有分形特征的低维动力学系统；应用Wolf方法得出了大于0的最大Lyapunov指数，给出了系统混沌存在的初步证据；利用关联积分求出了Kolmogorov熵，给出了对系统的混沌程度的估计以及对Brent和WTI原油价格进行有效性预测的时间尺度，如对于Brent日收益率的Kolmogorov熵为0.2787，相应的进行有效性预测的时间尺度小于36天。
(2)针对Brent和WTI原油价格、新加坡含铅和鹿特丹粗柴油价格等国际主要基准石油价格时间序列，应用R／S分析方法，探讨了国际油价系统中存在的分形特征，得到了不同时间标度下，上述市场油价的Hurst指数，发现了Hurst指数均大于0.5，从而说明上述系统是有偏的，具有正向持续性特征；引入V统计量分析了系统的长程记忆机制，发现均存在对历史信息的长期记忆性，并估算了长程记忆的非周期循环长度，如Brent的60日收益率的非周期循环长度约为683天；跟踪了不同时延下Hurst指数的演化轨迹，根据不同的动力学行为将其相应划分为三个阶段，并认为上述阶段的动力学行为分别由噪声交易商、生产商和基本面交易商所主导；应用多重分形分析方法，发现在被考察的系统中存在奇异多重分形，从而说明其分形结构存在不规则性和不均匀性。
(3)针对国际主要基准原油和成品油价格时间序列，结合投资者的投资时间尺度τ和收益预期ε进行研究，运用Zipf分析方法，将石油价格的τ-收益率序列映射为三字符序列(绝对频率)和二字符序列(相对频率)；通过在不同的时间标度下分析序列中价格波动的涨跌信息，得到价格看涨概率与看跌概率的偏差，发现在各特征时间标度下均存在大于0的偏差，且随着时间标度的增加而上升，这说明上述系统的价格行为都是不对称和有偏的；通过将绝对和相对频率结合τ和ε进行分析，发现τ和ε对于价格行为均会产生影响，总体上，时间标度越长，看涨概率越大；收益预期越高，对价格行为的扭曲越大；但是，投资者的收益预期一旦达到临界点，将不再能够扭曲价格行为，这意味着除非修改其过高的期望，否则投资者将被清除出市场。此外，尽管在定量结果上存在细微差别，就价格行为而言，Rotterdam成品油和Brent原油在定性意义上差别不大。
(4)引入了二维三状态类RFIM(Random Field Ising Model)市场模型，采用格点网络和Torus拓扑结构，引入了周期性边界条件，建立了一个由做市商和异构的agents组成的虚拟市场；同时，还引入了agent的自信度，agent间的耦合强度，agent的个性化收益率预期等参数，讨论了上述参数对虚拟市场价格收益率的影响。通过这个高度抽象化的模型，生成了大量的虚拟价格收益率数据，发现该市场可以很好地模拟金融市场的如波动聚集等典型现象；通过相空间重构技术，得到的关联积分展示出了和实证结果相符的明显的分形定性特征；在此基础上，进一步通过分形／多重分形分析方法，得到的Hurst指数与真实石油市场的实证结果比较接近。综上所述，发现该市场所生成的价格行为与真实市场的价格行为具有定性意义上的内在的一致性。这暗示了尽管真实市场展示出种种纷繁复杂的典型现象和动力学行为，其内在机理却可能是极其简单的。
在上述对国际石油价格问题的实证和仿真研究所得到的定性和定量结论的基础上，本文进一步对国际石油价格安全和相应的石油市场金融化改革等问题进行了政策研究，得出了相应的分析结论和政策建议，为中国石油战略和有关政策的制定提供了理论的和实证的依据以及决策参考。
In recent decades, with the rapid growth of China's economy and drastic fluctuations of international petroleum markets, oil price behaviors and dynamics have a great impact on both China's economy and social welfare. Petroleum markets, consisting of heterogeneous agents with different utilities, expectations and capabilities, are typical complex systems in that they are greatly influenced by many factors, such as macro-economic situations, international affairs, political and military outbursts, financial speculations, market psychology, etc, as well as fundamental factors like supply and demand. The mutual interactions among those factors make the market dynamics highly complex and even a minor disturbance of one factor can induce unexpectable outcomes. Numerous empirical studies put forward evidence that international petroleum markets are nonlinear dynamic systems with chaotic and fractal features. As for these complex systems, traditional linear paradigms are of nullification, while reductiomsm becomes one of major barriers to understand the true underlying dynamics and mechanisms of those markets.
In order to obtain the reliable analytical results and applicable strategies and policy suggestions, the dissertation applies the methods and approaches of Chaos and Fractal theories and Multi-Agent based System, to carry out systematical empirical and simulation study on the petroleum price dynamics mainly on the contexts of Complex Systems and Complexity Science, by investigating experimentally and empirically the underlying dynamics and mechanisms of those markets, thus to come to applicable conclusions of international price dynamics and behaviors, and thereby provide quantitative and qualitative evidence for the policy making of China's energy strategy.
The main contributions and findings of this dissertation can be summarized as follows:
(1) Using the Phase Space Reconstruction Technique (PSRT), the evidence of the existence of chaos are found in the time series of the monthly and daily Brent and WTI crude oil price fluctuations in the markets. By applying G-P algorithm, the low dimensional (less than 3) non-integer correlation dimensions are obtained, which imply that those above-mentioned systems are low dimensional deterministic chaotic systems with fractal features. Using a Wolf algorithm, the dissertation acquires positive largest Lyapunov exponents, thus identify the existence of chaos in all 4 systems under study. Furthermore, the dissertation also obtains positive Kolmogorov entropies which can be used for estimating the periods of effective prediction of Brent and WTI crude oil prices in markets, e.g., the Kolmogorov entropy of daily returns of Brent is 0.2787, which means the reliable prediction period be less than 36 days.
(2) The fractal behaviors for the prices are investigated in international petroleum price systems by using the Rescaled Range analysis (R/S analysis) based on the time series of Brent & WTI crude oil prices (daily spot) and Rotterdam & Singapore leaded gasoil prices (daily spot). The dissertation estimates the Hurst exponents of the systems under study, whose results are greater than 0.5 at all characteristic time scales, which imply that those systems are biased and consistent with positive persistency and fractal features. Furthermore, using V statistics, the dissertation discovers long-term memory effects in the systems and estimate the lengths of the persistent memory of historical information, e.g., 683 days is the approximate non-periodic cycles of the long-term memory in Brent 60-day returns. By tracing the evolution tracks of H(t)\s.t , three phases divided by different system dynamic behaviors are found and thus we put forward a hypothesis that the dynamics of the three phases are dominated by the three categories of heterogeneous agents, which are noise traders, producers and fundamentalists respectively. Finally, the empirical study also demonstrates nontrivial multifractal spectra in the petroleum price systems, which gives evidence of irregularity and heterogeneity in the fractal structures of the systems.
(3) Based on the time series of Brent crude oil and Rotterdam gasoil prices, the dissertation analyses the information of price fluctuations with the two important parametersτ(investor's time scale of investment) andε(investor's expectation of returns) by using Zipf-type analysis, i.e. by mapping theτ- returns of prices into binary sequences (relative frequencies) and 3-charactered sequences (absolute frequencies), which containing the fundamental information of price fluctuations. According to the quantitative results of above mentioned analysis, the dissertation obtains some non-trivial findings. Firstly, by analyzing the deviations of the ups and downs at different time scales, the dissertation finds that there exist non-zero (mainly positive) deviations which are getting greater as the time scales increasing, which imply the price systems are biased and asymmetric. Secondly, this dissertation investigates the parametersτandεempirically and identifies various types of investors' cognition patterns of price behaviors. Thirdly, the dissertation discusses the causes of formation of those cognition patterns and enormous distortion of price behaviors by the patterns and finds that generally speaking, the higher the parametersτgets, the probabilities of ups are greater; the greedier the investors are, the more distortions of price behaviors are from the actual price dynamics. Fourthly, as long asεreaches its critical points, it will not be able to distort the price behaviors because otherwise the investors will be cleared out of the markets. Finally, the comparisons between Brent and Rotterdam price systems show that although there are some minor differences of numerical results in the two systems, they are fundamentally similar regarding of their price behaviors.
(4) A virtual financial market model is introduced which is based upon an analogue of two-dimensional and three-state random field Ising model (RFIM) under a market maker scenario. By applying the grid network and torus topology, we introduced the periodic boundary condition and parameters of self confidence and idiocratical expectations of agents to the virtual market with heterogeneous agents and a market maker. Combining the scaling/multiscaling analysis, we acquired some non-trivial findings: first, in accordance with many empirical results, the price returns of this virtual market generated by this RFIM-type model display stylized facts in real markets, e.g. volatility clustering; secondly, we find that the inherent price behaviors have the surprising similarities with the real financial market returns in a qualitative sense; in addition to the above-mentioned findings, we find that the quantitative results, e.g. Hurst exponents, of the virtual markets are highly similar to those empirical results of the real ones. Our findings imply that although the real markets demonstrate complex superficial behaviors and phenomena, the innate dynamics of the real markets may be fundamentally simple.
Based on the above-mentioned quantitative and qualitative results, this dissertation carries out further policy studies of domestic petroleum markets and petroleum price risks respectively. Some applicable policy suggestions are proposed for China's energy strategy and policy-making of improving China's petroleum price security on the background of economical globalization and financial petroleum markets nowadays.
Through the above-mentioned systematic analyses of empirical and experimental results as well as relevant policy study, this dissertation arrives at a series of conclusions and policy suggestions.
(1)应用相空间重构技术，对Brent和WTI原油价格收益率的时间序列进行相空间重构；应用G-P算法，求得了不大于3的分数维吸引子的关联维度，表明上述系统是具有分形特征的低维动力学系统；应用Wolf方法得出了大于0的最大Lyapunov指数，给出了系统混沌存在的初步证据；利用关联积分求出了Kolmogorov熵，给出了对系统的混沌程度的估计以及对Brent和WTI原油价格进行有效性预测的时间尺度，如对于Brent日收益率的Kolmogorov熵为0.2787，相应的进行有效性预测的时间尺度小于36天。
(2)针对Brent和WTI原油价格、新加坡含铅和鹿特丹粗柴油价格等国际主要基准石油价格时间序列，应用R／S分析方法，探讨了国际油价系统中存在的分形特征，得到了不同时间标度下，上述市场油价的Hurst指数，发现了Hurst指数均大于0.5，从而说明上述系统是有偏的，具有正向持续性特征；引入V统计量分析了系统的长程记忆机制，发现均存在对历史信息的长期记忆性，并估算了长程记忆的非周期循环长度，如Brent的60日收益率的非周期循环长度约为683天；跟踪了不同时延下Hurst指数的演化轨迹，根据不同的动力学行为将其相应划分为三个阶段，并认为上述阶段的动力学行为分别由噪声交易商、生产商和基本面交易商所主导；应用多重分形分析方法，发现在被考察的系统中存在奇异多重分形，从而说明其分形结构存在不规则性和不均匀性。
(3)针对国际主要基准原油和成品油价格时间序列，结合投资者的投资时间尺度τ和收益预期ε进行研究，运用Zipf分析方法，将石油价格的τ-收益率序列映射为三字符序列(绝对频率)和二字符序列(相对频率)；通过在不同的时间标度下分析序列中价格波动的涨跌信息，得到价格看涨概率与看跌概率的偏差，发现在各特征时间标度下均存在大于0的偏差，且随着时间标度的增加而上升，这说明上述系统的价格行为都是不对称和有偏的；通过将绝对和相对频率结合τ和ε进行分析，发现τ和ε对于价格行为均会产生影响，总体上，时间标度越长，看涨概率越大；收益预期越高，对价格行为的扭曲越大；但是，投资者的收益预期一旦达到临界点，将不再能够扭曲价格行为，这意味着除非修改其过高的期望，否则投资者将被清除出市场。此外，尽管在定量结果上存在细微差别，就价格行为而言，Rotterdam成品油和Brent原油在定性意义上差别不大。
(4)引入了二维三状态类RFIM(Random Field Ising Model)市场模型，采用格点网络和Torus拓扑结构，引入了周期性边界条件，建立了一个由做市商和异构的agents组成的虚拟市场；同时，还引入了agent的自信度，agent间的耦合强度，agent的个性化收益率预期等参数，讨论了上述参数对虚拟市场价格收益率的影响。通过这个高度抽象化的模型，生成了大量的虚拟价格收益率数据，发现该市场可以很好地模拟金融市场的如波动聚集等典型现象；通过相空间重构技术，得到的关联积分展示出了和实证结果相符的明显的分形定性特征；在此基础上，进一步通过分形／多重分形分析方法，得到的Hurst指数与真实石油市场的实证结果比较接近。综上所述，发现该市场所生成的价格行为与真实市场的价格行为具有定性意义上的内在的一致性。这暗示了尽管真实市场展示出种种纷繁复杂的典型现象和动力学行为，其内在机理却可能是极其简单的。
在上述对国际石油价格问题的实证和仿真研究所得到的定性和定量结论的基础上，本文进一步对国际石油价格安全和相应的石油市场金融化改革等问题进行了政策研究，得出了相应的分析结论和政策建议，为中国石油战略和有关政策的制定提供了理论的和实证的依据以及决策参考。
In recent decades, with the rapid growth of China's economy and drastic fluctuations of international petroleum markets, oil price behaviors and dynamics have a great impact on both China's economy and social welfare. Petroleum markets, consisting of heterogeneous agents with different utilities, expectations and capabilities, are typical complex systems in that they are greatly influenced by many factors, such as macro-economic situations, international affairs, political and military outbursts, financial speculations, market psychology, etc, as well as fundamental factors like supply and demand. The mutual interactions among those factors make the market dynamics highly complex and even a minor disturbance of one factor can induce unexpectable outcomes. Numerous empirical studies put forward evidence that international petroleum markets are nonlinear dynamic systems with chaotic and fractal features. As for these complex systems, traditional linear paradigms are of nullification, while reductiomsm becomes one of major barriers to understand the true underlying dynamics and mechanisms of those markets.
In order to obtain the reliable analytical results and applicable strategies and policy suggestions, the dissertation applies the methods and approaches of Chaos and Fractal theories and Multi-Agent based System, to carry out systematical empirical and simulation study on the petroleum price dynamics mainly on the contexts of Complex Systems and Complexity Science, by investigating experimentally and empirically the underlying dynamics and mechanisms of those markets, thus to come to applicable conclusions of international price dynamics and behaviors, and thereby provide quantitative and qualitative evidence for the policy making of China's energy strategy.
The main contributions and findings of this dissertation can be summarized as follows:
(1) Using the Phase Space Reconstruction Technique (PSRT), the evidence of the existence of chaos are found in the time series of the monthly and daily Brent and WTI crude oil price fluctuations in the markets. By applying G-P algorithm, the low dimensional (less than 3) non-integer correlation dimensions are obtained, which imply that those above-mentioned systems are low dimensional deterministic chaotic systems with fractal features. Using a Wolf algorithm, the dissertation acquires positive largest Lyapunov exponents, thus identify the existence of chaos in all 4 systems under study. Furthermore, the dissertation also obtains positive Kolmogorov entropies which can be used for estimating the periods of effective prediction of Brent and WTI crude oil prices in markets, e.g., the Kolmogorov entropy of daily returns of Brent is 0.2787, which means the reliable prediction period be less than 36 days.
(2) The fractal behaviors for the prices are investigated in international petroleum price systems by using the Rescaled Range analysis (R/S analysis) based on the time series of Brent & WTI crude oil prices (daily spot) and Rotterdam & Singapore leaded gasoil prices (daily spot). The dissertation estimates the Hurst exponents of the systems under study, whose results are greater than 0.5 at all characteristic time scales, which imply that those systems are biased and consistent with positive persistency and fractal features. Furthermore, using V statistics, the dissertation discovers long-term memory effects in the systems and estimate the lengths of the persistent memory of historical information, e.g., 683 days is the approximate non-periodic cycles of the long-term memory in Brent 60-day returns. By tracing the evolution tracks of H(t)\s.t , three phases divided by different system dynamic behaviors are found and thus we put forward a hypothesis that the dynamics of the three phases are dominated by the three categories of heterogeneous agents, which are noise traders, producers and fundamentalists respectively. Finally, the empirical study also demonstrates nontrivial multifractal spectra in the petroleum price systems, which gives evidence of irregularity and heterogeneity in the fractal structures of the systems.
(3) Based on the time series of Brent crude oil and Rotterdam gasoil prices, the dissertation analyses the information of price fluctuations with the two important parametersτ(investor's time scale of investment) andε(investor's expectation of returns) by using Zipf-type analysis, i.e. by mapping theτ- returns of prices into binary sequences (relative frequencies) and 3-charactered sequences (absolute frequencies), which containing the fundamental information of price fluctuations. According to the quantitative results of above mentioned analysis, the dissertation obtains some non-trivial findings. Firstly, by analyzing the deviations of the ups and downs at different time scales, the dissertation finds that there exist non-zero (mainly positive) deviations which are getting greater as the time scales increasing, which imply the price systems are biased and asymmetric. Secondly, this dissertation investigates the parametersτandεempirically and identifies various types of investors' cognition patterns of price behaviors. Thirdly, the dissertation discusses the causes of formation of those cognition patterns and enormous distortion of price behaviors by the patterns and finds that generally speaking, the higher the parametersτgets, the probabilities of ups are greater; the greedier the investors are, the more distortions of price behaviors are from the actual price dynamics. Fourthly, as long asεreaches its critical points, it will not be able to distort the price behaviors because otherwise the investors will be cleared out of the markets. Finally, the comparisons between Brent and Rotterdam price systems show that although there are some minor differences of numerical results in the two systems, they are fundamentally similar regarding of their price behaviors.
(4) A virtual financial market model is introduced which is based upon an analogue of two-dimensional and three-state random field Ising model (RFIM) under a market maker scenario. By applying the grid network and torus topology, we introduced the periodic boundary condition and parameters of self confidence and idiocratical expectations of agents to the virtual market with heterogeneous agents and a market maker. Combining the scaling/multiscaling analysis, we acquired some non-trivial findings: first, in accordance with many empirical results, the price returns of this virtual market generated by this RFIM-type model display stylized facts in real markets, e.g. volatility clustering; secondly, we find that the inherent price behaviors have the surprising similarities with the real financial market returns in a qualitative sense; in addition to the above-mentioned findings, we find that the quantitative results, e.g. Hurst exponents, of the virtual markets are highly similar to those empirical results of the real ones. Our findings imply that although the real markets demonstrate complex superficial behaviors and phenomena, the innate dynamics of the real markets may be fundamentally simple.
Based on the above-mentioned quantitative and qualitative results, this dissertation carries out further policy studies of domestic petroleum markets and petroleum price risks respectively. Some applicable policy suggestions are proposed for China's energy strategy and policy-making of improving China's petroleum price security on the background of economical globalization and financial petroleum markets nowadays.
Through the above-mentioned systematic analyses of empirical and experimental results as well as relevant policy study, this dissertation arrives at a series of conclusions and policy suggestions.
引文
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