基于套利定价理论的采矿权估价模型构建研究
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摘要
采矿权估价研究的最终目标是能够使矿产企业在从事生产经营活动中获取利润,采矿权价值是采矿权合约所承载的矿产资源储藏量价值,其价值通过矿产品的销售而转移,并以价格来表现。因此,采矿权的估价不仅要反应矿产资源储藏量价值的变化规律,还要符合矿产品市场价格的变化动态。由于矿产资源的禀赋,垄断是矿产资源市场的基本特征之一,随着金融资本、投机资本渗透于从勘探到矿产品市场流通的各个环节,及金融资本和产业资本相结合,使矿产品尤其是大宗矿产品被指数化金融化,矿产资源采矿权所表现的金融属性,严重冲击现有的采矿权估价模式。金融资本和产业资本垄断与操纵市场价格使矿产企业将承担着巨大的价格波动风险。在这样的市场环境中,矿产企业既要规避价格波动风险,又要实现获利目标,当然需要规避价格风险的工具。那么,基于套利定价理论的采矿权估价方法或许是矿产企业为采矿权估价的较好选择。
本文分析了采矿权的基本属性、价值特征、市场特点和现行采矿权估价方法；探讨了采矿权市场上套利机会的存在性、存在原因及其判别方法。表明应用套利定价理论为采矿权估价既符合采矿权市场的特点,顺应矿产品市场变化的趋势,又符合国家对稀缺性矿产资源可持续利用方针的精要,是可行的和必要的。
根据建模需要,选取套利收益、采矿权的经济价值区间、矿产品价格、价格波动率、矿产资源储藏量、开采速度和回采率为主要建模参数。针对采掘业的特点和各参数在矿产资源市场上的变化特征,构建了套利收益变动模型,并模拟了套利者的行为模式；以本量利的分析方法,推导出测算开采风险的距离和可能产生的停止开采频率,为矿产开采企业预测开采风险提供数量化的分析工具,并以此来判断采矿权的有效价值区间；探讨了在市场信息的作用下,矿产品价格在均衡与非均衡之间转变的动力学演变,区分了在影响矿产品价格的因素中能够均驱使价格回复均值的因素和不能回复的因素,用以说明在储藏量一定的情况下,储藏量随开采进程而减少,这种减少导致的矿产品价格变化是刚性的,不能回复的；在储藏量一定的条件下,探讨了开采速度、回采率、开采成本和市场结构等导致储藏量减少的耗竭性因素对开采行为和矿产品价格的冲击,确定在垄断条件下的最优开采条件和最佳开采速度,构建矿产品价格服从跳跃一一扩散过程的动态模型,并模拟了其运动趋势；将矿产资源开采划分四个阶段,分别建立各阶段采矿权价值的计算模型,以此求解各阶段的波动率,在一定程度上解决波动率的时变性问题；根据开采实践数据分别计算了矿山在评估年限和矿山服务年限内各年度的采矿权价值,并画出了采矿权价值的年度分布图。图形显示采矿权价值分布与矿产品价格动态趋势相吻合,以此验证了相关参数在矿产品和采矿权价格模型中的合理性。通过对估价参数的研究,构建了基于套利定价理论的采矿权估价模型。
The final objective of mining rights evaluation study is to enable mining enterprises gain profit in production and operating activities.The value of mining right, i.e. the value of mineral reserves specified in mining rights contract, is transferred by sales of mineral products and expressed by price. Therefore, mining rights evaluation shall not only reflect the changing law of the value of mineral reserves, but also conform to the trends of market price. Monopoly is one of the basic features of mineral resources market due to the nature of mineral resources. As the financial capital and risk capital infiltrate into the whole mineral industry from exploration to marketing and the combination of financial capital and industrial capital, the mineral products, especially bulk products have been indexed and financialized. The financial attributes of mining rights exert a strong impact on current mining rights evaluation model. Mining enterprises will face great risk of price fluctuation when market price is monopolized and manipulated by financial capital and industrial capital. In such market circumstances, mining enterprises need a tool which can help them avoid risk of price fluctuation and achieve profit target. Then, mining rights evaluation method based on arbitrage pricing theory may be a good choice for mining enterprises.
This paper analyzes the basic attributes, value characteristics, market features and current evaluation method of mining rights; discusses the presence of arbitrage chances in mining rights market, the reasons of it and how to identify it. This paper shows that it is necessary and feasible to use arbitrage pricing theory to evaluate the mining rights, as this method conforms to the features and trends of mining rights market, as well as the national regulation on sustainable use of rare mineral resources.
Based on requirement, the following items have been selected as main modeling parameters:arbitrage income, economic value interval of mining rights, mineral prices, price fluctuation ratio, mineral reserves, mining rate and recovery ratio. According to the features of extractive industry and each parameter's change characteristics in mineral resources market, arbitrage income fluctuant model has been established and arbitrager's behavioral pattern simulated. Thought cost-volume-profit (CVP) analysis, the distance involved in mining risk has been derived as well as the frequency of potential stopping mining event, which can be used as an analysis tool for mining enterprises to quantify the mining risk and identify the valid value interval of mining rights. This paper discusses the dynamic evolution of mineral prices from equilibrium to disequilibrium driven by market information, distinguishes which factors influencing mineral prices can drive the price recover average level and which cannot, in order to explain that under the circumstance of given mineral reserves, the mineral resources will decrease as the mining operation is proceeding, as a result, the price change caused by this decrease is rigid and non-recoverable. Further, this paper, under the circumstance of given mineral reserves, discusses the impact on mining activities and mineral prices caused by factors leading to decrease of mineral reserves such as mining rate, recovery ratio, mining cost and market structure. In this paper, the best mining condition and mining rate has been determined under monopoly environment, dynamic model of jump-diffusion process for mineral products established and its move trends stimulated. This paper divides the mining operation into four stages, and establishes models for each stage to compute the value of mining rights, so as to get the fluctuation rate of each stage, and solve the time variance of fluctuation rate to some extent. The annual mining rights values during the evaluation period and service period of mines have been calculated by using data of mining practice. And annual distribution map of price has been drawn to indicate that the distribution of mining rights value is in accordance with dynamic trends of mineral prices, which justify the relevant parameters applied in models of mineral products and prices of mining rights. Finally, the mining rights evaluation model based on arbitrage pricing theory has been established through studies of evaluation parameters.
本文分析了采矿权的基本属性、价值特征、市场特点和现行采矿权估价方法；探讨了采矿权市场上套利机会的存在性、存在原因及其判别方法。表明应用套利定价理论为采矿权估价既符合采矿权市场的特点,顺应矿产品市场变化的趋势,又符合国家对稀缺性矿产资源可持续利用方针的精要,是可行的和必要的。
根据建模需要,选取套利收益、采矿权的经济价值区间、矿产品价格、价格波动率、矿产资源储藏量、开采速度和回采率为主要建模参数。针对采掘业的特点和各参数在矿产资源市场上的变化特征,构建了套利收益变动模型,并模拟了套利者的行为模式；以本量利的分析方法,推导出测算开采风险的距离和可能产生的停止开采频率,为矿产开采企业预测开采风险提供数量化的分析工具,并以此来判断采矿权的有效价值区间；探讨了在市场信息的作用下,矿产品价格在均衡与非均衡之间转变的动力学演变,区分了在影响矿产品价格的因素中能够均驱使价格回复均值的因素和不能回复的因素,用以说明在储藏量一定的情况下,储藏量随开采进程而减少,这种减少导致的矿产品价格变化是刚性的,不能回复的；在储藏量一定的条件下,探讨了开采速度、回采率、开采成本和市场结构等导致储藏量减少的耗竭性因素对开采行为和矿产品价格的冲击,确定在垄断条件下的最优开采条件和最佳开采速度,构建矿产品价格服从跳跃一一扩散过程的动态模型,并模拟了其运动趋势；将矿产资源开采划分四个阶段,分别建立各阶段采矿权价值的计算模型,以此求解各阶段的波动率,在一定程度上解决波动率的时变性问题；根据开采实践数据分别计算了矿山在评估年限和矿山服务年限内各年度的采矿权价值,并画出了采矿权价值的年度分布图。图形显示采矿权价值分布与矿产品价格动态趋势相吻合,以此验证了相关参数在矿产品和采矿权价格模型中的合理性。通过对估价参数的研究,构建了基于套利定价理论的采矿权估价模型。
The final objective of mining rights evaluation study is to enable mining enterprises gain profit in production and operating activities.The value of mining right, i.e. the value of mineral reserves specified in mining rights contract, is transferred by sales of mineral products and expressed by price. Therefore, mining rights evaluation shall not only reflect the changing law of the value of mineral reserves, but also conform to the trends of market price. Monopoly is one of the basic features of mineral resources market due to the nature of mineral resources. As the financial capital and risk capital infiltrate into the whole mineral industry from exploration to marketing and the combination of financial capital and industrial capital, the mineral products, especially bulk products have been indexed and financialized. The financial attributes of mining rights exert a strong impact on current mining rights evaluation model. Mining enterprises will face great risk of price fluctuation when market price is monopolized and manipulated by financial capital and industrial capital. In such market circumstances, mining enterprises need a tool which can help them avoid risk of price fluctuation and achieve profit target. Then, mining rights evaluation method based on arbitrage pricing theory may be a good choice for mining enterprises.
This paper analyzes the basic attributes, value characteristics, market features and current evaluation method of mining rights; discusses the presence of arbitrage chances in mining rights market, the reasons of it and how to identify it. This paper shows that it is necessary and feasible to use arbitrage pricing theory to evaluate the mining rights, as this method conforms to the features and trends of mining rights market, as well as the national regulation on sustainable use of rare mineral resources.
Based on requirement, the following items have been selected as main modeling parameters:arbitrage income, economic value interval of mining rights, mineral prices, price fluctuation ratio, mineral reserves, mining rate and recovery ratio. According to the features of extractive industry and each parameter's change characteristics in mineral resources market, arbitrage income fluctuant model has been established and arbitrager's behavioral pattern simulated. Thought cost-volume-profit (CVP) analysis, the distance involved in mining risk has been derived as well as the frequency of potential stopping mining event, which can be used as an analysis tool for mining enterprises to quantify the mining risk and identify the valid value interval of mining rights. This paper discusses the dynamic evolution of mineral prices from equilibrium to disequilibrium driven by market information, distinguishes which factors influencing mineral prices can drive the price recover average level and which cannot, in order to explain that under the circumstance of given mineral reserves, the mineral resources will decrease as the mining operation is proceeding, as a result, the price change caused by this decrease is rigid and non-recoverable. Further, this paper, under the circumstance of given mineral reserves, discusses the impact on mining activities and mineral prices caused by factors leading to decrease of mineral reserves such as mining rate, recovery ratio, mining cost and market structure. In this paper, the best mining condition and mining rate has been determined under monopoly environment, dynamic model of jump-diffusion process for mineral products established and its move trends stimulated. This paper divides the mining operation into four stages, and establishes models for each stage to compute the value of mining rights, so as to get the fluctuation rate of each stage, and solve the time variance of fluctuation rate to some extent. The annual mining rights values during the evaluation period and service period of mines have been calculated by using data of mining practice. And annual distribution map of price has been drawn to indicate that the distribution of mining rights value is in accordance with dynamic trends of mineral prices, which justify the relevant parameters applied in models of mineral products and prices of mining rights. Finally, the mining rights evaluation model based on arbitrage pricing theory has been established through studies of evaluation parameters.
引文
①《桂林矿产地质研究院栗木钽铌锡多金属矿采矿权评估报告书》(矿通评报字[2009]第89号)。
①王红英裴毅飞刘洁.“铁矿石金融化”的本质及潜在风险,百度文库：中期研究院2010年8月9日。
②警惕铁矿石金融化风险”,2010年11月2日《中国证券报》。
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