随机波动率在铜矿矿业权价值评估中的应用

    Application of stochastic volatility in the evaluation of copper mining right value

    • 摘要: 矿业权相关的经济活动涉及金额巨大、不确定性高、投资风险大,实物期权法考虑到矿业权开发和管理的不确定性,能提高管理者的决策灵活性,在评估矿业权价值时具有优越性。波动率是实物期权法中的一个重要参数,对价值评估至关重要。然而该参数通常认为是矿产资源价格的波动,并且在整个生命周期中恒定不变,存在一定的局限性。以铜矿产资源为例,通过分析铜价格收益率的特征,建立基于广义自回归条件异方差(GARCH)族模型的矿产资源价格波动率模型,进而在矿山服务年限内生成随机价格波动率,进一步引入成本波动率,评估矿业权价值。实例计算结果表明:t分布下EGARCH(1,1)模型的拟合效果最优,加入了成本波动率的矿业权价值高于由单一价格波动率确定的矿业权价值。不仅考虑了价格波动率随机变化的实际情况,也考虑了成本波动率对矿产资源项目波动的影响。新方法得到的矿业权价值评估结果更加客观真实,能够为实物期权法的发展提供理论支撑,有利于管理者更好地掌握灵活性价值,根据未来信息进行决策。

       

      Abstract: Vast capital, a great degree of uncertainty, and high investment risk are the characteristics of the economic activities of mining right. With the application of the real option method, uncertainty can be considered in the process of mining right development and management. It is significant for managers to increase the importance of flexibility in making decisions, thus, the method offers significant advantages in evaluating the value of mining right. As an important parameter in the real option pricing model, volatility plays a key role in the value evaluation. However, there are some restrictions that the parameter is assumed to be equivalent to the volatility of mineral product prices and is mostly treated as a constant during the complete life cycle. Taking copper mineral resources as an example, a mineral resource price volatility model based on generalized autoregressive conditional heteroscedasticity (GARCH) family models is established by analyzing the characteristics of copper price yield. Stochastic price volatility is subsequently generated during the mine service life, and cost volatility is additionally introduced to assess the mining rights value. The results indicate the EGARCH(1,1) model has the best-fitting effect under the t distribution and the mining right value with cost volatility is higher than that determined by single price volatility. Based on the actual occurrence of random variation in volatility, the impact of price and cost volatility on the natural resources value is examined. The new approach increases the objectivity and realism of valuation results and can help managers better understand the flexibility value and make decisions based on future information.

       

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