证券交易所数据的贝叶斯极值分析
Bayesian Extreme Value Analysis of Stock Exchange Data
摘要：
偿付能力II指令和偿付能力评估和管理（南非的对应版本）给出了基于99.5%风险价值（VaR）计算的偿付能力资本要求。这一计算涉及到对单个风险的汇总。当考虑金融工具的对数回报时，特别是股票价格，不时会观察到极端的损失，这些损失通常不适合为常规交易行为提出的任何模型。精确建模这些极端损失的问题得到解决，这反过来又有助于计算尾部概率，如99.5%的风险价值。重点是广义帕累托分布（GPD）超过阈值的拟合。我们展示了如何客观贝叶斯方法可以提高参数估计和计算的风险措施。最后，我们考虑阈值的选择。所有方面都用约翰内斯堡证券交易所（JSE）的股票损失来说明。
英文摘要：
The Solvency II Directive and Solvency Assessment and Management (the South African equivalent) give a Solvency Capital Requirement which is based on a 99.5% Value-at-Risk (VaR) calculation. This calculation involves aggregating individual risks. When considering log returns of financial instruments, especially with share prices, there are extreme losses that are observed from time to time that often do not fit whatever model is proposed for the regular trading behaviour. The problem of accurately modelling these extreme losses is addressed, which, in turn, assists with the calculation of tail probabilities such as the 99.5% VaR. The focus is on the fitting of the Generalized Pareto Distribution (GPD) beyond a threshold. We show how objective Bayes methods can improve parameter estimation and the calculation of risk measures. Lastly we consider the choice of threshold. All aspects are illustrated using share losses on the Johannesburg Stock Exchange (JSE).
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