|
|
- 2018
极值指标下平稳序列的风险测度
|
Abstract:
平稳金融序列存在相依性，不满足独立同分布假设下极值理论的条件约束.讨论了极值指标下平稳随机序列的风险测度，通过估计极值指标θ并修正广义极值分布的位置参数和尺度参数，得到平稳随机序列的风险值.实证和检验表明平稳金融序列需要极值指标修正模型，提高风险值估计的准确度.
The stationary financial sequence is not independent while it does not satisfy the requirement of the conditional constraint of the extreme value theory under the consumption of modified independent identical distribution (i.i.d.). In this paper, we discuss the risk measurement of the stationary random sequence under the extremal index, and derive the valve at risk of the stationary random sequence by estimating the extremal index and modifying the position parameter and the scale parameter of the GEV. Empirical and test results show that the stationary financial sequence needs the extremal index to improve the accuracy of the VaR estimation
| [1] | RUEY S T. Analysis of Financial Time Series[M]. 3rd ed. Hoboken: John Wiley & Sons, 2012. |
| [2] | 赵智, 李兴绪. 非寿险中巨额损失数据的拟合与精算[J]. 数理统计与管理, 2010, 29(5): 336-347. |
| [3] | 宋坤, 陈野华. 基于变点理论的POT模型阈值确定方法——对操作风险经济资本的度量[J]. 统计与信息论坛, 2011, 26(7): 23-27. |
| [4] | TOTI？ S, BULAJI？ M, VLASTELICA T. Empirical Comparison of Conventional Methods and Extreme Value Theory Approach in Value-at-Risk Assessment[J]. Business Management, 2011, 5(33): 12810-12818. |
| [5] | BHATTACHARYYA M, SIDDARTH M. A Comparison of VaR Estimation Procedures for Leptokurtic Equity Index Returns[J]. Journal of Mathematical Finance, 2012, 2(1): 13-30. DOI:10.4236/jmf.2012.21002 |
| [6] | ALEXANDER M N, RUDIGER F. Estimation of Tail-Related Risk Measures for Heteroscedastic Financial Time Series:an Extreme Value Approach[J]. Journal of Empirical Finance, 2000, 7: 271-300. DOI:10.1016/S0927-5398(00)00012-8 |
| [7] | LEADBETTER M R, LINDGREN G, ROOTZEN H. Extremes and Related Properties of Random Sequences and Processes[M]. Berlin: Springer, 1983. |
| [8] | LOYNES R. Extreme Values in Uniformly Mixing Stationary Stochastic Processes[J]. Annals of Mathematical Statistics, 1965, 36: 993-999. DOI:10.1214/aoms/1177700071 |
