[论文解读] Bayesian Semi-parametric Realized-CARE Models for Tail Risk Forecasting Incorporating Range and Realized Measures

Richard Gerlach, Chao Wang|arXiv (Cornell University)|Sep 11, 2015

Financial Risk and Volatility Modeling参考文献 40被引用 4

一句话总结

本文提出了一种贝叶斯半参数Realized- CARE模型，将范围和已实现测度（已实现方差与已实现范围）整合到CARE框架内的测量方程中，从而提升尾部风险预测能力。通过二次拟合方法，该模型提高了分位数水平网格搜索的精度与速度，在6只指数和3种资产的VaR与预期短缺风险预测中，优于GARCH、CARE与Realized-GARCH模型，尤其在子采样已实现范围下表现更优。

ABSTRACT

A new framework named Realized Conditional Autoregressive Expectile (Realized- CARE) is proposed, through incorporating a measurement equation into the conventional CARE model, in a framework analogous to Realized-GARCH. The Range and realized measures (Realized Variance and Realized Range) are employed as the dependent variables of the measurement equation, since they have proven more efficient than return for volatility estimation. The dependence between Range & realized measures and expectile can be modelled with this measurement equation. The grid search accuracy of the expectile level will be potentially improved with introducing this measurement equation. In addition, through employing a quadratic fitting target search, the speed of grid search is significantly improved. Bayesian adaptive Markov Chain Monte Carlo is used for estimation, and demonstrates its superiority compared to maximum likelihood in a simulation study. Furthermore, we propose an innovative sub-sampled Realized Range and also adopt an existing scaling scheme, in order to deal with the micro-structure noise of the high frequency volatility measures. Compared to the CARE, the parametric GARCH and the Realized-GARCH models, Value-at-Risk and Expected Shortfall forecasting results of 6 indices and 3 assets series favor the proposed Realized-CARE model, especially the Realized-CARE model with Realized Range and sub-sampled Realized Range.

研究动机与目标

• 通过将高频范围与已实现测度整合进CARE框架，提升尾部风险预测的准确性。
• 通过子采样已实现范围与现有缩放方案，缓解高频波动率测度中的微结构噪声问题。
• 在贝叶斯估计框架下，利用二次拟合方法提升分位数水平网格搜索的效率与准确性。
• 证明所提出的Realized-CARE模型在风险度量预测方面，优于参数化的GARCH、CARE与Realized-GARCH模型。

提出的方法

• 在传统CARE模型中引入测量方程，将分位数与范围及已实现测度（已实现方差与已实现范围）关联。
• 采用贝叶斯自适应马尔可夫链蒙特卡洛方法进行估计，相比最大似然法，提升了稳健性与准确性。
• 应用二次拟合目标搜索，加速最优分位数水平的网格搜索过程。
• 引入子采样已实现范围，以减轻高频数据中的微结构噪声。
• 采用现有缩放方案，进一步降低已实现测度中的噪声。
• 在测量方程中通过半参数、灵活的结构建模分位数与已实现测度之间的依赖关系。

实验结果

研究问题

• RQ1 将范围与已实现测度整合进CARE模型，能否提升尾部风险预测性能？
• RQ2 所提出的测量方程在多大程度上提升了分位数水平网格搜索的准确度与速度？
• RQ3 在Realized-CARE背景下，贝叶斯自适应MCMC估计方法是否优于最大似然法？
• RQ4 对已实现范围进行子采样在多大程度上可减少微结构噪声并提升预测准确性？
• RQ5 Realized-CARE模型在VaR与预期短缺风险预测方面，与GARCH、CARE及Realized-GARCH模型相比表现如何？

主要发现

• 在6只指数与3种资产的预测中，采用已实现范围与子采样已实现范围的Realized-CARE模型在VaR与预期短缺风险预测方面表现最强。
• 在模拟研究中，贝叶斯自适应MCMC估计方法相比最大似然法展现出更优的准确性。
• 二次拟合目标搜索显著提升了分位数水平网格搜索的速度，且未牺牲准确性。
• 将范围与已实现测度整合进测量方程，增强了模型捕捉尾部风险动态的能力。
• 子采样已实现范围能有效减少微结构噪声，提升波动率测度的可靠性。
• 所提出的模型在样本外风险预测准确性方面，始终优于参数化的GARCH、CARE与Realized-GARCH模型。