论文标题
蒙特 - 卡洛的估计
Monte-Carlo Estimation of CoVaR
论文作者
论文摘要
$ {\ rm covar} $是财务系统风险的最重要措施之一。它被定义为有条件有条件的金融投资组合有危险的风险。在本文中，我们首先开发了基于蒙特 - 卡洛模拟的Covar的批处理估计量，并研究其一致性和渐近态性。我们表明，批处理估计器的最佳收敛速率为$ n^{ - 1/3} $，其中$ n $是样本尺寸。然后，我们开发出对投资组合损失的Delta-Gamma近似值下的重要性抽样估计器，我们表明估算器的收敛速度为$ n^{ - 1/2} $。数值实验支持我们的理论发现，并表明两个估计器都可以很好地工作。
${\rm CoVaR}$ is one of the most important measures of financial systemic risks. It is defined as the risk of a financial portfolio conditional on another financial portfolio being at risk. In this paper we first develop a Monte-Carlo simulation-based batching estimator of CoVaR and study its consistency and asymptotic normality. We show that the optimal rate of convergence of the batching estimator is $n^{-1/3}$, where $n$ is the sample size. We then develop an importance-sampling inspired estimator under the delta-gamma approximations to the portfolio losses, and we show that the rate of convergence of the estimator is $n^{-1/2}$. Numerical experiments support our theoretical findings and show that both estimators work well.
