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arXiv · 2210.06148

Monte-Carlo Estimation of CoVaR

Weihuan Huang·Nifei Lin·L. Jeff Hong
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Abstract

${\rm CoVaR}$ 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.

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Weihuan Huang, Nifei Lin, L. Jeff Hong. 2022-10-12. Monte-Carlo Estimation of CoVaR. https://arxiv.org/abs/2210.06148

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