Conditional value-at-risk (CVaR) and conditional expected shortfall (CES) are widely adopted risk measures which help monitor potential tail risk while adapting to evolving market information. In this paper, we propose an approach to constructing simultaneous confidence bands (SCBs) for tail risk as measured by CVaR and CES, with the confidence bands uniformly valid for a set of tail levels. We consider one-sided tail risk (downside or upside tail risk) as well as relative tail risk (the ratio of upside to downside tail risk). A general class of location-scale models with heavy-tailed innovations is employed to filter out the return dynamics. Then, CVaR and CES are estimated with the aid of extreme value theory. In the asymptotic theory, we consider two scenarios: (i) the extreme scenario that allows for extrapolation beyond the range of the available data and (ii) the intermediate scenario that works exclusively in the case where the available data are adequate relative to the tail level. For finite-sample implementation, we propose a novel bootstrap procedure to circumvent the slow convergence rates of the SCBs as well as infeasibility of approximating the limiting distributions. A series of Monte Carlo simulations confirm that our approach works well in finite samples.

有条件风险价值（CVaR）和有条件预期缺口（CES）是广泛采用的风险衡量标准，有助于监控潜在的尾部风险，同时适应不断变化的市场信息。在本文中，我们提出了一种通过 CVaR 和 CES 衡量的尾部风险构建同步置信带 (SCB) 的方法，置信带对于一组尾部水平一致有效。我们考虑单边尾部风险（下行或上行尾部风险）以及相对尾部风险（上行与下行尾部风险之比）。采用一类具有重尾创新的位置尺度模型来过滤返回动态。然后，借助极值理论估计CVaR和CES。在渐近理论中，我们考虑两种情况：(i) 允许在可用数据范围之外进行推断的极端情景，以及 (ii) 仅在可用数据相对于尾部水平足够的情况下才适用的中间情景。对于有限样本实现，我们提出了一种新颖的引导程序来避免 SCB 收敛速度慢以及逼近极限分布的不可行性。一系列蒙特卡洛模拟证实我们的方法在有限样本中效果良好。