Simulating risk measures via asymptotic expansions for relative errors
提出一种基于相对误差渐近展开的通用框架，用于模拟风险价值（VaR）和预期亏损（ES）等风险度量，适用于广泛的相关数据，在0.001分位数水平下仍快速准确。
Abstract Risk measures, such as value‐at‐risk and expected shortfall, are widely used in finance. With the necessary sample size being computed using asymptotic expansions for relative errors, we propose a general framework to simulate these risk measures for a wide class of dependent data. The asymptotic expansions are new even for independent and identical data. An extensive numerical study is conducted to compare the proposed algorithm against existing algorithms, showing that the new algorithm is easy to implement, fast and accurate, even at the 0.001 quantile level. Applications to the estimation of intra‐horizon risk and to a comparison of the relative errors of value‐at‐risk and expected shortfall are also given.