Compared with current risks, future risks are more important for investment decisions and risk management. This paper modifies the Square Root of Time Rule with the boosting additive quantile regression model to forecast multi-period horizon market risk. In J. P. Morgan's RiskMetrics Model, the k-period horizon value at risk (VaR) equals to . Since its assumptions are too strict, expected capacity of Risk Metrics is not so well. Taylor relaxed assumptions of this model, used the GARCH model to replace the IGARCH model, and obtained multi-period horizon VaR, which is a nonlinear function of the one-step-ahead volatility forecast .The conditional mean μ_t is zero in Taylor's model, but Tsay pointed out that this assumption (μ_t = 0) does not always hold. Therefore, we relax this assumption about the conditional mean, and obtain the VaR which is mixed function consisting of two parts, one is a linear function of conditional mean, and the other is a nonlinear function of , given the holding horizon k. For our mixed VaR function, we chose a more appropriate method, the boosting additive quantile regression model, to forecast multi-period horizon VaR. Taking log-returns of the Hang Seng Index from January 1, 2007 to November 1, 2016 as the sample, weforecast the 5-, 10-, 15-, and 20-day horizon VaRs, and compare the prediction accuracy of Morgan's model withour quantile regression model through likelihood ratio tests. Results show that VaR based on the quantile regression model is not only more accurate, but also sensitive to volatility, and is conducive to maintaining a reasonable risk reserve level for financial institutions, enabling them to pay less for regulation andachieve incentive compatibility.

中文翻译：

---

以boosting加性分位数回归为例，运用深度学习方法评估多期市场风险

与当前风险相比，未来风险对于投资决策和风险管理更为重要。本文利用增强加性分位数回归模型修正时间平方根规则来预测多期跨期市场风险。在 JP Morgan 的 RiskMetrics 模型中，k期风险值 (VaR) 等于。由于其假设过于严格，Risk Metrics 的预期能力不是很好。泰勒放宽了该模型的假设，用 GARCH 模型代替了 IGARCH 模型，得到了多期跨期 VaR，它是一步超前波动率预测的非线性函数。泰勒模型中的条件均值μt_为零, 但 Tsay 指出这个假设 ( μ_t = 0) 并不总是成立。因此，我们放宽对条件均值的假设，得到VaR，它是由两部分组成的混合函数，一个是条件均值的线性函数，另一个是 的非线性函数，给定保持期k. 对于我们的混合 VaR 函数，我们选择了一种更合适的方法，即增强加性分位数回归模型来预测多期跨期 VaR。以恒生指数 2007 年 1 月 1 日至 2016 年 11 月 1 日的对数收益为样本，预测 5、10、15 和 20 天的 VaR，并将 Morgan 模型的预测精度与通过似然比检验的分位数回归模型。结果表明，基于分位数回归模型的VaR不仅更加准确，而且对波动性敏感，有利于金融机构保持合理的风险准备金水平，降低监管成本，实现激励相容。