Core Viewpoint - The article emphasizes the underestimation of risks in the current market environment, highlighting the need for awareness and preparedness among investors as uncertainties rise due to various global factors [1][3][4]. Group 1: Current Market Risks - Engel identifies several sources of uncertainty for 2025, including tariff policies, anti-science sentiments in the U.S., immigration issues, and ongoing wars, which are increasing market volatility without sufficient caution from investors [3][4]. - The prevailing market optimism may be a false sense of security, as Engel warns that these issues may not resolve in a way that enhances economic resilience or growth [4][5]. Group 2: ARCH Model Insights - Engel's ARCH model, introduced in 1982, quantifies the phenomenon of "volatility clustering" in financial markets, indicating that high volatility is often followed by more high volatility [8]. - The model serves as a tool for monitoring global financial conditions rather than predicting specific market movements, focusing on when volatility is likely to rise or fall [9]. Group 3: Trade Wars, AI, and Policy - Engel compares current trade wars to the Smoot-Hawley Tariff Act of the 1930s, suggesting that tariffs are detrimental to both parties involved and are unlikely to be sustainable [12]. - He views AI not as an independent source of market volatility but as a probabilistic tool that should assist human decision-making, cautioning against over-reliance on automated trading systems [12]. - Engel stresses the importance of gradual and predictable policy adjustments to mitigate risks, as sudden changes can lead to reduced investment and consumption, further slowing economic growth [12]. Group 4: Strategies for Individual Investors - For non-professional investors, Engel advises against attempting market timing and suggests using volatility control indices that adjust positions based on market volatility levels [15]. - He recommends constructing a diversified investment portfolio with a defined volatility target, emphasizing disciplined risk management over speculative market predictions [16]. Group 5: Future Outlook - Engel expresses concern about three major issues for 2026: escalation of wars, the re-emergence of stagflation, and stagnation in climate action, while remaining hopeful about improved U.S.-China relations [19][20]. - He believes that better collaboration between the U.S. and China could help address inflation and deflation issues, benefiting both countries and the global economy [20].

以上的传统方法所计量的VaR在剧烈波动的金融市场下很容易失效，核心原因在于其静态分布的假设在一定程度上忽略了 波动的时变性，导致无法量化波动率的动态变化。一般认为，金融市场中高波动率时期往往伴随着持续的高波动，低波动率时 期则延续低波动，即金融市场中资产价格的变化具有一定的趋同性，这种现象被称为波动率聚集，最早由法国数学家曼德布洛 特（Benoit Mandelbrot）提出，在数学上可以表示为在一段时间内，资产收益率绝对值的自相关函数为正，这种性质使得资产 收益率的波动率存在一定程度上的可预测性，而不是完全随机变化。GARCH类模型作为现代的金融时间序列模型，便是基于 波动聚集特性进行建模，能够更好地处理金融数据存在的尖峰肥尾特征和异方差问题。 GARCH模型（广义自回归条件异方差模型）是ARCH模型（自回归条件异方差模型）的延伸，即广义上的ARCH模型，相 比于ARCH模型，GARCH模型通过加入 项，能够捕捉历史波动对当前波动的累计效应，将ARCH模型 所依赖的高阶残差项通过历史残差平方的递归函数进行替代，更为符合金融数据波动的持续性特征。 一、引言 随着资本市场的不断深化发展，证券公司所面临市场风险的 ...