基于ARCH-Expectile方法的VaR和ES尾部风险测量

甄别和确定风险因素的贡献是资产或资产组合风险管理的重要研究内容。近十年，下端风险越来越受到关注，在险价值（Value at Risk，VaR）和预期不足（Expected Shortfall，ES）是资产组合风险管理中两个常用的风险度量工具。Kuan等^1]在一类条件自回归模型（CARE）下提出了基于expectile的VaR度量-EVaR。本文扩展了Kuan等^2]的CARE模型到带有异方差的数据，引入ARCH效应提出了一个线性ARCH-Expectile模型，旨在确定资产或资产组合的风险来源以及评估各风险因素的贡献大小，并应用expectile间接评估VaR和ES风险大小。同时给出了参数的两步估计算法，并建立了参数估计的大样本理论。最后，将本文所提出的方法应用于民生银行股票损益的风险分析，从公司基本面、市场流动性和宏观层面三个方面选取影响股票损益的风险因素，分析结果表明，各风险因素随股票极端损失大小的水平不同，其风险因素的来源及其大小和方向也是随之变化的。

VaR and ES Measurements based on ARCH-Expectile Model

Determining contributions to an asset or portfolio of assets risk is an important topic in risk management. A downside risk is of primary concern during the last decade. Value at risk and expected shortfall have become two popular downside risk measurements associated with portfolio of assets. Kuan et al^1].proposed an expectile-based VaR for various CARE model. In this paper, a linear ARCH-Expectile model is proposed to extend Kuan et al. CARE models by introducing an ARCH effect modeling financial data with heteroscedasticity. Based on the coefficient estimates of the proposed expectile model, not only the contribution to portfolio downside risk of risk factors can be analyzed the magnitude of downside risk can also be evaluated. Meanwhile, a two-step estimating procedure is provided and the asymptotic properties of estimators are extablished. Finally, the proposed method is applied to analysis the risk of a company's stock from three aspects of market liquidity, company fundamentals and micro fundamentals. The empirical results find that the risk factors and their magnitude and direction, which impact on return of the stock, are varying with the level of tail losses.