Assessing Tail Risk Using Expectile Regressions with Partially Varying Coefficients

Cai, Zucong; Fang, Ying; Tian, Dingshi

doi:10.3724/sp.j.1383.304011

Cited by 11 publications

(12 citation statements)

References 23 publications

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“…Xie et al (2014) proposed a varying coefficient expectile model. Afterwards, Cai et al (2018) extended their work to consider a more general case, i.e., a partially varying coefficient expectile model.…”

Section: Nonparametric and Semiparametric Modelsmentioning

confidence: 99%

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Econometric modeling of risk measures: A selective review of the recent literature

Tian

Cai

Fang

2019

Appl. Math. J. Chin. Univ.

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Since the financial crisis in 2008, the risk measures which are the core of risk management, have received increasing attention among economists and practitioners. In this review, the concentrate is on recent developments in the estimation of the most popular risk measures, namely, value at risk (VaR), expected shortfall (ES), and expectile. After introducing the concept of risk measures, the focus is on discussion and comparison of their econometric modeling. Then, parametric and nonparametric estimations of tail dependence are investigated. Finally, we conclude with insights into future research directions.

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Section: Nonparametric and Semiparametric Modelsmentioning

confidence: 99%

“…A purely nonparametric expectile model may suffer from the curse of dimensionality. To address this problem, Cai et al (2018) proposed a partially varying coefficient expectile model,…”

Section: A Partially Varying-coefficient Expectile Modelmentioning

confidence: 99%

Econometric modeling of risk measures: A selective review of the recent literature

Tian

Cai

Fang

2019

Appl. Math. J. Chin. Univ.

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“…In many applications, however, the tail quantiles or tail expectiles of the variable Y of interest depend on some covariate X , and thus, it is important to incorporate the covariate information into a given analysis. For instance, risk managers in finance often seek to forecast the low conditional quantiles of a portfolios future returns, or the conditional expectiles on information from the past or assumptions on future interest rate changes (Cai et al, 2018). Therefore, our proposed work on high conditional expectiles is meaningful.…”

Section: Introductionmentioning

confidence: 99%

“…Kuan et al (2009) proposed conditional autoregressive expectile (CARE) models to assess VaR. Cai et al (2018) applied expectile regressions with partially varying coefficients to assess tail risk. Although expectile regression has found applications in various fields, to our knowledge, few works are concerned with the estimation of high conditional expectiles.…”

Section: Introductionmentioning

confidence: 99%

Estimation of High Conditional Tail Risk Based on Expectile Regression

Chen

Tan

2021

ASTIN Bull.

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Assessing conditional tail risk at very high or low levels is of great interest in numerous applications. Due to data sparsity in high tails, the widely used quantile regression method can suffer from high variability at the tails, especially for heavy-tailed distributions. As an alternative to quantile regression, expectile regression, which relies on the minimization of the asymmetric l2-norm and is more sensitive to the magnitudes of extreme losses than quantile regression, is considered. In this article, we develop a new estimation method for high conditional tail risk by first estimating the intermediate conditional expectiles in regression framework, and then estimating the underlying tail index via weighted combinations of the top order conditional expectiles. The resulting conditional tail index estimators are then used as the basis for extrapolating these intermediate conditional expectiles to high tails based on reasonable assumptions on tail behaviors. Finally, we use these high conditional tail expectiles to estimate alternative risk measures such as the Value at Risk (VaR) and Expected Shortfall (ES), both in high tails. The asymptotic properties of the proposed estimators are investigated. Simulation studies and real data analysis show that the proposed method outperforms alternative approaches.

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“…Spiegel 等 [40] 针对半参数期望分位数模型用样条方法进行了模型选择. Cai 等 [41] 研究了与本文相似的部分变系数期望分位数模型, 他们要求序列是 β-混合严平稳的, 而本文 α-混合序列的假设条件更弱、更一般, 在金融时间序列数据下本文的假设与估计方法更为合理. 本文针对满足 α-混合条件的金融时间序列, 考虑尾部更敏感的 EVaR 作为资产的一种风险度量, 并且将 Xie 等 [20] 的变系数期望分位数模型拓展到半参数变系数期望分位数模型, 对变系数参数与常系数参数分别进行半参有效估计.…”

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Semiparametric varying-coefficient expectile model for estimating value at risk on dependent samples

Wang¹,

Yong²,

Zeng³

2021

Sci. Sin.-Math.

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关键词 α-混合半参数变系数期望分位数在险价值三阶段估计 MSC (2020) 主题分类 62G05, 91G70 1 引言风险度量建模一直是统计学和金融计量学中重要的研究议题和前沿问题. 获得诺贝尔奖的美国经济学家 Markowitz [1] 在投资组合理论中, 首次提出了收益与风险的度量理论, 即期望代表收益与方差代表风险的度量方法, 从而开创了风险的量化时代. 随后以 Black 和 Scholes [2] 的资产定价理论为标王子剑等: 相依样本下半参数变系数期望分位数风险度量模型统计推断志, 风险度量推动了金融计量学与风险管理的发展. 此外发展出更多风险管理的方法, 包括著名的一般均衡理论 [3, 4] 和保费均衡原则 [5] 等. 根据风险度量的侧重点不同, 可以将常用的风险度量分为两大类: 基于矩的风险度量和基于分位点的风险度量. 有关矩的风险度量主要有方差 (variance)、半方差 (semi-variance)、绝对离差 (absolute deviation)、半绝对离差 (semi-absolute deviation)、低位部分矩 (lower partial moments, LPM) 和 G-均值等. 有关矩的风险度量, 主要采用概率统计中表示离散程度的矩 (moment) 来度量金融资产或投资组合的风险, 波动性越强, 风险越大. 另一类则是以风险价值 (value at risk, VaR) 和期望损益 (expected shortfall, ES) 为代表的分位数 (quantile) 风险度量. 风险价值和期望损益是资产组合常用的两个风险度量工具, 其中 VaR 是被如巴塞尔委员会等众多国外的金融机构所认可和提倡的风险度量方法.

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Assessing Tail Risk Using Expectile Regressions with Partially Varying Coefficients

Cited by 11 publications

References 23 publications

Econometric modeling of risk measures: A selective review of the recent literature

Econometric modeling of risk measures: A selective review of the recent literature

Estimation of High Conditional Tail Risk Based on Expectile Regression

Semiparametric varying-coefficient expectile model for estimating value at risk on dependent samples

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