Expected shortfall(ES) is a new method to measure market risk. In this paper, an example was presented to illustrate that the ES is coherent but value-at-risk(VaR) is not coherent. Three formulas for calculating the E...Expected shortfall(ES) is a new method to measure market risk. In this paper, an example was presented to illustrate that the ES is coherent but value-at-risk(VaR) is not coherent. Three formulas for calculating the ES based on historical simulation method, normal method and GARCH method were derived. Further, a numerical experiment on optimizing portfolio using ES was provided.展开更多
In this paper we consider the problem of estimating expected shortfall(ES)for discrete time stochastic volatility(SV)models.Specifically,we develop Monte Carlo methods to evaluate ES for a variety of commonly used SV ...In this paper we consider the problem of estimating expected shortfall(ES)for discrete time stochastic volatility(SV)models.Specifically,we develop Monte Carlo methods to evaluate ES for a variety of commonly used SV models.This includes both models where the innovations are independent of the volatility and where there is dependence.This dependence aims to capture the well-known leverage effect.The performance of our Monte Carlo methods is analyzed through simulations and empirical analyses of four major US indices.展开更多
This paper analyzes the relationship between the risk factor of each stock and the portfolio’s risk based on a small portfolio with four U.S.stocks,and the reason why these risk factors can be regarded as a market in...This paper analyzes the relationship between the risk factor of each stock and the portfolio’s risk based on a small portfolio with four U.S.stocks,and the reason why these risk factors can be regarded as a market invariant.Then,it evaluates the properties of the convex and coherent risk indicators of the capital requirement index composed of VaR and ES,and use three methods(the historical estimation method,boudoukh’s mixed method and Monte Carlo method)to estimate the risk measurement indicators VaR and ES respectively based on the assumption of multivariate normal distribution’risk factors and multivariate student t-copula distribution’s one,finally it figures out that these three calculation results are very close.展开更多
Value-at-Risk(VaR)and expected shortfall(ES)are two key risk measures in financial risk management.Comparing these two measures has been a hot debate,and most discussions focus on risk measure properties.This paper us...Value-at-Risk(VaR)and expected shortfall(ES)are two key risk measures in financial risk management.Comparing these two measures has been a hot debate,and most discussions focus on risk measure properties.This paper uses independent data and autoregressive models with normal or t-distribution to examine the effect of the heavy tail and dependence on comparing the nonparametric inference uncertainty of these two risk measures.Theoretical and numerical analyses suggest that VaR at 99%level is better than ES at 97.5%level for distributions with heavier tails.展开更多
Expected shortfall(ES)is a popular risk measure and plays an important role in risk and portfolio management.Recently,change-point detection of risk measures has been attracting much attention in finance.Based on the ...Expected shortfall(ES)is a popular risk measure and plays an important role in risk and portfolio management.Recently,change-point detection of risk measures has been attracting much attention in finance.Based on the self-normalized CUSUM statistic in Fan,Glynn and Pelger(2018)and the Wild Binary Segmentation(WBS)algorithm in Fryzlewicz(2014),this paper proposes a variant WBS procedure to detect and estimate change points of ES in time series.The strengthened Schwarz information criterion is also introduced to determine the number of change points.Monte Carlo simulation studies are conducted to assess the finite-sample performance of our variant WBS procedure about ES in time series.An empirical application is given to illustrate the usefulness of our procedure.展开更多
An expectile can be considered a generalization of a quantile.While expected shortfall is a quantile-based risk measure,we study its counterpart-the expectile-based expected shortfall-where expectile takes the place o...An expectile can be considered a generalization of a quantile.While expected shortfall is a quantile-based risk measure,we study its counterpart-the expectile-based expected shortfall-where expectile takes the place of a quantile.We provide its dual representation in terms of a Bochner integral.Among other properties,we show that it is bounded from below in terms of the convex combination of expected shortfalls,and also from above by the smallest law invariant,coherent,and comonotonic risk measures,for which we give the explicit formulation of the corresponding distortion function.As a benchmark to the industry standard expected shortfall,we further provide its comparative asymptotic behavior in terms of extreme value distributions.Based on these results,we finally explicitly compute the expectile-based expected shortfall for selected classes of distributions.展开更多
期望损失(Expected Shortfall,ES)是当今最流行的金融资产风险管理的工具之一,是一个理想的一致性风险度量.本文在α-混合序列具有幂衰减混合系数条件下,用两步核估计估算风险度量ES的值,第一步是在险价值(Value at Risk,VaR)的核估计,...期望损失(Expected Shortfall,ES)是当今最流行的金融资产风险管理的工具之一,是一个理想的一致性风险度量.本文在α-混合序列具有幂衰减混合系数条件下,用两步核估计估算风险度量ES的值,第一步是在险价值(Value at Risk,VaR)的核估计,第二步是ES的核估计.得到ES的核估计量的Bahadur表示,以及均方误差和渐近正态性的收敛速度.展开更多
经济资本配置是商业银行进行经济资本管理的一种有效方法,为了研究在商业银行经济资本配置中,在险价值(Value at Risk,VaR)和预期短缺(Expected Shortfall,ES)这两种风险量度所表现出的差异性,借助于信用组合损失分布的Vasicek单因素模...经济资本配置是商业银行进行经济资本管理的一种有效方法,为了研究在商业银行经济资本配置中,在险价值(Value at Risk,VaR)和预期短缺(Expected Shortfall,ES)这两种风险量度所表现出的差异性,借助于信用组合损失分布的Vasicek单因素模型框架,对VaR和ES两种风险量度下的经济资本配置实现方法进行推导,并通过案例,对这两种风险量度在经济资本配置上表现出的差异性进行比较分析。研究结果表明:尽管由ES确定的经济资本比由VaR确定的经济资本要保守,但基于ES的经济资本配置方法比基于VaR的经济资本配置方法更能反映资产的风险特征,更便于实施。展开更多
在风险管理中,风险量度估计的稳定性对金融机构的经济资本确定及风险分配起着重要的作用.本文从预期短缺(ES_α)估计的稳定性角度分析重要性抽样技术和 Monte Carlo 模拟在估计信用资产组合 ES_α方面的差异.结果表明,由于组合损失分布...在风险管理中,风险量度估计的稳定性对金融机构的经济资本确定及风险分配起着重要的作用.本文从预期短缺(ES_α)估计的稳定性角度分析重要性抽样技术和 Monte Carlo 模拟在估计信用资产组合 ES_α方面的差异.结果表明,由于组合损失分布尾部事件的稀有性,与传统的 Monte Carlo 模拟方法相比,运用重要性抽样方法估计的 ES_α比较稳定,且生成的风险贡献能够明显地体现出资产间不同的风险特征.展开更多
文摘Expected shortfall(ES) is a new method to measure market risk. In this paper, an example was presented to illustrate that the ES is coherent but value-at-risk(VaR) is not coherent. Three formulas for calculating the ES based on historical simulation method, normal method and GARCH method were derived. Further, a numerical experiment on optimizing portfolio using ES was provided.
文摘In this paper we consider the problem of estimating expected shortfall(ES)for discrete time stochastic volatility(SV)models.Specifically,we develop Monte Carlo methods to evaluate ES for a variety of commonly used SV models.This includes both models where the innovations are independent of the volatility and where there is dependence.This dependence aims to capture the well-known leverage effect.The performance of our Monte Carlo methods is analyzed through simulations and empirical analyses of four major US indices.
文摘This paper analyzes the relationship between the risk factor of each stock and the portfolio’s risk based on a small portfolio with four U.S.stocks,and the reason why these risk factors can be regarded as a market invariant.Then,it evaluates the properties of the convex and coherent risk indicators of the capital requirement index composed of VaR and ES,and use three methods(the historical estimation method,boudoukh’s mixed method and Monte Carlo method)to estimate the risk measurement indicators VaR and ES respectively based on the assumption of multivariate normal distribution’risk factors and multivariate student t-copula distribution’s one,finally it figures out that these three calculation results are very close.
文摘Value-at-Risk(VaR)and expected shortfall(ES)are two key risk measures in financial risk management.Comparing these two measures has been a hot debate,and most discussions focus on risk measure properties.This paper uses independent data and autoregressive models with normal or t-distribution to examine the effect of the heavy tail and dependence on comparing the nonparametric inference uncertainty of these two risk measures.Theoretical and numerical analyses suggest that VaR at 99%level is better than ES at 97.5%level for distributions with heavier tails.
基金supported in part by the NSFC(Nos.71973077 and 11771239)the Tsinghua University Initiative Scientific Research Program(No.2019Z07L01009).
文摘Expected shortfall(ES)is a popular risk measure and plays an important role in risk and portfolio management.Recently,change-point detection of risk measures has been attracting much attention in finance.Based on the self-normalized CUSUM statistic in Fan,Glynn and Pelger(2018)and the Wild Binary Segmentation(WBS)algorithm in Fryzlewicz(2014),this paper proposes a variant WBS procedure to detect and estimate change points of ES in time series.The strengthened Schwarz information criterion is also introduced to determine the number of change points.Monte Carlo simulation studies are conducted to assess the finite-sample performance of our variant WBS procedure about ES in time series.An empirical application is given to illustrate the usefulness of our procedure.
基金This research is supported by National Science Foundation of China(Grant No.11971310,11671257)“Assessment of Risk and Uncertainty in Finance”(Grant No.AF0710020)from Shanghai Jiao Tong University.
文摘An expectile can be considered a generalization of a quantile.While expected shortfall is a quantile-based risk measure,we study its counterpart-the expectile-based expected shortfall-where expectile takes the place of a quantile.We provide its dual representation in terms of a Bochner integral.Among other properties,we show that it is bounded from below in terms of the convex combination of expected shortfalls,and also from above by the smallest law invariant,coherent,and comonotonic risk measures,for which we give the explicit formulation of the corresponding distortion function.As a benchmark to the industry standard expected shortfall,we further provide its comparative asymptotic behavior in terms of extreme value distributions.Based on these results,we finally explicitly compute the expectile-based expected shortfall for selected classes of distributions.
文摘期望损失(Expected Shortfall,ES)是当今最流行的金融资产风险管理的工具之一,是一个理想的一致性风险度量.本文在α-混合序列具有幂衰减混合系数条件下,用两步核估计估算风险度量ES的值,第一步是在险价值(Value at Risk,VaR)的核估计,第二步是ES的核估计.得到ES的核估计量的Bahadur表示,以及均方误差和渐近正态性的收敛速度.
文摘经济资本配置是商业银行进行经济资本管理的一种有效方法,为了研究在商业银行经济资本配置中,在险价值(Value at Risk,VaR)和预期短缺(Expected Shortfall,ES)这两种风险量度所表现出的差异性,借助于信用组合损失分布的Vasicek单因素模型框架,对VaR和ES两种风险量度下的经济资本配置实现方法进行推导,并通过案例,对这两种风险量度在经济资本配置上表现出的差异性进行比较分析。研究结果表明:尽管由ES确定的经济资本比由VaR确定的经济资本要保守,但基于ES的经济资本配置方法比基于VaR的经济资本配置方法更能反映资产的风险特征,更便于实施。
文摘在风险管理中,风险量度估计的稳定性对金融机构的经济资本确定及风险分配起着重要的作用.本文从预期短缺(ES_α)估计的稳定性角度分析重要性抽样技术和 Monte Carlo 模拟在估计信用资产组合 ES_α方面的差异.结果表明,由于组合损失分布尾部事件的稀有性,与传统的 Monte Carlo 模拟方法相比,运用重要性抽样方法估计的 ES_α比较稳定,且生成的风险贡献能够明显地体现出资产间不同的风险特征.
