Analysis of Conditional Value-at-Risk for Newsvendor with Holding and Backorder Cost under Market Search

We consider a distribution system with one supplier and two retailers. For the two retailers, they face different demand and are both risk averse. We study a single period model which the supplier has ample goods and the retailers order goods separately. Market search is measured as the fraction of customers who unsatisfied with their ＂local＂ retailer due to stock-out, and search for the goods at the other retailer before leaving the system. We investigate how the retailers game for order quantity in a Conditional Value-at-Risk framework and study how risk averse degree, market search level, holding cost and backorder cost influence the optimal order strategies. Furthermore, we use uniform distribution to illustrate these results and obtain Nash equilibrium of order strategies.

On the volatility of daily stock returns of Total Nigeria Plc: evidence from GARCH models, value-at-risk and backtesting

This study investigates the volatility in daily stock returns for Total Nigeria Plc using nine variants of GARCH models:sGARCH,girGARCH,eGARCH,iGARCH,aGARCH,TGARCH,NGARCH,NAGARCH,and AVGARCH along with value at risk estimation and backtesting.We use daily data for Total Nigeria Plc returns for the period January 2,2001 to May 8,2017,and conclude that eGARCH and sGARCH perform better for normal innovations while NGARCH performs better for student t innovations.This investigation of the volatility,VaR,and backtesting of the daily stock price of Total Nigeria Plc is important as most previous studies covering the Nigerian stock market have not paid much attention to the application of backtesting as a primary approach.We found from the results of the estimations that the persistence of the GARCH models are stable except for few cases for which iGARCH and eGARCH were unstable.Additionally,for student t innovation,the sGARCH and girGARCH models failed to converge;the mean reverting number of days for returns differed from model to model.From the analysis of VaR and its backtesting,this study recommends shareholders and investors continue their business with Total Nigeria Plc because possible losses may be overcome in the future by improvements in stock prices.Furthermore,risk was reflected by significant up and down movement in the stock price at a 99%confidence level,suggesting that high risk brings a high return.

Empirical Analysis of Value-at-Risk Estimation Methods Using Extreme Value Theory

This paper investigates methods of value-at-risk (VaR) estimation using extreme value theory (EVT). It compares two different estimation methods, 'two-step subsample bootstrap' based on moment estimation and maximum likelihood estimation (MLE), according to their theoretical bases and computation procedures. Then, the estimation results are analyzed together with those of normal method and empirical method. The empirical research of foreign exchange data shows that the EVT methods have good characters in estimating VaR under extreme conditions and 'two-step subsample bootstrap' method is preferable to MLE.

Conditional Value-at-Risk for Random Immediate Reward Variables in Markov Decision Processes

We consider risk minimization problems for Markov decision processes. From a standpoint of making the risk of random reward variable at each time as small as possible, a risk measure is introduced using conditional value-at-risk for random immediate reward variables in Markov decision processes, under whose risk measure criteria the risk-optimal policies are characterized by the optimality equations for the discounted or average case. As an application, the inventory models are considered.

Uncertainty Comparison Between Value-at-Risk and Expected Shortfall

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.

Real-time Risk-averse Dispatch of an Integrated Electricity and Natural Gas System via Condi-tional Value-at-risk-based Lookup-table Ap-proximate Dynamic Programming

The real-time risk-averse dispatch problem of an integrated electricity and natural gas system(IEGS)is studied in this paper.It is formulated as a real-time conditional value-at-risk(CVaR)-based risk-averse dis-patch model in the Markov decision process framework.Because of its stochasticity,nonconvexity and nonlinearity,the model is difficult to analyze by traditional algorithms in an acceptable time.To address this non-deterministic polynomial-hard problem,a CVaR-based lookup-table approximate dynamic programming(CVaR-ADP)algo-rithm is proposed,and the risk-averse dispatch problem is decoupled into a series of tractable subproblems.The line pack is used as the state variable to describe the impact of one period’s decision on the future.This facilitates the reduction of load shedding and wind power curtailment.Through the proposed method,real-time decisions can be made according to the current information,while the value functions can be used to overview the whole opti-mization horizon to balance the current cost and future risk loss.Numerical simulations indicate that the pro-posed method can effectively measure and control the risk costs in extreme scenarios.Moreover,the decisions can be made within 10 s,which meets the requirement of the real-time dispatch of an IEGS.Index Terms—Integrated electricity and natural gas system,approximate dynamic programming,real-time dispatch,risk-averse,conditional value-at-risk.

金融市场风险测量的VaR方法及其应用

近年来 ,金融市场的波动性增加 ,金融机构需要准确的测量其市场风险。对市场风险的正确测量构成了市场风险管理的基础。在介绍广泛应用于测量市场风险的VaR的实质、计算方法及发展方向的基础上 。

基于VaR的供应链金融操作风险度量研究

供应链金融的风险包括市场风险、信用风险和操作风险等,但是对操作风险一直以来缺乏应有的关注。本文在介绍VaR及其在操作风险领域应用现状的基础上,分析了供应链金融中操作风险的存在形式,同时借鉴国内外学者的研究成果,构建了一个计算供应链金融操作风险VaR值的模型,可供银行据此配置合理的资本。

极值理论在风险度量中的应用——基于上证180指数

精确度量风险是金融风险管理的关键问题。本文引入广义帕雷托分布代替传统的正态分布等,精确描述金融收益的厚尾特征。并将基于广义帕雷托分布的VaR模型和其它模型方法,如GARCH(1,1)、GARCH(1,1)-t、历史模拟法、方差-协方差方法,进行比较分析。实证研究表明,基于广义帕雷托分布的VaR模型比传统的模型方法更适合厚尾分布高分位点的预测,并且其预测结果比较稳定。这使得基于广义帕雷托分布的VaR模型成为VaR度量方法中最稳健的方法之一。

RAROC方法在证券投资基金绩效评估中的应用

介绍了基于VaR的证券投资基金绩效评估方法———RAROC方法,通过该方法对基金投资绩效的分析来揭示投资风险,并对基于RAROC的绩效评估方法与传统的指数评估方法(夏普指数法、特雷诺指数法及詹森指数法)进行比较分析.结果表明:引进VaR风险度量模型,把经风险调整后的绩效评估方法RAROC应用到投资基金绩效评估中,能更客观、准确地反映证券投资基金的绩效.

广义双曲线分布模型在我国证券市场风险度量中的应用研究

经济的全球化、衍生产品的大量出现以及因此导致的金融市场的动荡使得金融机构越来越需要更有效的风险管理方法。而如何精确度量风险是风险管理的关键问题。本文试图从金融收益分布假设着手改善风险度量的精度。国外学者研究发现广义双曲线分布比其它分布形式可以更好地拟合实际收益分布特征。本文首次把广义双曲线分布应用到VaR的分析方法中计算我国股票指数的VaR。实证结果表明,基于广义双曲线分布的方法得到了较好的预测结果。

资产相关结构对投资组合风险测度的影响分析

文章从分析金融资产收益率的统计特征入手,以GARCH模型为基础,用非对称幂分布描述组合资产中各金融资产收益率的边缘分布函数,在多种Copula函数情形下计算组合资产的风险值VaR及ES。结果表明:基于由多元Clayton Copula和多元Gumbel Copula组成的混合Copula函数较好地刻画了多只股票的相关结构,而且ES比VaR能够较准确地估计组合资产的尾部风险。

基于卡尔曼滤波的投资组合时变风险估计

本文采用状态空间表示式,提出了一个具有时变的系统风险系数β的条件CAPM,然后利用卡尔曼滤波递归算法来估计时变β系数,最后通过夏普的对角线模型计算投资组合的VaR并进行返回检验。结果表明,该模型能够捕捉到金融市场的波动,而且对计算起到简化作用,特别适合对大投资组合的VaR估计。

基于VaR的商业银行信用风险管理研究

VaR方法是新巴塞尔资本协议所倡导的测量和控制金融风险的国际主流技术,文中比较分析了计算VaR的三种主要方法:参数法、半参数法和非参数法及其有效性检验,根据分析认为应用VaR方法有利于银行实现对信用风险的动态管理,风险资本金的优化配置,信用管理绩效评价的完善,使银行信用风险管理的科学化水平得到极大的提高.尽管VaR方法有其自身的局限性,当前在我国应用存在一些制约因素,但入世后的中国银行业与国际主流方法接轨已不可避免,我国应积极创造条件推动该方法在我国银行信用风险管理中的应用.

中国股票市场行业间金融传染检验和风险防范

运用一个新的金融传染检验统计量对2015年6月中旬中国股市暴跌时各行业间的传染效应进行检验.跟传统的金融传染检验统计量相比,他可从不同的分位数水平上检验金融传染;跟已有的分位数回归检验方法相比,他对于可能存在的模型误设是稳健的.本文首次检验了国内全部十个一级行业以及四个金融二级子行业之间的金融传染情况,并从市场风险的角度对不同行业间的传染关系和传染的可能途径进行了分析.新的金融传染检验统计量检验结果表明:在此次暴跌中大部分行业间存在金融传染,尤其是在低分位数下,而传统的检验方法忽略了这种传染效应的存在,这对市场风险的提示有着重大意义.

风险管理的CVaR法及其在银行信用风险度量中的运用

作为银行主要风险的信用风险,在中国经济体制转轨时期表现得更加尖锐。鉴于现有测度体系对风险度量方法的研究和探索存在一定缺陷,笔者通过引入一种VaR的修正模型CVaR,率先将此方法运用于度量信用风险,建立了具体的数学模型,给出了求解方法及步骤,从而测算出银行贷款组合的CVaR值,得到了银行信用风险的预警值,并总结出目前CVaR风险测度法在我国运用的难度,最后提出建议。

多阶段资产组合选择均值-VaR模型的研究

建立了多阶段情形下的均值-方差模型和均值-VaR模型,比较了这两种模型的性质,并给出了其最小方差组合性质以及在收益率的均值-标准差坐标下,不同的风险度量方法产生的不同的有效边缘,同时研究了VaR模型置信度趋于1时的极限性质.

Modeling dependence based on mixture copulas and its application in risk management

This paper is concerned with the statistical modeling of the dependence structure of multivariate financial data using the copula, and the application of copula functions in VaR valuation. After the introduction of the pure copula method and the maximum and minimum mixture copula method, authors present a new algorithm based on the more generalized mixture copula functions and the dependence measure, and apply the method to the portfolio of Shanghai stock composite index and Shenzhen stock component index. Comparing with the results from various methods, one can find that the mixture copula method is better than the pure Gaussian copula method and the maximum and minimum mixture copula method on different VaR level.

An Application of Bayesian Inference on the Modeling and Estimation of Operational Risk Using Banking Loss Data

Bayesian inference method has been presented in this paper for the modeling of operational risk. Bank internal and external data are divided into defined loss cells and then fitted into probability distributions. The distribution parameters and their uncertainties are estimated from posterior distributions derived using the Bayesian inference. Loss frequency is fitted into Poisson distributions. While the Poisson parameters, in a similar way, are defined by a posterior distribution developed using Bayesian inference. Bank operation loss typically has some low frequency but high magnitude loss data. These heavy tail low frequency loss data are divided into several buckets where the bucket frequencies are defined by the experts. A probability distribution, as defined by the internal and external data, is used for these data. A Poisson distribution is used for the bucket frequencies. However instead of using any distribution of the Poisson parameters, point estimations are used. Monte Carlo simulation is then carried out to calculate the capital charge of the in- ternal as well as the heavy tail high profile low frequency losses. The output of the Monte Carlo simulation defines the capital requirement that has to be allocated to cover potential operational risk losses for the next year.

Calculation of Expected Shortfall for Measuring Risk and Its Applications

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.