论银行市场风险的资本计提——兼评内部模型法的适用性

市场风险及其监管资本要求的计量历来为业界和监管当局所关注。近期,次贷危机爆发导致的市场动荡使得全球银行业和监管当局开始重新审视其市场风险管理和监管资本要求。文章结合国际银行业和监管机构计量市场风险及其监管资本要求的当前做法,针对我国银行业的实际情况,重点探索了内部模型法在我国银行业的适用性,尤其是从方法论、特殊风险计量、验证等角度探讨了内部模型法的主要工具——风险价值体系在我国银行业计量市场风险及其监管资本要求的适用性,并从方法论和应用层面提出了相应的政策建议。     

Model uncertainty and VaR aggregation

Despite well-known shortcomings as a risk measure, Value-at-Risk (VaR) is still the industry and regulatory standard for the calculation of risk capital in banking and insurance. This paper is concerned with the numerical estimation of the VaR for a portfolio position as a function of different dependence scenarios on the factors of the portfolio. Besides summarizing the most relevant analytical bounds, including a discussion of their sharpness, we introduce a numerical algorithm which allows for the computation of reliable (sharp) bounds for the VaR of high-dimensional portfolios with dimensions d possibly in the several hundreds. We show that additional positive dependence information will typically not improve the upper bound substantially. In contrast higher order marginal information on the model, when available, may lead to strongly improved bounds. Several examples of practical relevance show how explicit VaR bounds can be obtained. These bounds can be interpreted as a measure of model uncertainty induced by possible dependence scenarios.     

基于GARCH族模型的黄金市场的风险度量与预测研究

本文以上海和伦敦黄金市场的现货交易为对象,比较研究了不同分布假定下RiskMetrics、GARCH族及其衍生模型度量VaR值的精确程度,并对超前一天预测的VaR值进行了失败率检测和动态分位数测试。结果表明:两个市场的收益率分布均具有尖峰厚尾、波动集聚和长记忆性等特征;学生t分布很好的刻画了上海黄金市场的风险特征,而正态分布则适合描述伦敦黄金市场特征;上海黄金市场相比于伦敦黄金市场风险更大。     

On Bayesian Value at Risk: From Linear to Non-Linear Portfolios

This paper proposes the use of Bayesian approach to implement Value at Risk (VaR) model for both linear and non-linear portfolios. The Bayesian approach provides risk traders with the flexibility of adjusting their VaR models according to their subjective views. First, we deal with the case of linear portfolios. By imposing the conjugate-prior assumptions, a closed-form expression for the Bayesian VaR is obtained. The Bayesian VaR model can also be adjusted in order to deal with the ageing effect of the past data. By adopting Gerber-Shiu's option-pricing model, our Bayesian VaR model can also be applied to deal with non-linear portfolios of derivatives. We obtain an exact formula for the Bayesian VaR in the case of a single European call option. We adopt the method of back-testing to compare the non-adjusted and adjusted Bayesian VaR models with their corresponding classical counterparts in both linear and non-linear cases.     

How does the choice of Value-at-Risk estimator influence asset allocation decisions?

Considering the growing need for managing financial risk, Value-at-Risk (VaR) prediction and portfolio optimisation with a focus on VaR have taken up an important role in banking and finance. Motivated by recent results showing that the choice of VaR estimator does not crucially influence decision-making in certain practical applications (e.g. in investment rankings), this study analyses the important question of how asset allocation decisions are affected when alternative VaR estimation methodologies are used. Focusing on the most popular, successful and conceptually different conditional VaR estimation techniques (i.e. historical simulation, peak over threshold method and quantile regression) and the flexible portfolio model of Campbell et al. [J. Banking Finance. 2001, 25(9), 1789–1804], we show in an empirical example and in a simulation study that these methods tend to deliver similar asset weights. In other words, optimal portfolio allocations appear to be not very sensitive to the choice of VaR estimator. This finding, which is robust in a variety of distributional environments and pre-whitening settings, supports the notion that, depending on the specific application, simple standard methods (i.e. historical simulation) used by many commercial banks do not necessarily have to be replaced by more complex approaches (based on, e.g. extreme value theory).     

Value-at-Risk Prediction: A Comparison of Alternative Strategies

Given the growing need for managing financial risk, risk predictionplays an increasing role in banking and finance. In this studywe compare the out-of-sample performance of existing methodsand some new models for predicting value-at-risk (VaR) in aunivariate context. Using more than 30 years of the daily returndata on the NASDAQ Composite Index, we find that most approachesperform inadequately, although several models are acceptableunder current regulatory assessment rules for model adequacy.A hybrid method, combining a heavy-tailed generalized autoregressiveconditionally heteroskedastic (GARCH) filter with an extremevalue theory-based approach, performs best overall, closelyfollowed by a variant on a filtered historical simulation, anda new model based on heteroskedastic mixture distributions.Conditional autoregressive VaR (CAViaR) models perform inadequately,though an extension to a particular CAViaR model is shown tooutperform the others.     

On the coherence of expected shortfall

Expected shortfall (ES) in several variants has been proposed as remedy for the deficiencies of value-at-risk (VaR) which in general is not a coherent risk measure. In fact, most definitions of ES lead to the same results when applied to continuous loss distributions. Differences may appear when the underlying loss distributions have discontinuities. In this case even the coherence property of ES can get lost unless one took care of the details in its definition. We compare some of the definitions of ES, pointing out that there is one which is robust in the sense of yielding a coherent risk measure regardless of the underlying distributions. Moreover, this ES can be estimated effectively even in cases where the usual estimators for VaR fail.     

Risk management in the energy markets and Value-at-Risk modelling: a hybrid approach

This paper proposes a set of Value-at-Risk (VaR) models appropriate to capture the dynamics of energy prices and subsequently quantify energy price risk by calculating VaR and expected shortfall measures. Amongst the competing VaR methodologies evaluated in this paper, besides the commonly used benchmark models, a Monte Carlo (MC) simulation approach and a hybrid MC with historical simulation approach, both assuming various processes for the underlying spot prices, are also being employed. All VaR models are empirically tested on eight spot energy commodities that trade futures contracts on the New York Mercantile Exchange (NYMEX) and the constructed Spot Energy Index. A two-stage evaluation and selection process is applied, combining statistical and economic measures, to choose amongst the competing VaR models. Finally, both long and short trading positions are considered as it is of utmost importance for energy traders and risk managers to be able to capture efficiently the characteristics of both tails of the distributions.     

收益率曲线动态与银行经济价值的利率风险

本文在收益率曲线动态的主成分分析基础上,运用MonteCarlo模拟的主成分VaR方法,以我国五家商业银行为样本研究银行账户经济价值利率风险的计量方法,并与巴塞尔委员会标准久期法的结果进行比较。同时,对VaR模型的有效性进行了样本外的返回检验。研究发现,五家银行的经济价值面临的是利率上升的风险;非正态主成分VaR模型估计的经济价值利率风险,都要大于正态主成分VaR模型的结果,这反映了利率波动的厚尾特征,正态假设有可能低估风险。     

基于VaR的开放式股票型基金市场风险的测量与评价

通过采用半参数法计算投资组合VaR,得到相应VaR的近似置信区间,并结合成分VaR、边际VaR对投资组合vaR进行分解,结果发现,VaR作为风险管理工具同样可以有效应用于开放式股票型基金市场风险的测量与评价.     

Translation-invariant and positive-homogeneous risk measures and optimal portfolio management

The problem of risk portfolio optimization with translation-invariant and positive-homogeneous risk measures, which includes value-at-risk (VaR) and tail conditional expectation (TCE), leads to the problem of minimizing a combination of a linear functional and a square root of a quadratic functional for the case of elliptical multivariate underlying distributions. In this paper, we provide an explicit closed-form solution of this minimization problem, and the condition under which this solution exists. The results are illustrated using the data of 10 stocks from NASDAQ/Computers. The distance between the VaR and TCE optimal portfolios has been investigated.     

State contingent banking and asset price bubbles: The case of Islamic banking industry

This paper examines how state contingent banking can help neutralize challenges like debt overhang and lack of optimal risk takings, problems associated with conventional banking that can eventually manifest in the creation of asset price bubbles and a financial crisis. Our analysis also contributes to the literature on Islamic banking which considers state contingent contracts as ideal from a religious perspective. We develop a model of banking with state contingent contracts on the liability and asset sides. Our model shows that in state contingent banking, the returns for the depositors, bank and the borrowers are more aligned with the real economy, which reduces the incentive for excessive borrowing, lending and investing. Our model also shows that with the state contingent banking on the liability side, during periods of heightened macroeconomic risk, depositors' payoff would be more volatile reducing the liquidity influx from the real economy to the banking sector. This neutralizes the pressure on state contingent banks to excessively lend on the asset side. Our model further demonstrates that state contingent contracts on the asset side can help avoid too much (or too little) lending by reducing the managerial discretion in charging low (or high) interest rates. With returns linked to the prices of the underlying assets, state contingent contracts may prevent lack of optimal risk taking.     

Value at risk estimation by quantile regression and kernel estimator

Risk management has attracted a great deal of attention, and Value at Risk (VaR) has emerged as a particularly popular and important measure for detecting the market risk of financial assets. The quantile regression method can generate VaR estimates without distributional assumptions; however, empirical evidence has shown the approach to be ineffective at evaluating the real level of downside risk in out-of-sample examination. This paper proposes a process in VaR estimation with methods of quantile regression and kernel estimator which applies the nonparametric technique with extreme quantile forecasts to realize a tail distribution and locate the VaR estimates. Empirical application of worldwide stock indices with 29 years of data is conducted and confirms the proposed approach outperforms others and provides highly reliable estimates.     

The Risk Map: A new tool for validating risk models

This paper presents a new method to validate risk models: the Risk Map. This method jointly accounts for the number and the magnitude of extreme losses and graphically summarizes all information about the performance of a risk model. It relies on the concept of a super exception, which is defined as a situation in which the loss exceeds both the standard Value-at-Risk (VaR) and a VaR defined at an extremely low probability. We then formally test whether the sequences of exceptions and super exceptions are rejected by standard model validation tests. We show that the Risk Map can be used to validate market, credit, operational, or systemic risk estimates (VaR, stressed VaR, expected shortfall, and CoVaR) or to assess the performance of the margin system of a clearing house.     

Analysing Perceived Downside Risk: the Component Value‐at‐Risk Framework

Multinational companies face increasing risks arising from external risk factors, e.g. exchange rates, interest rates and commodity prices, which they have learned to hedge using derivatives. However, despite increasing disclosure requirements, a firm's net risk profile may not be transparent to shareholders. We develop the ‘Component Value‐at‐Risk (VaR)’ framework for companies to identify the multi‐dimensional downside risk profile as perceived by shareholders. This framework allows for decomposing downside risk into components that are attributable to each of the underlying risk factors. The firm can compare this perceived VaR, including its composition and dynamics, to an internal VaR based on net exposures as it is known to the company. Any differences may lead to surprises at times of earnings announcements and thus constitute a litigation threat to the firm. It may reduce this information asymmetry through targeted communication efforts.     

基于动态因子Copula模型的我国银行系统性风险度量

本文基于2007年至2019年我国14家上市银行的股票收益率,构建偏态t-分布动态因子Copula模型,利用时变荷载因子刻画单家银行与整个系统的相关性,计算联合风险概率作为系统性风险整体水平的度量,基于关联性视角提出了新的单家机构系统脆弱性和系统重要性度量指标——系统脆弱性程度和系统重要性程度。该方法充分考虑了银行个体差异性和系统的内在关联性以及收益率的厚尾性和非对称性,从而能够捕捉到更多的信息且兼具时效性。研究表明:银行机构在风险聚集时期相关程度更大,联合风险概率能够准确识别出系统性风险事件且在我国推行宏观审慎评估体系以后有明显降低;整体而言,大型商业银行系统重要性水平最高,同时风险抗压能力也最强;本文使用的度量方法降低了数据获取成本且更具时效性,有助于为宏观审慎差异化监管工作提供借鉴和参考。     

Nonlinear portfolio selection using approximate parametric Value-at-Risk

As the skewed return distribution is a prominent feature in nonlinear portfolio selection problems which involve derivative assets with nonlinear payoff structures, Value-at-Risk (VaR) is particularly suitable to serve as a risk measure in nonlinear portfolio selection. Unfortunately, the nonlinear portfolio selection formulation using VaR risk measure is in general a computationally intractable optimization problem. We investigate in this paper nonlinear portfolio selection models using approximate parametric Value-at-Risk. More specifically, we use first-order and second-order approximations of VaR for constructing portfolio selection models, and show that the portfolio selection models based on Delta-only, Delta–Gamma-normal and worst-case Delta–Gamma VaR approximations can be reformulated as second-order cone programs, which are polynomially solvable using interior-point methods. Our simulation and empirical results suggest that the model using Delta–Gamma-normal VaR approximation performs the best in terms of a balance between approximation accuracy and computational efficiency.     

The impact of the choice of VaR models on the level of regulatory capital according to Basel II

The Basel II framework allows the calculation of the capital requirements for market risk with Value-at-Risk models. Since no special model is prescribed in the framework, banks may use simple models with questionable assumptions concerning their underlying distributions. Our numerical analysis reveals that simple VaR models that perform noticeably worse than comparable simple models with more realistic assumptions may lead to a lower level of regulatory capital for banks. For this reason, banks have a major incentive to implement bad models. This is obviously contrary to the interests of regulatory authorities.     

Value at risk,mispricing and expected returns

This study investigates how the relation between value-at-risk (VaR) and expected returns differs under different mispricing statuses. We find that a significantly negative VaR-return relation, defined as the VaR effect, is observed only for overpriced stocks, but not for underpriced stocks. Moreover, VaR has an amplification effect on mispricing, indicating that VaR captures risk that deters arbitrage and thus leads to an increase in mispricing. Our results are robust to alternative VaR definitions, subperiod analysis, different market states, and after controlling for other firm characteristics, well-known risk factors, and those variables that have been shown to have amplifying effects on mispricing. Finally, this study also examines the pricing effect of short sale constraints on the VaR effect under different mispricing statuses. Our findings suggest that the VaR effect observed in overpriced stocks becomes more severe as short sales are more constrained.     

Risk evaluations with robust approximate factor models

Approximate factor models and their extensions are widely used in economic analysis and forecasting due to their ability to extracting useful information from a large number of relevant variables. In these models, candidate predictors are typically subject to some common components. In this paper we propose a new method for robustly estimating the approximate factor models and use it in risk assessments. We consider a class of approximate factor models in which the candidate predictors are additionally subject to idiosyncratic large uncommon components such as jumps or outliers. By assuming that occurrences of the uncommon components are rare, we develop an estimation procedure to simultaneously disentangle and estimate the common and uncommon components. We then use the proposed method to investigate whether risks from the latent factors are priced for expected returns of Fama and French 100 size and book-to-market ratio portfolios. We find that while the risk from the common factor is priced for the 100 portfolios, the risks from the idiosyncratic factors are not. However, we find that model uncertainty risks of the idiosyncratic factors are priced, suggesting that with effective diversifications, only the predictable idiosyncratic risks can be reduced, but the unpredictable ones may still exist. We also illustrate how the proposed method can be adopted on evaluating value at risk (VaR) and find it can delivery comparable results as the conventional methods on VaR evaluations.