Forecasting High‐Frequency Risk Measures

This article proposes intraday high‐frequency risk (HFR) measures for market risk in the case of irregularly spaced high‐frequency data. In this context, we distinguish three concepts of value‐at‐risk (VaR): the total VaR, the marginal (or per‐time‐unit) VaR and the instantaneous VaR. Since the market risk is obviously related to the duration between two consecutive trades, these measures are completed with a duration risk measure, i.e. the time‐at‐risk (TaR). We propose a forecasting procedure for VaR and TaR for each trade or other market microstructure event. Subsequently, we perform a backtesting procedure specifically designed to assess the validity of the VaR and TaR forecasts on irregularly spaced data. The performance of the HFR measure is illustrated in an empirical application for two stocks (Bank of America and Microsoft) and an exchange‐traded fund based on Standard & Poor's 500 index. We show that the intraday HFR forecasts capture accurately the volatility and duration dynamics for these three assets. Copyright © 2015 John Wiley & Sons, Ltd.     

The impact of parameter and model uncertainty on market risk predictions from GARCH‐type models

We study the effect of parameter and model uncertainty on the left‐tail of predictive densities and in particular on VaR forecasts. To this end, we evaluate the predictive performance of several GARCH‐type models estimated via Bayesian and maximum likelihood techniques. In addition to individual models, several combination methods are considered, such as Bayesian model averaging and (censored) optimal pooling for linear, log or beta linear pools. Daily returns for a set of stock market indexes are predicted over about 13 years from the early 2000s. We find that Bayesian predictive densities improve the VaR backtest at the 1% risk level for single models and for linear and log pools. We also find that the robust VaR backtest exhibited by linear and log pools is better than the backtest of single models at the 5% risk level. Finally, the equally weighted linear pool of Bayesian predictives tends to be the best VaR forecaster in a set of 42 forecasting techniques.     

基于logistic分布的在险价值计算方法

针对Risk Metrics方法的不足,利用logistic分布对其进行了改进,并采用事后检验法对两种方法进行了比较,结果表明基于logistic分布的计算方法优于Risk Metrics方法.     

评估Value-at-Risk模型——条件矩检验方法

提出一种基于条件矩检验的Value-at-Risk （VaR）模型评估方法. 其基本思想是如果VaR模型无设定误差，则观察到的“突破”事件是鞅过程.因此可以通过检验“突破”事件是否为鞅对VaR模型进行设定检验. 采用条件矩检验方法对风险管理行业普遍使用的八种VaR 模型进行回测检验，作者发现条件历史模拟法表现最好，通过了各种检验，而无条件正态分布VaR模型表现最差，没有通过任何一种检验. 在风险管理实务中，作者推荐使用条件历史模拟法度量和管理金融风险.     

组合信用风险测度的藤copula方法

研究组合信用风险测度问题,用藤copula描述违约相依结构,提出一种测度组合信用风险的藤copula方法.实证结果表明:常用多元copula方法往往低估或高估风险值,而藤copula方法在各种常用的多元copula相依结构假定下的VaR和ES估计值与实际风险值很接近,VaP都通过了回测检验,ES回测检验指标也表明藤copula方法估计的ES更准确.因此,相对于常用多元copula,藤copula方法更具灵活性,能提高组合信用风险测度的准确性.     

Backtesting Value‐at‐Risk: A Generalized Markov Test

Testing the validity of value‐at‐risk (VaR) forecasts, or backtesting, is an integral part of modern market risk management and regulation. This is often done by applying independence and coverage tests developed by Christoffersen (International Economic Review, 1998; 39(4), 841–862) to so‐called hit‐sequences derived from VaR forecasts and realized losses. However, as pointed out in the literature, these aforementioned tests suffer from low rejection frequencies, or (empirical) power when applied to hit‐sequences derived from simulations matching empirical stylized characteristics of return data. One key observation of the studies is that higher‐order dependence in the hit‐sequences may cause the observed lower power performance. We propose to generalize the backtest framework for VaR forecasts, by extending the original first‐order dependence of Christoffersen to allow for a higher‐ or kth‐order dependence. We provide closed‐form expressions for the tests as well as asymptotic theory. Not only do the generalized tests have power against kth‐order dependence by definition, but also included simulations indicate improved power performance when replicating the aforementioned studies. Further, included simulations show much improved size properties of one of the suggested tests. Copyright © 2017 John Wiley & Sons, Ltd.     

Backtesting Aggregate Risk

This paper proposes the implementation of a VaR backtesting procedure able to overcome the subadditivity property failure of value‐at‐risk (VaR). More precisely, we propose the implementation of a multivariate portmanteau test statistic of Ljung–Box type applied to hits collected from several trading desks or divisions at once. Simulation \exercises illustrate that this method is testing for aggregate risk, accurately accounting both for diversification (negative hit cross‐correlation) and contagion/risk spillovers (positive hit cross‐correlation). An application using profit and loss and VaR data collected for two international major banks illustrates how our proposed backtesting procedure performs in a realistic environment. Copyright © 2015 John Wiley & Sons, Ltd.     

Measuring the market risk of freight rates: A forecast combination approach

This paper addresses the issue of freight rate risk measurement via value at risk (VaR) and forecast combination methodologies while focusing on detailed performance evaluation. We contribute to the literature in three ways: First, we reevaluate the performance of popular VaR estimation methods on freight rates amid the adverse economic consequences of the recent financial and sovereign debt crisis. Second, we provide a detailed and extensive backtesting and evaluation methodology. Last, we propose a forecast combination approach for estimating VaR. Our findings suggest that our combination methods produce more accurate estimates for all the sectors under scrutiny, while in some cases they may be viewed as conservative since they tend to overestimate nominal VaR.