A Bayesian approach for more reliable tail risk forecasts

This paper demonstrates that existing quantile regression models used for jointly forecasting Value-at-Risk (VaR) and expected shortfall (ES) are sensitive to initial conditions. Given the importance of these measures in financial systems, this sensitivity is a critical issue. A new Bayesian quantile regression approach is proposed for estimating joint VaR and ES models. By treating the initial values as unknown parameters, sensitivity issues can be dealt with. Furthermore, new additive-type models are developed for the ES component that are more robust to initial conditions. A novel approach using the open-faced sandwich (OFS) method is proposed which improves uncertainty quantification in risk forecasts. Simulation and empirical results highlight the improvements in risk forecasts ensuing from the proposed methods.     

An approximate long-memory range-based approach for value at risk estimation

This paper proposes new approximate long-memory VaR models that incorporate intra-day price ranges. These models use lagged intra-day range with the feature of considering different range components calculated over different time horizons. We also investigate the impact of the market overnight return on the VaR forecasts, which has not yet been considered with the range in VaR estimation. Model estimation is performed using linear quantile regression. An empirical analysis is conducted on 18 market indices. In spite of the simplicity of the proposed methods, the empirical results show that they successfully capture the main features of the financial returns and are competitive with established benchmark methods. The empirical results also show that several of the proposed range-based VaR models, utilizing both the intra-day range and the overnight returns, are able to outperform GARCH-based methods and CAViaR models.     

中国金融市场间极端风险溢出的监测预警研究——基于MVMQ-CAViaR方法的实现

为有效监测与预警中国金融市场间极端风险溢出的方向与程度,本文基于MVMQ-CAViaR方法,结合中国2013—2017年银行间市场、债券市场与股票市场相关数据,分析各金融市场间的极端风险传递过程。实证结果显示,股票市场与债券市场对银行间市场产生显著的单向极端风险溢出效应,而银行间市场对另外两个市场无极端风险传递效果,这表明股票市场与债券市场的极端风险向银行间市场的传递过程具有不可逆性。从风险传递的强度来看,债券市场对股票市场和银行间市场的极端风险溢出效应更加显著。因此,决策部门应重点关注债券市场的极端风险水平变化,缓释债券市场与股票市场对银行间市场的极端风险冲击,以有效防范和化解不同金融市场间极端风险的传染与暴露。     

A Bayesian encompassing test using combined value-at-risk estimates

The Value at Risk (VaR) is a risk measure that is widely used by financial institutions in allocating risk. VaR forecast estimation involves the conditional evaluation of quantiles based on the currently available information. Recent advances in VaR evaluation incorporate conditional variance into the quantile estimation, yielding the Conditional Autoregressive VaR (CAViaR) models. However, the large number of alternative CAViaR models raises the issue of identifying the optimal quantile predictor. To resolve this uncertainty, we propose a Bayesian encompassing test that evaluates various CAViaR models predictions against a combined CAViaR model based on the encompassing principle. This test provides a basis for forecasting combined conditional VaR estimates when there are evidences against the encompassing principle. We illustrate this test using simulated and financial daily return data series. The results demonstrate that there are evidences for using combined conditional VaR estimates when forecasting quantile risk.     

An Extensive Comparison of Some Well‐Established Value at Risk Methods

In the last two decades, several methods for estimating Value at Risk have been proposed in the literature. Four of the most successful approaches are conditional autoregressive Value at Risk, extreme value theory, filtered historical simulation and time‐varying higher order conditional moments. In this paper, we compare their performances under both an empirical investigation using 80 assets and a large Monte Carlo simulation. From our analysis, we conclude that most of the methods seem not to imply huge numerical difficulties and, according to usual backtests and performance measurements, extreme value theory presents the best results most of the times, followed by filtered historical simulation.     

Portfolio selection based on predictive joint return distribution

A predictive joint return distribution can provide more useful information than moment-based risk measures in portfolio selection. This article develops a D-vine copula-CAViaR method to estimate and predict the joint probability distribution of multiple financial returns. Furthermore, we construct a portfolio model via the generalized Omega ratio inferred from the predicted joint return distribution. The superiority of our method is illustrated through an empirical application on five international stock market indices.     

Tail risk of coal futures in China's market

This study evaluates the downside tail risk of coal futures contracts (coke, coking coal and thermal coal) traded in the Chinese market between 2011 and 2021, measured by value at risk (VaR). We examine the one-day-ahead VaR forecasting performance with a hybrid econometric and deep learning model (GARCH-LSTM), GARCH family models, extreme value theory models, quantile regression models and two naïve models (historical simulation and exponentially weighted moving average). We use four backtesting techniques and the model confidence set to identify the optimal models. The results suggest that the models focusing on tail risk or utilising long short-term memory generate more effective risk management.