Intraday risk management in International stock markets: A conditional EVT approach

The study compares the predictive ability of various models in estimating intraday Value-at-Risk (VaR) and Expected Shortfall (ES) using high frequency share price index data from sixteen different countries across the world for a period of seven and half months from September 20, 2013 to May 07, 2014. The main emphasis of the study has been given to Extreme Value Theory (EVT) and to evaluate how well Conditional EVT model performs in modeling tails of distributions and in estimating and forecasting intraday VaR and ES measures. We have followed McNeil and Frey's (2000) two stage approach called Conditional EVT to estimate dynamic intraday VaR and ES. We have compared the accuracy of Conditional EVT approach to intraday VaR and ES estimation with other competing models. The best performing model is found to be the Conditional EVT in estimating both the quantiles for the entire sample. The study is useful for market participants (such as intraday traders and market makers) involved in frequent intraday trading in such equity markets.     

Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach

We propose a method for estimating Value at Risk (VaR) and related risk measures describing the tail of the conditional distribution of a heteroscedastic financial return series. Our approach combines pseudo-maximum-likelihood fitting of GARCH models to estimate the current volatility and extreme value theory (EVT) for estimating the tail of the innovation distribution of the GARCH model. We use our method to estimate conditional quantiles (VaR) and conditional expected shortfalls (the expected size of a return exceeding VaR), this being an alternative measure of tail risk with better theoretical properties than the quantile. Using backtesting of historical daily return series we show that our procedure gives better 1-day estimates than methods which ignore the heavy tails of the innovations or the stochastic nature of the volatility. With the help of our fitted models we adopt a Monte Carlo approach to estimating the conditional quantiles of returns over multiple-day horizons and find that this outperforms the simple square-root-of-time scaling method.     

After VaR: The Theory, Estimation, and Insurance Applications of Quantile-Based Risk Measures

We discuss a number of quantile‐based risk measures (QBRMs) that have recently been developed in the financial risk and actuarial/insurance literatures. The measures considered include the Value‐at‐Risk (VaR), coherent risk measures, spectral risk measures, and distortion risk measures. We discuss and compare the properties of these different measures, and point out that the VaR is seriously flawed. We then discuss how QBRMs can be estimated, and discuss some of the many ways they might be applied to insurance risk problems. These applications are typically very complex, and this complexity means that the most appropriate estimation method will often be some form of stochastic simulation.     

Managing extreme risks in tranquil and volatile markets using conditional extreme value theory

Financial risk management typically deals with low-probability events in the tails of asset price distributions. To capture the behavior of these tails, one should therefore rely on models that explicitly focus on the tails. Extreme value theory (EVT)-based models do exactly that, and in this paper, we apply both unconditional and conditional EVT models to the management of extreme market risks in stock markets. We find conditional EVT models to give particularly accurate Value-at-Risk (VaR) measures, and a comparison with traditional (Generalized ARCH (GARCH)) approaches to calculate VaR demonstrates EVT as being the superior approach both for standard and more extreme VaR quantiles.     

Conditional VaR using EVT - Towards a planned margin scheme

This paper constructs a robust Value-at-Risk (VaR) measure for the Indian stock markets by combining two well-known facts about equity return time series — dynamic volatility resulting in the well-recognized phenomenon of volatility clustering, and non-normality giving rise to fat tails of the return distribution. While the phenomenon of volatility dynamics has been extensively studied using GARCH model and its many relatives, the application of Extreme Value Theory (EVT) is relatively recent in tracking extreme losses in the study of risk measurement. There are recent applications of Extreme Value Theory to estimate the unexpected losses due to extreme events and hence modify the current methodology of VaR. Extreme value theory (EVT) has been used to analyze financial data showing clear non-normal behavior. We combine the two methodologies to come up with a robust model with much enhanced predictive abilities. A robust model would obviate the need for imposing special ad hoc margins by the regulator in times of extreme volatility. A rule based margin system would increase efficiency of the price discovery process and also the market integrity with the regulator no longer seen as managing volatility.     

The ‘competition–stability/fragility’ nexus: A comparative analysis of Islamic and conventional banks

The ‘competition–stability/fragility’ nexus is one of the more debated issues in the banking literature. However, while there is ample evidence concerning the relationship between competition and stability/fragility in different countries and regions, no prior study investigates this in the context of Islamic and conventional banks. We do this using data on both types of banks drawn from 16 developing economies over the period 2000–12. We measure the lack of competition using the Lerner index, and stability using both accounting-based measures, comprising the Z-score and the nonperforming loan ratio, and market-based measures, including Merton's distance to default. We employ panel vector autoregression and two-stage quantile regression to estimate the relationship. Our results lend support to the competition–fragility hypothesis in both Islamic and conventional banks. We also find the magnitude of the market power effect on stability is greater for conventional banks than Islamic banks. Lastly, banks in the median quantile of stability have a greater ability to reduce credit risk through gaining market power than banks in the lower and upper quantiles.     

Financial crisis,Value-at-Risk forecasts and the puzzle of dependency modeling

Forecasting Value-at-Risk (VaR) for financial portfolios is a crucial task in applied financial risk management. In this paper, we compare VaR forecasts based on different models for return interdependencies: volatility spillover (Engle & Kroner, 1995), dynamic conditional correlations (Engle, 2002, 2009) and (elliptical) copulas (Embrechts et al., 2002). Moreover, competing models for marginal return distributions are applied. In particular, we apply extreme value theory (EVT) models to GARCH-filtered residuals to capture excess returns.Drawing on a sample of daily data covering both calm and turbulent market phases, we analyze portfolios consisting of German Stocks, national indices and FX-rates. VaR forecasts are evaluated using statistical backtesting and Basel II criteria. The extensive empirical application favors the elliptical copula approach combined with extreme value theory (EVT) models for individual returns. 99% VaR forecasts from the EVT-GARCH-copula model clearly outperform estimates from alternative models accounting for dynamic conditional correlations and volatility spillover for all asset classes in times of financial crisis.     

典型事实、极值理论与金融市场动态风险测度研究

本文在金融市场典型事实约束下,运用ARFIMA模型对金融市场条件收益率建模,运用GARCH、GJR、FIGARCH、APARCH、FIAPARCH等5种模型对金融波动率进行建模,进而运用极值理论(EVT)对标准收益的极端尾部风险建模来测度各股市的动态风险,并用返回测试(Back-testing)方法检验模型的适应性。实证结果表明,总的来说,FIAPARCH-EVT模型对各个市场具有较强的适应性,风险测度能力较为优越。进一步,本文在ARFIMA-FIAPARCH模型下,假定标准收益分别服从正态分布(N)、学生t分布(st)、有偏学生t分布(skst)、广义误差分布(GED)共4种分布,对各股市的动态风险测度的准确性进行检验,并和EVT方法的测度结果进行对比分析。结果表明,EVT方法风险测度能力优于其他方法,有偏学生t分布假设下的风险测度模型虽然略逊于EVT方法,但也不失为一种较好的方法;ARFIMA-FI-APARCH-EVT不仅在中国大陆沪深股市表现最为可靠,而且在其他市场也表现出同样的可靠性。     

Risk management under extreme events

This article presents two applications of extreme value theory (EVT) to financial markets: computation of value at risk (VaR) and cross-section dependence of extreme returns (i.e., tail dependence). We use a sample comprised of the United States, Europe, Asia, and Latin America. Our main findings are the following. First, on average, EVT gives the most accurate estimate of VaR. Second, tail dependence of paired returns decreases substantially when both heteroscedasticity and serial correlation are filtered out by a multivariate GARCH model. Both findings are in agreement with previous research in this area for other financial markets.     

Value-at-risk in a market subject to regime switching

Many empirical researches report that value-at-risk (VaR) measures understate the actual 1% quantile, while for Inui, K., Kijima, M. and Kitano, A., VaR is subject to a significant positive bias. Stat. Probab. Lett., 2005, 72, 299–311. proved that VaR measures overstate significantly when historical simulation VaR is applied to fat-tail distributions. This paper resolves the puzzle by developing a regime switching model to estimate portfolio VaR. It is shown that our model is able to correct the underestimation problem of risk.     

Systemic risk spillovers in the European banking and sovereign network

We propose a framework for estimating time-varying systemic risk contributions that is applicable to a high-dimensional and interconnected financial system. Tail risk dependencies and systemic risk contributions are estimated using a penalized two-stage fixed-effects quantile approach, which explicitly links time-varying interconnectedness to systemic risk contributions. For the purposes of surveillance and regulation of financial systems, network dependencies in extreme risks are more relevant than simple (mean) correlations. Thus, the framework provides a tool for supervisors, reflecting the market's view of tail dependences and systemic risk contributions. The model is applied to a system of 51 large European banks and 17 sovereigns during the period from 2006 through 2013, utilizing both equity and CDS prices. We provide new evidence on how banking sector fragmentation and sovereign-bank linkages evolved over the European sovereign debt crisis, and how they are reflected in estimated network statistics and systemic risk measures. Finally, our evidence provides an indication that the fragmentation of the European financial system has peaked.     

Risk Management for Linear and Non-Linear Assets: A Bootstrap Method with Importance Resampling to Evaluate Value-at-Risk

Many empirical studies suggest that the distribution of risk factors has heavy tails. One always assumes that the underlying risk factors follow a multivariate normal distribution that is a assumption in conflict with empirical evidence. We consider a multivariate t distribution for capturing the heavy tails and a quadratic function of the changes is generally used in the risk factor for a non-linear asset. Although Monte Carlo analysis is by far the most powerful method to evaluate a portfolio Value-at-Risk (VaR), a major drawback of this method is that it is computationally demanding. In this paper, we first transform the assets into the risk on the returns by using a quadratic approximation for the portfolio. Second, we model the return’s risk factors by using a multivariate normal as well as a multivariate t distribution. Then we provide a bootstrap algorithm with importance resampling and develop the Laplace method to improve the efficiency of simulation, to estimate the portfolio loss probability and evaluate the portfolio VaR. It is a very powerful tool that propose importance sampling to reduce the number of random number generators in the bootstrap setting. In the simulation study and sensitivity analysis of the bootstrap method, we observe that the estimate for the quantile and tail probability with importance resampling is more efficient than the naive Monte Carlo method. We also note that the estimates of the quantile and the tail probability are not sensitive to the estimated parameters for the multivariate normal and the multivariate t distribution. The research of Shih-Kuei Lin was partially supported by the National Science Council under grants NSC 93-2146-H-259-023. The research of Cheng-Der Fuh was partially supported by the National Science Council under grants NSC 94-2118-M-001-028.     

Re-Examining the Determinants of Islamic Bank Performance: New Evidence from Dynamic GMM,Quantile Regression,and Wavelet Coherence Approaches

This study is the first attempt to conduct a comparative analysis of the internal and external determinants of the Islamic banks’ profitability in the GCC region applying dynamic GMM, quantile regression, and wavelet coherence approaches. The dynamic GMM tends to indicate that equity financing and operating efficiency and macroeconomic variables such as money supply, and inflation are significantly related to Islamic banks’ performance. The bank-specific variables such as credit risk, equity ratio, and cost-efficiency ratios are not significant at different percentiles. ROA is driven by credit risk, equity ratio, and cost-efficiency ratios (as evidenced in wavelet coherence analysis).     

Backtesting extreme value theory models of expected shortfall

We use stock market data to analyze the quality of alternative models and procedures for forecasting expected shortfall (ES) at different significance levels. We compute ES forecasts from conditional models applied to the full distribution of returns as well as from models that focus on tail events using extreme value theory (EVT). We also apply the semiparametric filtered historical simulation (FHS) approach to ES forecasting to obtain 10-day ES forecasts. At the 10-day horizon we combine FHS with EVT. The performance of the different models is assessed using six different ES backtests recently proposed in the literature. Our results suggest that conditional EVT-based models produce more accurate 1-day and 10-day ES forecasts than do non-EVT based models. Under either approach, asymmetric probability distributions for return innovations tend to produce better forecasts. Incorporating EVT in parametric or semiparametric approaches also improves ES forecasting performance. These qualitative results are also valid for the recent crisis period, even though all models then underestimate the level of risk. FHS narrows the range of numerical forecasts obtained from alternative models, thereby reducing model risk. Combining EVT and FHS seems to be best approach for obtaining accurate ES forecasts.     

Banking systemic vulnerabilities: A tail-risk dynamic CIMDO approach

This study proposes a novel framework which combines marginal probabilities of default estimated from a structural credit risk model with the consistent information multivariate density optimization (CIMDO) methodology and the generalized dynamic factor model (GDFM) supplemented by a dynamic t-copula. The framework models banks’ default dependence explicitly and captures the time-varying non-linearities and feedback effects typical of financial markets. It measures banking systemic credit risk in the three forms categorized by the European Central Bank: (1) credit risk common to all banks; (2) credit risk in the banking system conditional on distress on a specific bank or combinations of banks; and (3) the buildup of banking system vulnerabilities over time which may unravel disorderly. In addition, the estimates of the common components of the banking sector short-term and conditional forward default measures contain early warning features, and the identification of their drivers is useful for macroprudential policy. Finally, the framework produces robust out-of-sample forecasts of the banking systemic credit risk measures. This paper advances the agenda of making macroprudential policy operational.     

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 Some alternative estimates of the adjustment coefficient in risk theory

Abstract

Recently, Csörgö and Steinebach proposed to estimate the adjustment coefficient in risk theory via a quantile type estimate based upon a sequence of intermediate order statistics. In the present paper, further alternative estimators are discussed which may be viewed as convex combinations of a Hill type and a quantile type estimate. Consistency is proved and rates of convergence are studied. Some simulation results are presented to illustrate the finite sample behavior of the proposed estimators.     

Option-Implied Risk Aversion Estimates

Using a utility function to adjust the risk‐neutral PDF embedded in cross sections of options, we obtain measures of the risk aversion implied in option prices. Using FTSE 100 and S&P 500 options, and both power and exponential‐utility functions, we estimate the representative agent's relative risk aversion (RRA) at different horizons. The estimated coefficients of RRA are all reasonable. The RRA estimates are remarkably consistent across utility functions and across markets for given horizons. The degree of RRA declines broadly with the forecast horizon and is lower during periods of high market volatility.     

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.     

Quantile forecasts of daily exchange rate returns from forecasts of realized volatility

Quantile forecasts are central to risk management decisions because of the widespread use of Value-at-Risk. A quantile forecast is the product of two factors: the model used to forecast volatility, and the method of computing quantiles from the volatility forecasts. In this paper we calculate and evaluate quantile forecasts of the daily exchange rate returns of five currencies. The forecasting models that have been used in recent analyses of the predictability of daily realized volatility permit a comparison of the predictive power of different measures of intraday variation and intraday returns in forecasting exchange rate variability. The methods of computing quantile forecasts include making distributional assumptions for future daily returns as well as using the empirical distribution of predicted standardized returns with both rolling and recursive samples. Our main findings are that the Heterogenous Autoregressive model provides more accurate volatility and quantile forecasts for currencies which experience shifts in volatility, such as the Canadian dollar, and that the use of the empirical distribution to calculate quantiles can improve forecasts when there are shifts.