Realizing the extremes: Estimation of tail-risk measures from a high-frequency perspective

This article applies realized volatility forecasting to Extreme Value Theory (EVT). We propose a two-step approach where returns are first pre-whitened with a high-frequency based volatility model, and then an EVT based model is fitted to the tails of the standardized residuals. This realized EVT approach is compared to the conditional EVT of McNeil & Frey (2000). We assess both approaches' ability to filter the dependence in the extremes and to produce stable out-of-sample VaR and ES estimates for one-day and ten-day time horizons. The main finding is that GARCH-type models perform well in filtering the dependence, while the realized EVT approach seems preferable in forecasting, especially at longer time horizons.     

基于Copula-GARCH-EVT的中国开放式基金投资组合风险度量

文章结合CARCH模型和EVT理论刻画了单个金融资产收益率的波动性和尾部分布,并将Copula函数和Monte Carlo技术应用于证券投资组合的VaR计算方法.通过对光大红利基金的实证研究,得到前十大重仓中单只股票及其投资组合的风险值,结果表明,基于Copula-GARCH-EVT的VaR方法具有重要的经济应用价值.     

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.     

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。     

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.     

El efecto de la volatilidad del peso mexicano en los rendimientos y riesgo de la Bolsa Mexicana de Valores

The effect of heavy tails due to rare events and different levels of asymmetry associated with high volatility clustering in the emerging financial markets requires sophisticated models for statistical modelling of such stylized facts. This article applies extreme value theory (EVT) to quantify tail risk on the daily returns of Mexican stock market under aggregation of foreign exchange rate risk from January 1971 to December 2010. This study focuses on the maximum-block method and generalized extreme value distribution (GEVD) to model the asymptotic behavior of extreme returns in US dollars. The empirical results show that EVT-Based VaR measured at high confidence levels performs better than simulation historical and delta-normal VaR models on capturing fat-tails in the returns of highly volatile stock markets. Additionally, international investors holding long positions in Mexican stock market are more prone to experience larger potential losses than investors with short positions during local currency depreciation and financial crisis periods.     

Exchange market pressure in India

We empirically investigate episodes of currency market stress in India during the period January 1992–August 2014 with the help of a monthly EMP index for India constructed for this period. We analyse the distribution of the extreme values of the EMP index by using Extreme Value Theory (EVT) and utilize the knowledge of the extreme values of our EMP index to identify currency market stress in India during this period. We analyse these stress episodes in the context of the prevailing economic situation. We also present a decomposition of the contribution of different factors towards exchange market pressure.     

A new unbiased additive robust volatility estimation using extreme values of asset prices

Financial Markets and Portfolio Management - We propose a new unbiased robust volatility estimator based on extreme values of asset prices. We show that the proposed Add Extreme Value Robust...     

A parametric alternative to the Hill estimator for heavy-tailed distributions

Despite its wide use, the Hill estimator and its plot remain to be difficult to use in Extreme Value Theory (EVT) due to substantial sampling variations in extreme sample quantiles. In this paper, we propose a new plot we call the eigenvalue plot which can be seen as a generalization of the Hill plot. The theory behind the plot is based on a heavy-tailed parametric distribution class called the scaled Log phase-type (LogPH) distributions, a generalization of the ordinary LogPH distribution class which was previously used to model insurance claims data. We show that its tail property and moment condition are well aligned with EVT. Based on our findings, we construct the eigenvalue plot from fitting a shifted PH distribution to the excess log data with a minimal phase size. Through various numerical examples we illustrate and compare our method against the Hill plot.     

A folding methodology for multivariate extremes: estimation of the spectral probability measure and actuarial applications

In this paper, the folding methodology developed in the context of univariate Extreme Value Theory (EVT) by You et al. is extended to a multivariate framework. Under the usual EVT assumption of regularly varying tails, our multivariate folding allows for the estimation of the spectral probability measure. A new weakly consistent estimator based on the classical empirical estimator is proposed. Its behaviour is illustrated through simulations and an actuarial application relative to reinsurance pricing in the case of an insurance data-set.     

The Effect of VaR Based Risk Management on Asset Prices and the Volatility Smile

Value-at-risk (VaR) has become the standard criterion for assessing risk in the financial industry. Given the widespread usage of VaR, it becomes increasingly important to study the effects of VaR based risk management on the prices of stocks and options. We solve a continuous-time asset pricing model, based on Lucas (1978) and Basak and Shapiro (2001), to investigate these effects. We find that the presence of risk managers tends to reduce market volatility, as intended. However, in some cases VaR risk management undesirably raises the probability of extreme losses. Finally, we demonstrate that option prices in an economy with VaR risk managers display a volatility smile.     

Estimation of tail‐related risk measures in the Indian stock market: An extreme value approach

The purpose of the study is to estimate tail-related risk measures using extreme value theory (EVT) in the Indian stock market. The study employs a two stage approach of conditional EVT originally proposed by McNeil and Frey (2000) to estimate dynamic Value at Risk (VaR) and expected shortfall (ES). The dynamic risk measures have been estimated for different percentiles for negative and positive returns. The estimates of risk measures computed under different quantile levels exhibit strong stability across a range of the selected thresholds, implying the accuracy and reliability of the estimated quantile based risk measures.     

Effectiveness of copula-extreme value theory in estimating value-at-risk: empirical evidence from Asian emerging markets

A traditional Monte Carlo simulation using linear correlations induces estimation bias in measuring portfolio value-at-risk (VaR), due to the well-documented existence of fat-tail, skewness, truncations, and non-linear relations in return distributions. In this paper, we consider the above issues in modeling VaR and evaluate the effectiveness of using copula-extreme-value-based semiparametric approaches. To assess portfolio risk in six Asian markets, we incorporate a combination of extreme value theory (EVT) and various copulas to build joint distributions of returns. A backtesting analysis using a Monte Carlo VaR simulation suggests that the Clayton copula-EVT evinces the best performance regardless of the shapes of the return distributions, and that in general the copulas with the EVT provide better estimations of VaRs than the copulas with conventionally employed empirical distributions. These findings still hold in conditional-coverage-based backtesting. These findings indicate the economic significance of incorporating the down-side shock in risk management.     

Forecasting value‐at‐risk in oil prices in the presence of volatility shifts

Recent evidence suggests shifts (structural breaks) in the volatility of returns causes non‐normality by significantly increasing kurtosis. In this paper, we endogenously detect significant shifts in the volatility of oil prices and incorporate this information to estimate Value‐at‐Risk (VaR) to accurately forecast large declines in oil prices. Our out‐of‐sample performance results indicate that the model, which incorporates both time varying volatility (without making any distributional assumptions) and shifts in volatility, produces more accurate VaR forecasts than several benchmark methods. We make a timely contribution as the recent more frequent occurrences of unexpected large oil price declines has gained significant attention because of its substantial impact on the financial markets and the global economy.     

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.     

Predicting tail-related risk measures: The consequences of using GARCH filters for non-GARCH data

We investigate the consequences for Value-at-Risk and expected shortfall purposes of using a GARCH filter on various mis-specified processes. In general, we find that the McNeil and Frey (McNeil, A.J. and R. Frey, 2000, Estimation of Tail-Related Risk Measures for Heteroscedastic Financial Time Series: An Extreme Value Approach, Journal of Empirical Finance 7, 271–300.) two step procedure has very good forecasting properties. Using an unconditional non-filtered tail estimate also appears to perform satisfactorily for expected shortfall measurements but less so for VaR computations. Methods assuming specific densities such as the Gaussian or Student-t may yield wrong predictions. Thus, the use of an adequacy test for filtered data to given densities appears relevant. The paper builds on recent techniques to obtain thresholds for extreme value computations. Statistical tests for the expected shortfall, based on the circular bootstrap, are developed.     

The role of autoregressive conditional skewness and kurtosis in the estimation of conditional VaR

This paper investigates the role of high-order moments in the estimation of conditional value at risk (VaR). We use the skewed generalized t distribution (SGT) with time-varying parameters to provide an accurate characterization of the tails of the standardized return distribution. We allow the high-order moments of the SGT density to depend on the past information set, and hence relax the conventional assumption in conditional VaR calculation that the distribution of standardized returns is iid. The maximum likelihood estimates show that the time-varying conditional volatility, skewness, tail-thickness, and peakedness parameters of the SGT density are statistically significant. The in-sample and out-of-sample performance results indicate that the conditional SGT-GARCH approach with autoregressive conditional skewness and kurtosis provides very accurate and robust estimates of the actual VaR thresholds.