Forecasting extreme financial risk: A score-driven approach

This paper develops a new class of dynamic models for forecasting extreme financial risk. This class of models is driven by the score of the conditional distribution with respect to both the duration between extreme events and the magnitude of these events. It is shown that the models are a feasible method for modeling the time-varying arrival intensity and magnitude of extreme events. It is also demonstrated how exogenous variables such as realized measures of volatility can easily be incorporated. An empirical analysis based on a set of major equity indices shows that both the arrival intensity and the size of extreme events vary greatly during times of market turmoil. The proposed framework performs well relative to competing approaches in forecasting extreme tail risk measures.     

Risk spillover analysis of China’s financial sectors based on a new GARCH copula quantile regression model

This study employs a new GARCH copula quantile regression model to estimate the conditional value at risk for systemic risk spillover analysis. To be specific, thirteen copula quantile regression models are derived to capture the asymmetry and nonlinearity of the tail dependence between financial returns. Using Chinese stock market data over the period from January 2007 to October 2020, this paper investigates the risk spillovers from the banking, securities, and insurance sectors to the entire financial system. The empirical results indicate that (i) three financial sectors contribute significantly to the financial system, and the insurance sector displays the largest risk spillover effects on the financial system, followed by the banking sector and subsequently the securities sector; (ii) the time-varying risk spillovers are much larger during the global financial crisis than during the periods of the banking liquidity crisis, the stock market crash and the COVID-19 pandemic. Our results provide important implications for supervisory authorities and portfolio managers who want to maintain the stability of China’s financial system and optimize investment portfolios.     

Systemic risk in European financial and energy sectors: Dynamic factor copula approach

We perform an analysis of systemic risk in financial and energy sectors in Europe using daily time series of CDS spreads. We employ the factor copula model with GAS dynamics from Oh and Patton (2018) for the purpose of estimating dependency structures between market participants. Based on the estimated models, we perform Monte Carlo simulations to obtain future values of CDS spreads, and then measure the probability of systemic events at given time points. We conclude that substantially higher systemic risk is present in the financial sector compared to the energy sector. We also find that the most systemically vulnerable financial and energy companies come from Spain.     

GARCH-MIDAS-GAS-copula model for CoVaR and risk spillover in stock markets

This study proposes a generalized autoregressive conditional heteroskedasticity (GARCH)-mixed data sampling (MIDAS)-generalized autoregressive score (GAS)-copula model to calculate conditional value at risk (CoVaR). Our approach leverages the GARCH-MIDAS model to enhance stock market volatility modeling and incorporates the GAS mechanism to create a copula with dynamic parameters. This approach allows for the precise calculation of both CoVaR and its changes over time (delta CoVaR). The results of our study demonstrate a significant improvement in CoVaR calculation accuracy compared to other models, showcasing the effectiveness of the GARCH-MIDAS-GAS-copula model. In addition, the CoVaR indicator provides a more comprehensive view of risk spillover relationships compared to value at risk (VaR), offering deeper insights into the asymmetrical risk transmission dynamics between the Chinese and US stock markets, providing valuable information for risk management and investment decisions.     

Statistics of extreme events in risk management: The impact of the subprime and global financial crisis on the German stock market

Given the growing need for managing financial risk and the recent global crisis, risk prediction is a crucial issue in banking and finance. In this paper, we show how recent advances in the statistical analysis of extreme events can provide solid methodological fundamentals for modeling extreme events. Our approach uses self-exciting marked point processes for estimating the tail of loss distributions. The main result is that the time between extreme events plays an important role in the statistical analysis of these events and could therefore be useful to forecast the size and intensity of future extreme events in financial markets. We illustrate this point by measuring the impact of the subprime and global financial crisis on the German stock market in extenso, and briefly as a benchmark in the US stock market. With the help of our fitted models, we backtest the Value at Risk at various quantiles to assess the likeliness of different extreme movements on the DAX, S&P 500 and Nasdaq stock market indices during the crisis. The results show that the proposed models provide accurate risk measures according to the Basel Committee and make better use of the available information.     

Modeling Financial Sector Joint Tail Risk in the Euro Area

We develop a novel high‐dimensional non‐Gaussian modeling framework to infer measures of conditional and joint default risk for numerous financial sector firms. The model is based on a dynamic generalized hyperbolic skewed‐t block equicorrelation copula with time‐varying volatility and dependence parameters that naturally accommodates asymmetries and heavy tails, as well as nonlinear and time‐varying default dependence. We apply a conditional law of large numbers in this setting to define joint and conditional risk measures that can be evaluated quickly and reliably. We apply the modeling framework to assess the joint risk from multiple defaults in the euro area during the 2008–2012 financial and sovereign debt crisis. We document unprecedented tail risks between 2011 and 2012, as well as their steep decline following subsequent policy actions. Copyright © 2016 John Wiley & Sons, Ltd.     

Predicting the portfolio risk of high-dimensional international stock indices with dynamic spatial dependence

The spatial dependence of assets, which relates to similarities in economic, political, or cultural systems and other aspects, has been confirmed through empirical research; however, spatial dependence has rarely been applied to financial risk measurement. To fill this gap in the literature, a dynamic spatial GARCH-copula (sGC) model is proposed in this paper to evaluate the portfolio risk of international stock indices. In this model, a spatial GARCH is used as the marginal distribution and vine copula is adopted as the joint distribution of indices. Then, the proposed model is applied empirically to assess portfolio risk. Results show that, first, the proposed risk prediction model with spatial dependence outperforms a model neglecting spatial effects per the Kupiec test, Z test and Christoffersen test. Risk prediction during periods of economic stability is also more accurate than during times of crisis. Second, risk measures for models with spatial dependence are higher than those without such dependence but lower than for vine copula models. Third, models including either spatial dependence or vine copulas alone exhibit relatively poor performance. Fourth, the model involving extreme value theory (EVT) generates the greatest value at risk to pass the Kupiec test, Z test and Christoffersen test; however, this model is not suitable for characterizing international indices with EVT based on negative values of the shape parameters of estimates. Findings offer important implications for personal investors, institutional investors, and national regulatory authorities.     

Upside/Downside spillovers between oil and Chinese stock sectors: From the global financial crisis to global pandemic

This paper examines the effects of the COVID-19 outbreak, recent oil price fall, and both global and European financial crises on dependence structure and asymmetric risk spillovers between crude oil and Chinese stock sectors. Using time-varying symmetric and asymmetric copula functions and the conditional Value at Risk measure, we provide evidence of positive tail dependence in most sectors using copula and conditional Value-at-Risk techniques. We can see the average dependence between oil and industries during the oil crisis. Moreover, we find strong evidence of bidirectional risk spillovers for all oil-sector pairs. The intensity of risk spillovers from oil to all stock sectors varies across sectors. The risk spillovers from sectors to oil are substantially larger than those from oil to sectors during COVID-19. Furthermore, the return spillover is time varying and sensitive to external shocks. The spillover strengths are higher during COVID-19 than financial and oil crises. Finally, oil do not exhibit neither hedge nor safe-haven characteristics irrespective of crisis periods.     

Estimation of multivariate models for time series of possibly different lengths

We consider the problem of estimating parametric multivariate density models when unequal amounts of data are available on each variable. We focus in particular on the case that the unknown parameter vector may be partitioned into elements relating only to a marginal distribution and elements relating to the copula. In such a case we propose using a multi‐stage maximum likelihood estimator (MSMLE) based on all available data rather than the usual one‐stage maximum likelihood estimator (1SMLE) based only on the overlapping data. We provide conditions under which the MSMLE is not less asymptotically efficient than the 1SMLE, and we examine the small sample efficiency of the estimators via simulations. The analysis in this paper is motivated by a model of the joint distribution of daily Japanese yen–US dollar and euro–US dollar exchange rates. We find significant evidence of time variation in the conditional copula of these exchange rates, and evidence of greater dependence during extreme events than under the normal distribution. Copyright © 2006 John Wiley & Sons, Ltd.     

High quantiles estimation with Quasi-PORT and DPOT: An application to value-at-risk for financial variables

Recurrent ⿿black swans⿿ financial events are a major concern for both investors and regulators because of the extreme price changes they cause, despite their very low probability of occurrence. In this paper, we use unconditional and conditional methods, such as the recently proposed high quantile (HQ) extreme value theory (EVT) models of DPOT (Duration-based Peak Over Threshold) and quasi-PORT (peaks over random threshold), to estimate the Value-at-Risk with very small probability values for an adequately long and major financial time series to obtain a reasonable number of violations for backtesting. We also compare these models and other alternative strategies through an out-of-sample accuracy investigation to determine their relative performance within the HQ context. Policy implications relevant to estimation of risk for extreme events are also provided.     

Extreme returns and intensity of trading

Asymmetric information models of market microstructure claim that variables such as trading intensity are proxies for latent information on the value of financial assets. We consider the interval‐valued time series (ITS) of low/high returns and explore the relationship between these extreme returns and the intensity of trading. We assume that the returns (or prices) are generated by a latent process with some unknown conditional density. At each period of time, from this density, we have some random draws (trades) and the lowest and highest returns are the realized extreme observations of the latent process over the sample of draws. In this context, we propose a semiparametric model of extreme returns that exploits the results provided by extreme value theory. If properly centered and standardized extremes have well‐defined limiting distributions, the conditional mean of extreme returns is a nonlinear function of the conditional moments of the latent process and of the conditional intensity of the process that governs the number of draws. We implement a two‐step estimation procedure. First, we estimate parametrically the regressors that will enter into the nonlinear function, and in a second step we estimate nonparametrically the conditional mean of extreme returns as a function of the generated regressors. Unlike current models for ITS, the proposed semiparametric model is robust to misspecification of the conditional density of the latent process. We fit several nonlinear and linear models to the 5‐minute and 1‐minute low/high returns to seven major banks and technology stocks, and find that the nonlinear specification is superior to the current linear models and that the conditional volatility of the latent process and the conditional intensity of the trading process are major drivers of the dynamics of extreme returns.     

GENERALIZED AUTOREGRESSIVE SCORE MODELS WITH APPLICATIONS

We propose a class of observation‐driven time series models referred to as generalized autoregressive score (GAS) models. The mechanism to update the parameters over time is the scaled score of the likelihood function. This new approach provides a unified and consistent framework for introducing time‐varying parameters in a wide class of nonlinear models. The GAS model encompasses other well‐known models such as the generalized autoregressive conditional heteroskedasticity, autoregressive conditional duration, autoregressive conditional intensity, and Poisson count models with time‐varying mean. In addition, our approach can lead to new formulations of observation‐driven models. We illustrate our framework by introducing new model specifications for time‐varying copula functions and for multivariate point processes with time‐varying parameters. We study the models in detail and provide simulation and empirical evidence. Copyright © 2012 John Wiley & Sons, Ltd.     

The recurrence of financial distress: A survival analysis

Companies often suffer periods of financial distress before filing for bankruptcy. Unlike one-off bankruptcies, financial distress can occur repeatedly within the same individual firm. This paper is focused on the recurrence of financial distress and studies the Chinese stock market, where Special Treatment – an official indicator of financial distress – can be repeatedly applied to a listed company. We employ a stratified hazard model to predict the probability of subsequent distress with variables, including duration dependency, event-based factors, institutional variables, financial ratios, market-based variables and macroeconomic conditions. Our empirical results show that accounting and market-based variables have limited power in predicting the recurrence of distress, whereas the duration of recovery, restructuring events and their interaction terms with the accounting and macroeconomic factors affect the recurrent risk significantly. Tested on out-of-time samples, our proposed hazard models show a robust performance in the prediction of recurrent risk over time.     

A time-varying copula approach for constructing a daily financial systemic stress index

This paper develops a financial systemic stress index (FSSI) for the US financial market. We propose a time-varying copula method to model the dependence structure among financial sectors in order to build a correlated financial stress model that can signal systemic financial risks. The copula method is preferable to the traditional approach, enabling the modeling of non-linear correlations. Our analyses show that the dependencies across banking, security, and forex markets are best modeled by Archimedian copulas. Finally, we conduct a Markov Switching Autoregressive (MS-AR) model for FSSI and identify high financial stress episodes taking place in 2008–2009, 2011 and 2020.     

Risk spillover between the US and the remaining G7 stock markets using time-varying copulas with Markov switching: Evidence from over a century of data

This paper analyses the risk spillover effect between the US stock market and the remaining G7 stock markets by measuring the conditional Value-at-Risk (CoVaR) using time-varying copula models with Markov switching and data that covers more than 100 years. The main results suggest that the dependence structure varies with time and has distinct high and low dependence regimes. Our findings verify the existence of risk spillover between the US stock market and the remaining G7 stock markets. Furthermore, the results imply the following: 1) abnormal spikes of dynamic CoVaR were induced by well-known historical economic shocks; 2) The value of upside risk spillover is significantly larger than the downside risk spillover and 3) The magnitudes of risk spillover from the remaining G7 countries to the US are significantly larger than that from the US to these countries.     

Time series copulas for heteroskedastic data

We propose parametric copulas that capture serial dependence in stationary heteroskedastic time series. We suggest copulas for first‐order Markov series, and then extend them to higher orders and multivariate series. We derive the copula of a volatility proxy, based on which we propose new measures of volatility dependence, including co‐movement and spillover in multivariate series. In general, these depend upon the marginal distributions of the series. Using exchange rate returns, we show that the resulting copula models can capture their marginal distributions more accurately than univariate and multivariate generalized autoregressive conditional heteroskedasticity models, and produce more accurate value‐at‐risk forecasts.     

Modelling security market events in continuous time: Intensity based,multivariate point process models

A continuous time econometric modelling framework for multivariate financial market event (or ‘transactions’) data is developed in which the model is specified via the vector conditional intensity. Generalised Hawkes models are introduced that incorporate inhibitory events and dependence between trading days. Novel omnibus specification tests based on a multivariate random time change theorem are proposed. A bivariate point process model of the timing of trades and mid-quote changes is then presented for a New York Stock Exchange stock and related to the market microstructure literature. The two-way interaction of trades and quote changes in continuous time is found to be important empirically.     

Forecasting risk measures using intraday data in a generalized autoregressive score framework

A new framework for the joint estimation and forecasting of dynamic value at risk (VaR) and expected shortfall (ES) is proposed by our incorporating intraday information into a generalized autoregressive score (GAS) model introduced by Patton et al., 2019 to estimate risk measures in a quantile regression set-up. We consider four intraday measures: the realized volatility at 5-min and 10-min sampling frequencies, and the overnight return incorporated into these two realized volatilities. In a forecasting study, the set of newly proposed semiparametric models are applied to four international stock market indices (S&P 500, Dow Jones Industrial Average, Nikkei 225 and FTSE 100) and are compared with a range of parametric, nonparametric and semiparametric models, including historical simulations, generalized autoregressive conditional heteroscedasticity (GARCH) models and the original GAS models. VaR and ES forecasts are backtested individually, and the joint loss function is used for comparisons. Our results show that GAS models, enhanced with the realized volatility measures, outperform the benchmark models consistently across all indices and various probability levels.     

GARCH models,tail indexes and error distributions: An empirical investigation

We perform a large simulation study to examine the extent to which various generalized autoregressive conditional heteroskedasticity (GARCH) models capture extreme events in stock market returns. We estimate Hill's tail indexes for individual S&P 500 stock market returns and compare these to the tail indexes produced by simulating GARCH models. Our results suggest that actual and simulated values differ greatly for GARCH models with normal conditional distributions, which underestimate the tail risk. By contrast, the GARCH models with Student's t conditional distributions capture the tail shape more accurately, with GARCH and GJR-GARCH being the top performers.     

Copula-based multivariate GARCH model with uncorrelated dependent errors

Multivariate GARCH (MGARCH) models are usually estimated under multivariate normality. In this paper, for non-elliptically distributed financial returns, we propose copula-based multivariate GARCH (C-MGARCH) model with uncorrelated dependent errors, which are generated through a linear combination of dependent random variables. The dependence structure is controlled by a copula function. Our new C-MGARCH model nests a conventional MGARCH model as a special case. The aim of this paper is to model MGARCH for non-normal multivariate distributions using copulas. We model the conditional correlation (by MGARCH) and the remaining dependence (by a copula) separately and simultaneously. We apply this idea to three MGARCH models, namely, the dynamic conditional correlation (DCC) model of Engle [Engle, R.F., 2002. Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models. Journal of Business and Economic Statistics 20, 339–350], the varying correlation (VC) model of Tse and Tsui [Tse, Y.K., Tsui, A.K., 2002. A multivariate generalized autoregressive conditional heteroscedasticity model with time-varying correlations. Journal of Business and Economic Statistics 20, 351–362], and the BEKK model of Engle and Kroner [Engle, R.F., Kroner, K.F., 1995. Multivariate simultaneous generalized ARCH. Econometric Theory 11, 122–150]. Empirical analysis with three foreign exchange rates indicates that the C-MGARCH models outperform DCC, VC, and BEKK in terms of in-sample model selection and out-of-sample multivariate density forecast, and in terms of these criteria the choice of copula functions is more important than the choice of the volatility models.