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One of the implications of the intertemporal capital asset pricing model (ICAPM) is a positive and linear relationship between the conditional mean and conditional variance of returns to the market portfolio. Empirically, however, it is often observed that there is a negative skewness in equity returns. This article shows that a negative skewness is only compatible with a positive risk premium if the innovation distribution is asymmetric with a negative skewness. We extend recent work using the EGARCH-in-Mean specification to allow for asymmetric innovations, and give results for the unconditional skewness of returns. We apply the model to the prediction of Value-at-Risk of the largest stock market indices, and demonstrate its good performance. Keywords: Exponential GARCH, in-mean, risk premium, ICAPM, unconditional skewness, asymmetric distribution, portfolio selection, Value-at-Risk.

We analyze the upside and downside risk connectedness among international stock markets. We characterize the connectedness among international stock returns using the Diebold and Yilmaz spillover index approach and compute the upside and downside value-at-risk. We document that the connectedness level of the downside risk is higher than that of the upside risk and that stock markets are more sensitive when the stock market declines. We also find that specific periods (e.g., the global financial crisis, the European debt crisis, and the COVID-19 turmoil) intensify the spillover effects across international stock markets. Our results demonstrate that the EU, Ger-many, and the US acted as net transmitters of dynamic connectedness; however, Japan (JP), China (CH), and India (IN) acted as net receivers of dynamic connectedness during the sample period. These findings provide significant new information to policymakers and market participants.

A new semi-parametric Expected Shortfall (ES) estimation and forecasting framework is proposed. The proposed approach is based on a two-step estimation procedure. The first step involves the estimation of Value-at-Risk (VaR) at different quantile levels through a set of quantile time series regressions. Then, the ES is computed as a weighted average of the estimated quantiles. The quantiles weighting structure is parsimoniously parameterized by means of a Beta weight function whose coefficients are optimized by minimizing a joint VaR and ES loss function of the Fissler-Ziegel class. The properties of the proposed approach are first evaluated with an extensive simulation study using two data generating processes. Two forecasting studies with different out-of-sample sizes are then conducted, one of which focuses on the 2008 Global Financial Crisis (GFC) period. The proposed models are applied to 7 stock market indices and their forecasting performances are compared to those of a range of parametric, non-parametric and semi-parametric models, including GARCH, Conditional AutoRegressive Expectile (CARE), joint VaR and ES quantile regression models and simple average of quantiles. The results of the forecasting experiments provide clear evidence in support of proposed models., 38 pages, 2 figures and 6 tables

We analyze the systemic risk of Italian banks with the ΔCoVaR from a bivariate normal GARCH model. The results show that it is a good measure of systemic risk and is applicable to the ranking of Italian other systemically important institutions. Using an elastic-net approach, we identify the balance sheet and market variables that explain the ΔCoVaR of Italian banks. The analysis confirms that these variables are key determinants of systemic importance and highlights how higher capitalization is beneficial to tackling systemic risk. And, we detect a connection between ΔCoVaR and some variables for trading and investment banking.

The ECB announcement to reduce capital requirements for market risk to smooth pro-cyclicality, published in April 2020, is a good starting point to discuss the impact of regulation on individual banks on the stability of the whole banking and financial system. A large number of theoretical articles and a few empirical papers back the existence of an amplification effect on market volatility caused by the use of risk management measures (e.g. value-at-risk, VaR, for market risk) for regulatory purposes. However, to the best of my knowledge, no paper has empirically investigated the direct relation between the level of tightness of VaR risk limits and market volatility. In this article, I show that market volatility is positively related to past values of the measure of the tightness of the market risk limit, with an overshooting process of adjustment toward equilibrium. The analysis is limited to Italy. The empirical results, based on a unique dataset of VaR values and on other publicly available market data, are in line with the theoretical findings and are novel empirical evidence. They open the way to additional research on how to manage the channels of transmission of the amplification and overshooting effects from the risk management measure to systemic variables, to avoid unintended consequences of the application of individual supervision measures on the whole system.

This paper examines the dynamic relation between Bitcoin spot and futures markets during the Covid-19 pandemic. Using hourly data from 2020 combined with quantile impulse response analysis and predictability in the distribution test, we attempt to ascertain whether spot or futures markets lead in the price discovery process under a variety of market conditions. Granger predictability based on the left tail, the right tail, and the center of the distribution show bidirectional predictability between spot and futures markets suggesting significant feedback effects following normal and extreme gains/losses where neither market dominates in price discovery. Using a CAViaR model and the associated impulse response functions with estimates for dynamic tail dependence, we document spillovers between quantiles of spot and futures returns. Estimates of impulse response functions at various risk levels show the futures market has an edge in influencing the spot market and figures more prominently in the price discovery process.

This paper reassessed the hedging properties of four major safe-haven currencies (US dollar, Swiss franc, euro, yen) in international stock portfolios covering most representative world macroeconomic areas. The main contribution to the existing literature is the emphasis on optimal hedging and asset-allocation strategies. A further distinguishing feature is an accurate comparison, inside a multivariate framework, between value-at-risk simulations assuming equal or optimal asset weights in hedged global stock portfolios. The US dollar stands out as the best safe-haven currency, while adding the US currency to single-hedged global stock portfolios including either the Swiss franc or the euro yields smooth risk profiles during major financial crises, and average risk indicators lower than that of a benchmark fully hedged portfolio.

Early empirical evidence suggests that the realised generalised autoregressive conditional heteroskedasticity (GARCH) model provides significant forecasting gains over the standard GARCH models in volatility forecasting. We extend this literature in quantile forecasting by implementing conditional extreme value theory (EVT) framework with realised GARCH. We generate one-step-ahead value-at-risk (VaR) and expected shortfall (ES) forecasts for the S&P CNX NIFTY index using 14 standalone GARCH and GARCH-EVT models. In out-of-sample comparisons, the GARCH-EVT specification generally outperforms the standalone GARCH models. In general, the realised-GARCH EVT models provide the best forecasting performance. This finding is robust to the choice of different realised volatility estimators used to estimate realised GARCH.

The central role of Value-at-Risk (VaR) within bank market risk regulation received significant criticism from financial media and government investigations into the events of the 2007–2009 financial crisis. Impending reform of bank market risk regulation under the Fundamental Review of the Trading Book (FRTB) demotes VaR, replacing it with a layered framework centred on expected shortfall (ES). However, many of these criticisms assume full integration of internal and regulatory market risk models and further, a linear relationship between risk models and regulatory capital. We examine bank practitioners’ perspectives and experienced realities to better understand the operational relationship between internal and regulatory market risk models, and between risk models and capital. This has important policy implications for the efficacy of the reforms to banking regulation, financial stability and navigating the dichotomy of private and public interests.

With the COVID-19 pandemic sweeping the world, the development of China's energy industry has been hampered. Although previous studies have shown the global influence of COVID-19 on energy prices and macroeconomic indicators, very few of them examined the impact on China independently, considering the special role of China in this pandemic and economy. In this study, we investigate the impact of the pandemic on several major China energy prices using the ARIMA-GARCH model. Combined with the Value-at-Risk (VaR) theory, we further explore the market risk, which indicates an increase in the tail risk of energy price volatility and the dramatic turbulence in energy markets. In addition, a Vector Autoregressive (VAR) model is developed to analyze how the main macroeconomic indicators are affected when energy prices fluctuate. According to the model results, energy price fluctuations caused by the COVID-19 have a negative impact on economic growth and inflation, with a higher contribution to the latter changes. Based on the modeling analysis results, this paper makes constructive suggestions on how to stabilize energy prices and recover the economic development in the context of the COVID-19 pandemic.

The present study focuses on the analysis of systemic risk in the American and European financial systems for the period from 20 August 2004 to 28 February 2014. The global crisis in 2007 has brought attention to the urgent need to understand the systemic risk issues and the stability of financial systems along with their actors. To assess systemic risk, Adrian and Brunnermeier (2011) advocated the use of conditional value-at-risk (CoVaR) methodology in integrating quantile regression. Instead of the value-at-risk (VaR), which is unable to detect systemic risk, we seek to use the CoVaR methodology to calculate the systemic risk levels of the United States and European markets. In the light of related findings, we conclude that the insurance sector contributes most to the systemic risk in the USA, while in the Eurozone, it is the financial services sector that is highly interconnected with systemic risk. © 2020, Vysoka Skola Ekonomicka. All rights reserved.

Since Bitcoin introduction in 2008, the cryptocurrency market has grown into hundreds-of-billion-dollar market. The cryptocurrency market is well known as very volatile, mainly for the fact that the cryptocurrencies have not the price to fall back upon and that anybody can join the trading (no license or approval is required). Since empirical literature suggests that GARCH-type models dominate as VaR estimators the overall objective of this paper is to perform comprehensive volatility and VaR estimation for three major digital assets and conclude which method gives the best results in terms of risk management. The methods we used are parametric (GARCH and EWMA model), non-parametric (historical VaR) and Monte Carlo simulation (given by Geometric Brownian Motion). We conclude that the best method for value-at-risk estimation for cryptocurrencies is the Monte Carlo simulation due to the heavy diffusion (stochastic) process and robustness of the results.

In this paper, we propose a new approach to analyze financial contagion using a causality-based complex network and value-at-risk (VaR). We innovatively combine the use of VaR and an expected shortfall (ES)-based causality network with impulse response analysis to discover features of financial contagion. We improve the current research methods by building a Granger causality network on VaR and ES and using conclusions drawn from network analysis as a foundational step before impulse response analysis. First of all, we select 30 stock indices that are very well-known globally and collect their trading data. After calculating the risk indicators of VaR and ES, we perform the Granger causality test on them and then build networks based on their respective Granger causality square matrix. Next, we examine the networks’ topological features to discover different degrees of risk transmission among all stock indices in the system. Lastly, we identify the most and the least active stock indices in the risk transmission network and conduct impulse response analysis on them. We discover that BSESN (India S&P BSE SENSEX) is the most risk-sensitive stock index as its VaR significantly increases by 0.03–0.04% and its ES jumps even more, by 0.07–0.08%, in response to an impulse from a few key stock indices. We also find that either PSI20 or XU100 is the most risk-proof stock index, depending on whether we choose VaR or ES as a risk indicator.

This paper investigates an optimal reinsurance policy using a risk model with dependent claim and insurance premium by assuming that the insurance premium is random. Their dependence structure is modeled using Sarmanov’s bivariate exponential distribution and the Farlie–Gumbel–Morgenstern (FGM) copula-based bivariate exponential distribution. The reinsurance premium paid by the insurer to the reinsurer is fixed and is charged by the expected value premium principle (EVPP) and standard deviation premium principle (SDPP). The main objective of this paper is to determine the proportion and retention limit of the optimal combination of proportional and stop-loss reinsurance for the insurer. Specifically, with a constrained reinsurance premium, we use the minimization of the Value-at-Risk (VaR) of the insurer’s net cost. When determining the optimal proportion and retention limit, we provide some numerical examples to illustrate the theoretical results. We show that the dependence parameter, the probability of claim occurrence, and the confidence level have effects on the optimal VaR of the insurer’s net cost.

In this work, we consider the problem of estimating the probability distribution, the quantile or the conditional expectation above the quantile, the so called conditional-value-at-risk, of output quantities of complex random differential models by the MLMC method. We follow the approach of (reference), which recasts the estimation of the above quantities to the computation of suitable parametric expectations. In this work, we present novel computable error estimators for the estimation of such quantities, which are then used to optimally tune the MLMC hierarchy in a continuation type adaptive algorithm. We demonstrate the efficiency and robustness of our adaptive continuation-MLMC in an array of numerical test cases., Comment: 35 pages, 48 figures. Data available at https://doi.org/10.5281/zenodo.7025018

In this study we examine the time-varying causal effect of the novel COVID-19 pandemic in the major oil-importing and oil-exporting countries on the oil price changes, stock market volatilities and the economic uncertainty using the wavelet coherence and network analysis. During the period of the pandemic, we explore such relationship by resorting to the wavelet coherence and gaussian graphical model (GGM) frameworks. Wavelet analysis enables us to measure the dynamics of the causal effect of the novel covid-19 pandemic in the time–frequency space. Regarding the findings displayed herein, we first found that the COVID-19 pandemic has a severe influence on oil prices, stock market indices, and the economic uncertainty. Second the intensity of the causality effect is stronger in the longer horizon than in the short ones, suggesting that the causality exercise continues. Our findings also provide evidence that the COVID-19 pandemic and oil price changes in oil-importing countries mirror those in oil-exporting countries and vice versa. Further, the COVID-19 pandemic has a profound immediate time–frequency effect on the US, Japanese, South Korean, Indian, and Canadian economic uncertainties. A better understanding of oil and stock market prices in the oil-importing and oil-exporting countries is vital for investors and policymakers, specially since the novel unprecedented COVID-19 crisis has been recognized among the most serious ever happened. Thus, the findings suggest that the authorities should strongly take efficient actions to minimize risk.

Portfolio credit risk is often concerned with the tail distribution of the total loss, defined to be the sum of default losses incurred from a collection of individual loans made out to the obligors. The default for an individual loan occurs when the assets of a company (or individual) fall below a certain threshold. These assets are typically modeled according to a factor model, thereby introducing a strong dependence both among the individual loans, and potentially also among the multivariate vector of common factors. In this paper, we derive sharp tail asymptotics under two regimes: (i) a large loss regime, where the total number of defaults increases asymptotically to infinity; and (ii) a small default regime, where the loss threshold for an individual loan is allowed to tend asymptotically to negative infinity. Extending beyond the well-studied Gaussian distributional assumptions, we establish that—while the thresholds in the large loss regime are characterized by idiosyncratic factors specific to the individual loans—the rate of decay is governed by the common factors. Conversely, in the small default regime, we establish that the tail of the loss distribution is governed by systemic factors. We also discuss estimates for Value-at-Risk, and observe that our results may be extended to cases where the number of factors diverges to infinity.

Studying a renewable energy integrated power system’s features is essential, especially for deregulated systems. The unpredictability of renewable sources is the main barrier to integrating renewable energy-producing units with the current electrical grid. Due to its unpredictable nature, integrating wind power into an existing power system requires significant consideration. In a deregulated electricity market, this paper examines the implications of wind farm (WF) integration with CAES on electric losses, voltage profile, generation costs, and system economics. Comparative research was done to determine the impact of wind farm integration on regulated and deregulated environments. Four randomly chosen locations in India were chosen for this investigation, together with real-time information on each location’s real wind speed (RWS) and predicted wind speed (PWS). Surplus charge rates and deficit charge rates were created to assess the imbalance cost arising from the discrepancy between predicted and real wind speeds to calculate the system economics. When the effect of imbalance cost is considered, the daily system profit shows a variation of about 1.9% for the locations under study. Customers are always seeking electricity that is dependable, affordable, and efficient due to the reorganization of the power system. As a result, the system security limit could be exceeded or the system might function dangerously. The final section of this paper presents an economic risk analysis using heuristic algorithms such as sequential quadratic programming (SQP), artificial bee colony algorithms (ABC), and moth flame optimization algorithms (MFO). It also discusses how the CAES is used to correct the deviation of WF integration in the real-time electricity market. Economic risk analysis tools include value-at-risk (VaR) and conditional value-at-risk (CVaR). The entire piece of work was validated using a modified IEEE 30-bus test system. This works shows that with a three-fold increase in wind generation, the risk coefficient values improves by 1%.

This paper studies properties of functions having monotone tails. We extend Theorem 1 of Dhaene et al. (2002a) and show how the tail quantiles of a random variable transformed with a monotone tail function can be expressed as the transformed tail quantiles of the original random variable. The main result is intuitive, in that Dhaene et al. (2002a)’s properties still hold, but only for certain quantile values. However, the proof presents some complications that arise especially when the function involved has discontinuities.We consider different situations where monotone tail functions occur and can be useful, such as the evaluation of the payoff of option trading strategies and the present value of insurance contracts providing both death and survival benefits. The paper also applies monotone tail functions to study quadrant perfect dependence, and shows how this dependence structure integrates within the framework of monotone tail functions. Moreover, we apply the theory to the problem of risk reduction and investigate conditions on a hedger ensuring efficient reductions of required economic capital.

Cryptocurrency investments are often perceived as uncertain and risky. In this study, we assessed if this is indeed the case, using a sample of seven cryptocurrencies and considered a period that encompassed the first real global shock in the life of these relatively new financial assets, the COVID-19 pandemic. Uncertainty was evaluated using Shannon’s symbolic entropy. To measure risk, we use value-at-risk and conditional value-at-risk. The results indicate that, except for Tether, the analyzed cryptocurrencies’ returns exhibited similar patterns of uncertainty and risk. Levels of uncertainty were close to the maximum values, but high uncertainty is not always associated with high risk. During the pandemic crisis, uncertainty increased while risk decreased, suggesting that the considered assets may have safe haven properties.

A reinsurance contract should consider the conflicting interests of the insurer and the reinsurer. An optimal reinsurance contract for one party may not be optimal for another party and it might be unacceptable for another party. Therefore, in this paper, we study the optimal reinsurance models from the perspective of both the insurer and the reinsurer by minimizing their total costs under the criteria of loss function which is defined by the joint value-at-risk, assuming that the reinsurance premium principles satisfy risk loading and stop-loss ordering preserving. We derive the optimal reinsurance policies over three ceded loss function sets, the change-loss reinsurance is optimal among the class of increasing convex ceded loss functions; when the constraints on both ceded and retained loss functions are relaxed to increasing functions, the layer reinsurance is shown to be optimal; the quota-share reinsurance with a limit is always optimal when the ceded loss functions are in the class of increasing concave functions. We further use the expectation premium principle and Dutch premium principle to illustrate the application of our results by deriving the optimal parameters.

According to in-depth research, a wide range of problems in applied science involve estimating the probability of compound stochastic sums of heavy-tailed risks over a large threshold. Many researchers have explored this issue from different aspects in recent times. There are two main difficulties here: one is how to deal with the heavy tail of risk, and another is how to handle the dependence of the aggregated processes. Aimed at these two main problems, we investigate the asymptotic properties of the tail of compound stochastic sums of heavy-tailed risks in a general dependence framework, and some approximate bounds and key characteristics related to value-at-risk are also derived. Several practical examples are given to demonstrate the effectiveness of the approximation results. Furthermore, the main results in this paper can be applied to studies of stochastic models in finance and econometrics and studies of dependent netput processes of the M/G/1 queuing systems, etc.

We evaluate the impact of extreme market shifts on equity portfolios and study the difference in negative and positive reactions to market jumps with implications for portfolio risk management. Employing high-frequency data for the constituents of the S&P500 index over the period 2 January 2003 to 30 December 2017, we investigate to what extent the portfolio exposure to the downside and upside jumps can be mitigated. We contrast the risk exposure of individual stocks with those of the portfolios as the number of holdings increases. Varying the jump identification threshold, we show that the number of holdings required to stabilise portfolios’ sensitivities to negative jumps is higher than when positive jumps are considered and that the asymmetry is more prominent for more extreme events. Ignoring this asymmetry results in under-diversification of portfolios and increases exposure to sudden extreme negative market shifts.

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link. We investigate the dynamics of the relationship between returns and extreme downside risk in different states of the market by combining the framework of Bali, Demirtas, and Levy (2009) with a Markov switching mechanism. We show that the risk-return relationship identified by Bali, Demirtas, and Levy (2009) is highly significant in the low volatility state but disappears during periods of market turbulence. This is puzzling since it is during such periods that downside risk should be most prominent. We show that the absence of the risk-return relationship in the high volatility state is due to leverage and volatility feedback effects arising from increased persistence in volatility. To better filter out these effects, we propose a simple modification that yields a positive tail risk-return relationship in all states of market volatility.

We analyse four stochastic claims reserving methods in terms of their capability to estimate reserve risk and how successful they are at predicting distributions and VaRs of claim developments in particular. Both actual data and hypothetical claim triangles support our results. The appropriateness of the Solvency II risk margin on a one-year horizon and of the IFRS 17 risk adjustment in the long run largely vary by the chosen risk model. Despite the fact that IFRS 17 does not uniquely prescribe the metric for risk adjustment, we expect that VaR will be widely applied by insurance firms. Overall, actual data suggest that VaRs are predominantly underestimated by the models. Nevertheless, the 99.5%-VaRs under Solvency II are mostly sufficient on a 10-year-horizon to cover liabilities.

When the uni-variate risk measure analysis is generalized into the multi-variate setting, many complex theoretical and applied problems arise, and therefore the mathematical models used for risk quantification usually present model risk. As a result, regulators have started to require that the internal models used by financial institutions are more precise. For this task, we propose a novel multi-variate risk measure, based on the notion of the Wasserstein barycenter. The proposed approach robustly characterizes the company’s exposure, filtering the partial information available from individual sources into an aggregate risk measure, providing an easily computable estimation of the total risk incurred. The new approach allows effective computation of Wasserstein barycenter risk measures in any location–scatter family, including the Gaussian case. In such cases, the Wasserstein barycenter Value-at-Risk belongs to the same family, thus it is characterized just by its mean and deviation. It is important to highlight that the proposed risk measure is expressed in closed analytic forms which facilitate its use in day-to-day risk management. The performance of the new multi-variate risk measures is illustrated in United States market indices of high volatility during the global financial crisis (2008) and during the COVID-19 pandemic situation, showing that the proposed approach provides the best forecasts of risk measures not only for “normal periods”, but also for periods of high volatility.

Risk capital models are widely applied by insurance companies both for the solvency assessment and for risk management. The main topics of the dissertation are the development of models used for assessment of Value-at-Risk for mortality risk and calculation of the related mortality projections. When calculating the Value-at-Risk for mortality risk stochastic mortality projections are used as an input. For the purpose of generation of the projections we develop the classical Lee-Carter model, the modification of this model derived using Poisson regression, and Lee-Cater model modifications derived using state space models. The state space Lee-Carter models, linear state space model and state space model with regime switching, allow us to take into account a change in mortality trend and to consider changes of mortality variance in time. For estimation of state space model parameters, we applied Gibbs sampler, which is one of Markov Chain Monte Carlo methods. The calculated mortality projections are used for calculation of Value-at-Risk for mortality risk using two different methods: one-year VaR and run-off VaR. The application of the methods was illustrated using empirical mortality data of Lithuania and Sweden.

This paper examines why a financial entity's solvency capital estimation might be underestimated if the total amount required is obtained directly from a risk measurement. Using Monte Carlo simulation we show that, in some instances, a common risk measure such as Value-at-Risk is not subadditive when certain dependence structures are considered. Higher risk evaluations are obtained for independence between random variables than those obtained in the case of comonotonicity. The paper stresses, therefore, the relationship between dependence structures and capital estimation.

The measurement of currency risk through the VaR metrics is highlighted in this research work. The main VaR methods – relative, Historical Stimulation and Monte Karlo Stimulation are briefly presented. A study is conducted with real data on a specific currency pair – GBP/USD. The observations reflect a period of one year, a time horizon of one and ten days, and a 99% confidence interval. The results obtained are analyzed. The relevant conclusions are drawn.

The rapid growth of electric vehicles, solar roofs, and wind power suggests that the potential growth in green equity investments is an emerging trend. Accordingly, this study measured the predictors of excess equity returns in a portfolio of global green energy producers, from 2010 to 2019. Fixed-effects panel data regressions of daily returns, followed by quantile regressions, were performed. There was some support for the explanation of green equity returns by market returns and market risk (beta), as indicated by the single-factor Capital Asset Pricing Model (CAPM), and the multifactor Fama–French Three-Factor and Fama–French Five-Factor Models. The most significant predictors of green equity returns were Value-at-Risk at a 95% confidence level, and Value-at-Risk at a 99% confidence level. Expected Shortfall was another extreme risk value measure. The importance of extreme value measures suggests the presence of fat-tailed leptokurtic distributions, whereby excess returns were explained by the risk of loss given adverse conditions, primarily at 95% confidence. We conclude that the proliferation of small firms and new entrants in the renewable energy sector has led to the explanation of returns by extreme values of risk.

We introduce the industrial portfolio of a wind farm of a hypothetical company and its valuation consistent with the financial market. Next, we propose a static risk management policy originating from hedging against volumetric risk due to drops in wind intensity and we discuss the consequences. The hedging effectiveness firstly requires adequate modeling calibration and an extensive knowledge of these atypical financial (commodity) markets. In this hedging experiment, we find significant benefits for weather-sensitive companies, which can lead to new business opportunities. We provide a new financial econometrics approach to derive weather risk exposure in a typical wind farm. Our results show how accurate risk management can have a real benefit on corporate revenues. Specifically, we apply the spot market price simulation (SMaPS) model for the spot price of electricity. The parameters are calibrated using the prices of the French day-ahead market, and the historical series of the total hourly load is used as the final consumption. Next, we analyze wind speed and its relationship with electricity spot prices. As our main contribution, we demonstrate the effects of a hypothetical hedging strategy with collar options implemented against volumetric risk to satisfy demand at a specific time. Regarding the hedged portfolio, we observe that the “worst value” increases considerably while the earnings-at-risk (EaR) decreases. We consider only volumetric risk management, thus neglecting the market risk associated with electricity price volatility, allowing us to conclude that the hedging operation of our industrial portfolio provides substantial benefits in terms of the worst-case scenario.

International audience; In this paper, we discuss the application of extreme value theory in the context of stationary β-mixing sequences that belong to the Fréchet domain of attraction. In particular, we propose a methodology to construct bias-corrected tail estimators. Our approach is based on the combination of two estimators for the extreme value index to cancel the bias. The resulting estimator is used to estimate an extreme quantile. In a simulation study, we outline the performance of our proposals that we compare to alternative estimators recently introduced in the literature. Also, we compute the asymptotic variance in specific examples when possible. Our methodology is applied to two datasets on finance and environment.

© 2018 The Author(s) We perform a large-scale empirical study in order to compare the forecasting performances of single-regime and Markov-switching GARCH (MSGARCH) models from a risk management perspective. We find that MSGARCH models yield more accurate Value-at-Risk, expected shortfall, and left-tail distribution forecasts than their single-regime counterparts for daily, weekly, and ten-day equity log-returns. Also, our results indicate that accounting for parameter uncertainty improves the left-tail predictions, independently of the inclusion of the Markov-switching mechanism. ispartof: INTERNATIONAL JOURNAL OF FORECASTING vol:34 issue:4 pages:733-747 status: published

We consider the problem of determining risk bounds for the Value at Risk for risk vectors X where besides the marginal distributions also information on the distribution or on the expectation of some functionals Tj(X), 1 ≤ j ≤ m, is available. In particular this formulation includes the case where information on subgroup sums or maxima or on the correlations or covariances is available. Based on the method of dual bounds we obtain improved risk bounds compared to the marginal case. In general the explicit calculation of the dual bounds poses a challenge. We discuss various forms of relaxation of these bounds which are accessible and in some cases even lead to sharp bounds.

In the literature, there is no consensus as to which Value-at-Risk forecasting model is the best for measuring market risk in banks. In the study an analysis of Value-at-Risk forecasting model quality over varying economic stability periods for main indices from stock exchanges was conducted. The VaR forecasts from GARCH(1,1), GARCH-t(1,1), GARCH-st(1,1), QML-GARCH(1,1), CAViaR and historical simulation models in periods with contrasting volatility trends (increasing, constantly high and decreasing) for countries economically developed (the USA – S&P 500, Germany - DAX and Japan – Nikkei 225) and economically developing (China – SSE COMP, Poland – WIG20 and Turkey – XU100) were compared. The data samples used in the analysis were selected from the period 01.01.1999 – 24.03.2017. To assess the VaR forecast quality: excess ratio, Basel traffic light test, coverage tests (Kupiec test, Christoffersen test), Dynamic Quantile test, cost functions and Diebold-Marino test were used. Obtained results show that the quality of Value-at-Risk forecasts for the models varies depending on a volatility trend. However, GARCH-st (1,1) and QML-GARCH(1,1) were found to be the most robust models in the different volatility periods. The results show as well that the CAViaR model forecasts were less appropriate in the increasing volatility period. Moreover, no significant differences for the VaR forecast quality were found for the developed and developing countries.

International audience; This paper (this work was achieved through the Laboratory of Excellence on Financial Regulation (Labex ReFi) supported by PRESheSam under the reference ANR-10-LABEX-0095) analyses how risks are measured in financial institutions, for instance Market, Credit, Operational, among others with respect to the choice of risk measures, the choice of distributions used to model them and the level of confidence selected. We discuss and illustrate the characteristics, the paradoxes and the issues observed, comparing the Value-at-Risk and the Expected Shortfall in practice. This paper is built as a differential diagnosis and aims at discussing the reliability of the risk measures and making some recommendations. (This paper has been written in a very particular period of time as most regulatory papers written in the past 20 years are currently being questioned by both practitioners and regulators themselves. Some disarray has been observed among risk managers as most models required by the regulation have not been consistent with their own objective of risk management. The enlightenment brought by this paper is based on an academic analysis of the issues engendered by some pieces of regulation and its purpose is not to create any sort of controversy).

This study aims to overcome the problem of dimensionality, accurate estimation, and forecasting Value-at-Risk (VaR) and Expected Shortfall (ES) uncertainty intervals in high frequency data. A Bayesian bootstrapping and backtest density forecasts, which are based on a weighted threshold and quantile of a continuously ranked probability score, are developed. Developed backtesting procedures revealed that an estimated Seasonal autoregressive integrated moving average-generalized autoregressive score-generalized extreme value distribution (SARIMA–GAS–GEVD) with a skewed student-t distribution had the best prediction performance in forecasting and bootstrapping VaR and ES. Extension of this non-stationary distribution in literature is quite complicated since it requires specifications not only on how the usual Bayesian parameters change over time but also those with bulk distribution components. This implies that the combination of a stochastic econometric model with extreme value theory (EVT) procedures provides a robust basis necessary for the statistical backtesting and bootstrapping density predictions for VaR and ES.

Vietnam has been considered one of the few countries that put the COVID-19 pandemic under control and successfully achieved solid economic growth in 2020. However, the national economy has been hit hard by the pandemic in 2021. National borders across the countries have been closed for an extended time. As such, supporting local industries is essential to sustain economic growth. This study measures the market risks across industries in Vietnam before and during the COVID-19 period. Two important measures, the Value-at-Risk and the Conditional Value-at-Risk, are used for the 2012–2020 period. We then extend the analyses by estimating the market risks using the monthly VaR for the 2019–2020 period. Key findings from this study can be summarized as follows. First, market risks across the Vietnamese industries have changed significantly in response to the pandemic, both at the level and their rankings. Second, among the changes, the services industry appears to be hardest hit by the pandemic as expected, whereas the education sector has significantly improved its standing during these challenging times. Our analysis also confirms that complete lockdowns negatively affect the market risk of various Vietnamese industries. We note that the service industry is a critical contributor to the Vietnamese economy and that lockdown during the pandemic does matter to the market risk. Policy implications have emerged on these findings., Market risk, COVID-19 pandemic, Value-at-risk, Conditional value-at-risk, Vietnam.

We analyze the impact of the COVID-19 pandemic on the conditional variance of stock returns. We look at this effect from a global perspective, so we employ series of major stock market and sector indices. We use the Hansen’s Skewed-t distribution with EGARCH extended to control for sudden changes in volatility. We oversee the COVID-19 effect on measures of downside risk such as the Value-at-Risk. Our results show that there is a significant sudden shift up in the return distribution variance post the announcement of the pandemic, which must be explained properly to obtain reliable measures for financial risk management. Financial support from the Spanish Ministry of Economy and Competitiveness through grant ECO2017-87069-P is gratefully acknowledged by the second author.

In this work we introduce a novel approach to risk management, based on the study of concentration measures of the loss distribution.In particular we show that indices like the Gini one, especially when restricted to the tails by conditioning and truncation, represent a good way of assessing the variability of the larger losses – the most relevant ones – and the precision of common risk management measures like the Expected Shortfall. We then introduce what we call the Concentration Profile, that is a sequence of truncated Gini indices that, we show, is able to characterize the loss distribution, providing interesting information about tail risks.Combining concentration profiles and standard results from utility theory, we then develop a Concentration Map, which can be used to assess the risk attached to potential losses on the basis of the risk profile of the user, her beliefs and historical data.Finally, we use the sequence of truncated Gini indices as weights for the expected shortfall, defining the so-called Concentration Adjusted Expected Shortfall, a measure able to capture interesting additional features of tail risk.All tools are applied to empirical data to show how to use them in practice.

Mortality and mortality rate have become the major issues in insurance industries, for instance, life insurance and pension fund. Such industries will, in particular, be concerned with the quantification of risk attached, say longevity risk, to insurance products that may receive severe impacts from the fall of mortality rate. In this paper, we model the mortality rate by using an Autoregressive (AR) model with a conditional heteroscedasticity effect. This effect is accommodated by a stochastic model of Autoregressive Conditional Heteroscedastic (ARCH) as well as a Stochastic Volatility Autoregressive (SVAR) model. Furthermore, we do forecasting of what so-called Mortality-at-Risk (MaR) by adopting the Value-at-Risk framework and its improvement. The calculation of the MaR forecast for those two models is conducted with significantly different approaches., Autoregressive; ARCH; Life insurance; Pension fund; Time series forecasting; Stochastic volatility; Value-at-Risk

This paper studies a portfolio optimization problem with variance and Entropic Value-at-Risk (evar) as risk measures. As the variance measures the deviation around the expected return, the introduction of evar in the mean-variance framework helps to control the downside risk of portfolio returns. This study utilized the squared l2-norm to alleviate estimation risk problems arising from the mean estimate of random returns. To adequately represent the variance-evar risk measure of the resulting portfolio, this study pursues rescaling by the capital accessible after payment of transaction costs. The results of this paper extend the classical Markowitz model to the case of proportional transaction costs and enhance the efficiency of portfolio selection by alleviating estimation risk and controlling the downside risk of portfolio returns. The model seeks to meet the requirements of regulators and fund managers as it represents a balance between short tails and variance. The practical implications of the findings of this study are that the model when applied, will increase the amount of capital for investment, lower transaction cost and minimize risk associated with the deviation around the expected return at the expense of a small additional risk in short tails.

Recent literature has investigated the risk aggregation of a portfolio $X=(X_{i})_{1\leq i\leq n}$ under the sole assumption that the marginal distributions of the risks $X_{i} $ are specified, but not their dependence structure. There exists a range of possible values for any risk measure of $S=\sum_{i=1}^{n}X_{i}$ , and the dependence uncertainty spread, as measured by the difference between the upper and the lower bound on these values, is typically very wide. Obtaining bounds that are more practically useful requires additional information on dependence. Here, we study a partially specified factor model in which each risk $X_{i}$ has a known joint distribution with the common risk factor $Z$ , but we dispense with the conditional independence assumption that is typically made in fully specified factor models. We derive easy-to-compute bounds on risk measures such as Value-at-Risk ( $\mathrm{VaR}$ ) and law-invariant convex risk measures (e.g. Tail Value-at-Risk ( $\mathrm{TVaR}$ )) and demonstrate their asymptotic sharpness. We show that the dependence uncertainty spread is typically reduced substantially and that, contrary to the case in which only marginal information is used, it is not necessarily larger for $\mathrm{VaR}$ than for $\mathrm{TVaR}$ .

We examine the Croatian Kuna, the Czech Koruna, the Hungarian Forint, the Polish Złoty, the Romanian Leu, and the Swedish Krona whether their Euro exchange rates volatility exhibits true or spurious long memory. Recent research reveals long memory in foreign exchange rate volatility and we confirm this finding for these currency pairs by examining the long memory behavior of squared residuals by means of the V/S test. However, by using the ICSS approach we also find structural breaks in the unconditional variance. Literature suggests that structural breaks might lead to spurious long memory behavior. In a refined test strategy, we distinguish true from spurious long memory for the six exchange rates. Our findings suggest that Czech Koruna and Hungarian Forint only feature spurious long memory, while the rest of the series have both structural breaks and true long memory. Lastly, we demonstrate how to extend existing models to jointly model both properties yielding superior fit and better Value-at-Risk forecasts. The results of our work help to avoid misspecification and provide a better understanding of the properties of the foreign exchange rate volatility.

Returns in financial assets display consistent excess kurtosis and skewness, implying the presence of large fluctuations not forecasted by Gaussian models. This paper applies a resampling method based on the bootstrap and a bias-correction step to improve Value-at-Risk (VaR) forecasting ability of the n-EGARCH (normal EGARCH) model and correct the VaR for both long and short positions. Our aim is to utilize the advantages of this model, but still use the bootstrap resampling method to accurate for the tendency of the model tomiscalculate the VaR. Empirical results indicate that the bias-correction method can improve the n-GARCH and n-EGARCH VaR forecasts so much that the acquired VaR predictions are different from the proposed probability. Additionally, allowing asymmetry in the conditional variance using the EGARCH model with normal distribution instead of GARCH improves the performance of the bias-correction method in forecasting the VaR for almost all considered indices. Moreover, the bias-corrected n-EGARCH model performs better than the simple t-EGARCH model. Thus, it seems that this model can take account of both the asymmetry in the conditional variance and leptokurtosis in returns distribution. However, we find that the superiority of the bias-corrected n-EGARCH model over the t-EGARCH model is not completely confirmed for short positions based on the censored likelihood scoring rule.

A unifying probabilistic framework is developed to analyze and compare the impact of the psychological biases of overconfidence and underconfidence on managerial perceptions about the expected value, overall risk, downside risk, value-at-risk and expected shortfall of decision-making economic variables. The results depict that overconfident managers overestimate their expected values and underestimate downside risk, VaR and ES of decision-making variables. Underconfident managers, on the other hand, underestimate their expected values and overestimate downside risk, value-at-risk, and expected shortfall.

In this paper, we consider a random vector X=(X1,X2) following a multivariate Skew Normal distribution and we provide an explicit formula for the expected value of X conditioned to the event X≤X¯¯¯¯, with X¯¯¯¯∈R2. Such a conditional expectation has an intuitive interpretation in the context of risk measures. This is a post-peer-review, pre-copyedit version of an article published in Computational Management Science . The final authenticated version is available online at: http://dx.doi.org/10.1007/s10287-019-00350-8

The valuation of the exposure to real estate market risk has traditionally been difficult due to the lack of appropriate data, returns that do not follow a normal distribution and a lack of adequate methodology. However, regulations such as Basel II, Basel III and Solvency II make it possible to assess real estate market risk using an internal model and through Value at Risk. The study develops a procedure to provide an internal model that values real estate market risk and calculates the capital that guarantees it. Monte Carlo simulations are used to calculate Value at Risk. As result, capital requirements can be established from these results to help with portfolio decision-making of insurance companies that hold real estate. Data used in the study is taken from the General Council of Notaries registered dwellings databases from the Spanish National Statistics Institute covering the time period of 2007-2017. This paper contributes to the literature by proposing a model that incorporates the characteristics of investments, allowing a real and market measure of the risk of loss from real estate. This work was supported by Consolidated Research Group Eusko Jaurlaritza/Gobierno Vasco EJ/GV: IT 897-16. The authors acknowledge language help from Julie Walker-Jones.

Mathematics and statistics are widely used in financial problems. In particular, quantile computation methods are an interesting field of study in order to obtain new and better ways to measure risk with Value-at-Risk (VaR) and Expected Shortfall (ES). We will be interested in considering the quantile computation with ordinary differential equations (ODEs), and specifically with numerical methods as Euler and Runge-Kutta which will let us find numerical solutions to these ODEs, and consequently numerical quantiles. The studied problem will be centered in the delta-gamma framework, where the quantile computation of non-central chi-square distribution will be needed. Thus, implementations of numerical methods and several numerical experiments will be done, comparing the results with other quantile computation methods and understanding the possibilities which ODEs offer us to solve the quantile computation problem.