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Planning and scheduling approaches in real manufacturing environments entail the need to cope with random attributes and variables to match the characteristics of real scheduling problems where uncertain events are frequent. Moreover, the capability of devising robust schedules, which are less sensitive to the disruptive effects of unexpected events, is a major request in real applications. In this paper, a branch-and-bound approach is proposed to solve the two-machine permutation flow shop scheduling problem with stochastic processing times. The objective is the minimisation of the value-at-risk of the makespan, to support decision-makers in the trade-off between the expected performance and the mitigation of the impact of extreme scenarios. A Markovian Activity Network (MAN) model is adopted to estimate the distribution of the makespan and assess the value-at-risk for both partial and complete schedules. Phase-type distributions are used to enable general distributions for processing times while maintaining the capability to exploit a Markovian approach. The effectiveness and performance of the proposed approach are demonstrated through a set of computational experiments. [ABSTRACT FROM AUTHOR]

AbstractWe consider a general multivariate model where univariate marginal distributions are known up to a parameter vector and we are interested in estimating that parameter vector without specifying the joint distribution, except for the marginals. If we assume independence between the marginals and maximize the resulting quasi-likelihood, we obtain a consistent but inefficient QMLE estimator. If we assume a parametric copula (other than independence) we obtain a full MLE, which is efficient but only under a correct copula specification and may be biased if the copula is misspecified. Instead we propose a sieve MLE estimator (SMLE) which improves over QMLE but does not have the drawbacks of full MLE. We model the unknown part of the joint distribution using the Bernstein-Kantorovich polynomial copula and assess the resulting improvement over QMLE and over misspecified FMLE in terms of relative efficiency and robustness. We derive the asymptotic distribution of the new estimator and show that it reaches the relevant semiparametric efficiency bound. Simulations suggest that the sieve MLE can be almost as efficient as FMLE relative to QMLE provided there is enough dependence between the marginals. We demonstrate practical value of the new estimator with financial risk management examples, where the use of SMLE leads to superior Value-at-Risk predictions. The paper comes with supplementary materials which include all proofs, codes and datasets, details of implementation and an additional application to insurance claims. [ABSTRACT FROM AUTHOR]

In this work, a new heavy‐tailed Lomax model is proposed for the reliability and actuarial risk analysis. Simulations are conducted to investigate how the estimators behave. Parameters are derived through maximum likelihood estimation techniques. The efficacy of the newly proposed heavy‐tailed Loma distribution is illustrated using the USA indemnity loss datasets. The findings clearly indicate that the new loss model offers a superior parametric fit compared to other competing distributions. Analyzing metrics such as value‐at‐risk, tail mean variance, tail variance, peaks over a random threshold value‐at‐risk (PORT‐VAR), and the mean‐of‐order‐P (MOP(P)) can aid in risk assessment and in identifying and describing significant events or outliers within the USA indemnity loss. This research introduces PORT‐VAR estimators tailored specifically for risk analysis using the USA indemnity loss dataset. The study emphasizes determining the optimal order of P based on the true mean value to enhance the characterization of critical events in the dataset. [ABSTRACT FROM AUTHOR]

A semi-parametric joint Value-at-Risk (VaR) and Expected Shortfall (ES) forecasting framework employing multiple realized measures is developed. The proposed framework extends the realized exponential GARCH model to be semi-parametrically estimated, via a joint loss function, whilst extending existing quantile time series models to incorporate multiple realized measures. A quasi-likelihood is built, employing the asymmetric Laplace distribution that is directly linked to a joint loss function, which enables Bayesian inference for the proposed model. An adaptive Markov Chain Monte Carlo method is used for the model estimation. The empirical section evaluates the performance of the proposed framework with six stock markets from January 2000 to June 2022, covering the period of COVID-19. Three realized measures, including 5-minute realized variance, bi-power variation, and realized kernel, are incorporated and evaluated in the proposed framework. One-step-ahead 1% and 2.5% VaR and ES forecasting results of the proposed model are compared to a range of parametric and semi-parametric models, lending support to the effectiveness of the proposed framework. [ABSTRACT FROM AUTHOR]

This research introduces a realized double hysteretic GARCH (R-dhGARCH) model with a skew Student's t distribution designed to improve quantile forecasts by allowing regime-switching in both volatility and measurement equations. The nonlinear model is flexible, accommodating both explosive persistence and high volatility in the first regime and effectively capturing extreme values within the volatility and measurement equations. Bayesian methods are proposed for estimating the unknown parameters of a target model while also forecasting value-at-risk (VaR) and expected shortfall (ES) simultaneously. An adaptive MCMC algorithm serves to sample from nonstandard posterior distributions. Illustrations of the proposed methods occur through a simulation study as well as from real examples. In the simulation study, parameter estimates and tail forecasts undergo evaluation. Daily data from four stock markets form the VaR and ES forecasts for a four-year out-of-sample period, including the COVID-19 pandemic period. Backtests, scoring functions, and Murphy diagrams help assess the models' forecasts. The results show that the R-dhGARCH model outperforms other models in the U.S., Japan, and South Korea markets. [ABSTRACT FROM AUTHOR]

Bayesian optimization due to its flexibility and sample efficiency has become a standard approach for simulation optimization. To reduce this problem, one can resort to cheaper surrogates of the objective function. Examples are ubiquitous, from protein engineering or material science to tuning machine learning algorithms, where one could use a subset of the full training set or even a smaller related dataset. Cheap information sources in the optimization scheme have been studied in the literature as the multi-fidelity optimization problem. Of course, cheaper sources may hold some promise toward tractability, but cheaper models offer an incomplete model inducing unknown bias and epistemic uncertainty. In this manuscript, we are concerned with the discrete case, where f x , w i is the value of the performance measure associated with the environmental condition w i and p (w i) represents the relevance of the condition w i (i.e., the probability of occurrence or the fraction of time this condition occurs). The main contribution of this paper is the proposal of a Gaussian-based framework, called augmented Gaussian process (AGP), based on sparsification, originally proposed for continuous functions and its generalization in this paper to stochastic optimization using different risk profiles for combinatorial optimization. The AGP leverages sample and cost-efficient Bayesian optimization (BO) of multiple information sources and supports a new acquisition function to select the new source–location pair considering the cost of the source and the (location-dependent) model discrepancy. An extensive set of computational results supports risk-aware optimization based on CVaR (conditional value-at-risk). Computational experiments confirm the actual performance of the MISO-AGP method and the hyperparameter optimization on benchmark functions and real-world problems. [ABSTRACT FROM AUTHOR]

In actuarial modeling, right-skewed distributions are of paramount importance. Typically, they have the property of becoming unimodal and symmetric after applying some increasing concave transformation $ \mathsf {T} $ T (e.g. log-transformation). In what follows, we refer to them as $ \mathsf {T} $ T-unimodal $ \mathsf {T} $ T-symmetric distributions. In this paper, we derive attainable bounds for the Value-at-Risk for such distributions when some partial information is available, such as information on the support, median, or certain moments. We also derive explicit upper and lower bounds for the Range Value-at-Risk under knowledge of unimodality, symmetry, mean, variance, and possibly bounded support. In passing, we provide a generalization of the Gauss inequality for symmetric distributions with known support. We show how these bounds improve on bounds available in the literature using a real-world automobile insurance claims dataset. [ABSTRACT FROM AUTHOR]

We investigate macroeconomic stress testing frameworks for corporate bond recovery rate analysis using machine learning techniques. In doing so, we simulate the macroeconomic effect of a broad range of 182 macroeconomic variables extracting key factors with methods such as (sparse) principal component analysis and sparse group least absolute selection and shrinkage operation (LASSO). Using the adverse stress testing scenario from the US Federal Reserve as the benchmark, we demonstrate that our least squares-support vector regression model produces sensible and potentially valuable risk measures such as value-at-risk and conditional value-at-risk for recovery rates during periods of macroeconomic stress. [ABSTRACT FROM AUTHOR]

Recently, the complex dependence patterns among various stocks gained more importance. Measuring the dependency structure is critical for investors to manage their portfolio risks. Since the global financial crisis, researchers have been more interested in studying the dynamics of dependency within stock markets by using novel methodologies. This study aims to investigate a Regular-Vine copula approach to estimate the interdependence structure of the Istanbul Stock Exchange index (ISE100). For this purpose, we consider 32 stocks related to 6 sectors belonging to ISE100. To reflect the time-varying impacts of the 2008–2009 global financial crisis, the dependence analysis is conducted over pre-, during-, and post-global financial crisis periods. Portfolio analysis is considered via a rolling window approach to capture the changes in the dependence. We compare the Regular-Vine-based generalized autoregressive conditional heteroskedasticity (GARCH) against the conventional GARCH model with different innovations. Value at risk and expected shortfall risk measures are used to validate the models. Additionally, for the constructed portfolios, return performance is summarized using both Sharpe and Sortino ratios. To test the ability of the considered Regular-Vine approach on ISE100, another evaluation has been done during the COVID-19 pandemic crisis with various parameter settings. The main findings across different risky periods illustrate the suitability of using the Regular-vine GARCH approach to model the complex dependence among stocks in emerging market conditions. [ABSTRACT FROM AUTHOR]

Aggregated long and short trading risk positions of speculative assets over time are likely to be unequal. This may be because of irrational decisions of traders and investors as well as catastrophic events that lead to pronounce or salient market crashes. Returns of such assets are therefore more likely to have one polynomial tail and one exponential tail. The generalized hyperbolic (GH) skewed Student‐t distribution is known to handle such situations quite well. In this paper, we use generalized autoregressive conditional heteroscedasticity (GARCH) models to empirically show the superiority of the GH skewed Student‐t distribution in forecasting the extreme tail risks of cryptocurrency returns in the presence of substantial skewness in comparison with some competing distributions. Furthermore, we show the practical significance of the GH skewed Student‐t distribution‐based risk forecasts in computing daily capital requirements. Evidence from the study suggests that the GH skewed Student‐t distribution model tends to be superior in forecasting volatility and expected shortfall (ES) but not value‐at‐risk. In addition, the distribution yields higher value‐at‐risk (VaR) exceptions but surprisingly avoids the red zone of the Basel II accord penalty zones and produces lower but optimal daily capital requirements. Therefore, in the presence of substantially skewed returns having exponential‐polynomial tails, we recommend the use of the GH skewed Student‐t distribution for parametric GARCH models in forecasting extreme tail risk. [ABSTRACT FROM AUTHOR]

In this paper, we presented a financial analysis of the values of financial losses for real data in light of a set of indicators for measuring financial risks. The value-at-risk (VAR), tail mean–variance (TMV), tail-VAR (TVAR), tail variance (TV), Peaks Over a Random Threshold Value-at-Risk (PORT-VAR) and the mean of order P (MOOP) indicators are used in identifying and describing important events or outliers within US financial indemnity loss data. Some extreme financial value theory (EFVT) models are compared in view of financial indemnity loss data and according to some confidence levels. The paper provided a clear financial framework for financial institutions to help them avoid large, sudden losses. Therefore, financial data with a long tail to the right were chosen, and several financial risk measures were used that study and analyze the behavior of the long tail.

Abstract Effective risk exposure descriptions can be made using continuous distributions. To illustrate the level of exposure to a certain danger, it is better to use a single number, or at the very least, a small set of numbers. These risk exposure numbers, which are commonly referred to as significant risk indicators, are unquestionably the output of a particular model. In this regard, five key indicators are utilized to define the risk exposure in the reinsurance revenues data. For this specific purpose we introduce a new distribution called odd log-logistic XGamma model . We estimated the parameters using maximum-likelihood method, least squares method and Bayesian method. Monte Carlo simulation study is performed under a set of conditions and controls. The risk exposure under the reinsurance revenue data was also described using five important risk indicators, including value-at-risk, tail-value-at-risk, tail variance, tail mean-variance, and mean excess loss function. These statistical measures were developed for the proposed new model.

In this paper, we presented a financial analysis of the values of financial losses for real data in light of a set of indicators for measuring financial risks. The value-at-risk (VAR), tail mean–variance (TMV), tail-VAR (TVAR), tail variance (TV), Peaks Over a Random Threshold Value-at-Risk (PORT-VAR) and the mean of order P (MOO P ) indicators are used in identifying and describing important events or outliers within US financial indemnity loss data. Some extreme financial value theory (EFVT) models are compared in view of financial indemnity loss data and according to some confidence levels. The paper provided a clear financial framework for financial institutions to help them avoid large, sudden losses. Therefore, financial data with a long tail to the right were chosen, and several financial risk measures were used that study and analyze the behavior of the long tail. [ABSTRACT FROM AUTHOR]

This study proposes a novel measure of systemic risk that is obtained by aggregating downside risk information from the cross section of assets. In contrast to existing studies, we expand the analysis of systemic risk to many assets and focus on marginal measures of tail risk that are aggregated using a Fisher-type test to detect the risk of systemic events. The presence of downside risk for each asset of the cross section is examined through a bootstrap test of first-order stochastic dominance between the underlying tail distribution and the tail distribution of the residuals of a multivariate DCC-GARCH model. The application of these methods to the cross section of the FTSE-100 stock returns provides overwhelming evidence on the presence of financial instability during the period 2006–2009. Interestingly, we also find compelling evidence of systemic risk during the 2012–2015 period coinciding with the European debt crisis and after the outbreak of the coronavirus disease 2019 pandemic. [ABSTRACT FROM AUTHOR]

This study investigates the role of the probability distribution in forecasting the volatility and value-at-risk (VaR) of cryptocurrency returns using generalized auto-regressive conditional heteroskedasticity (GARCH)-type models. We consider GARCH, EGARCH, GJR-GARCH, TGARCH and Realized GARCH models and show that the role of the probability distribution varies across different situations. A skewed and heavy-tailed distribution contributes to better performance in forecasting the VaR; however, it does not improve the accuracy of volatility forecasting. The results help us to better understand the role of the probability distribution in GARCH-type models. [ABSTRACT FROM AUTHOR]

This study investigates the volatility of the Euro-to-US Dollar exchange rate, specifically focusing on identifying long-memory characteristics. Through the analysis of daily data spanning from January 1, 2018, to January 10, 2023, the study uncovers a robust long-memory feature. Supporting this exploration, the study endorses the use of sophisticated models such as Fractionally Integrated Generalized Autoregressive Conditionally Heteroskedastic (FIGARCH) and Hyperbolic Generalized Autoregressive Conditionally Heteroskedastic (HYGARCH), incorporating both student and skewed student innovation distributions. The results underscore the superior performance of FIGARCH and HYGARCH models, particularly when coupled with a skewed student distribution. This collaborative approach enhances the predictability of crucial financial metrics, including Value at Risk (VaR) and Expected Shortfall (ESF), for both long and short trading positions. Significantly, the FIGARCH model, when utilizing a skewed student distribution, demonstrates exceptional predictive power. This outcome challenges the efficient market hypothesis and suggests the potential for generating outstanding returns. In light of these findings, this research contributes valuable insights for comprehending and navigating the intricacies of the Euro-to-US Dollar exchange rate, providing a forward-looking perspective for financial practitioners and researchers alike. [ABSTRACT FROM AUTHOR]

This paper considers the expected utility portfolio optimization problem with initial-time and intermediate-time Value-at-Risk constraints on terminal wealth. We derive the closed-form solutions which are optimal among all feasible controls at initial time, i.e., precommitted strategies. Moreover, the precommitted strategies are also optimal at the intermediate time for "bad" market states. A contingent claim on Merton's portfolio is constructed to replicate the optimal portfolio. We find that risk management with intermediate-time risk constraints is prudent in hedging "bad" intermediate market states and performs significantly better than the one terminal-wealth risk constraint solutions under the relative loss ratio measure. [ABSTRACT FROM AUTHOR]

We explore the application of spectral methods in risk management as means of validating VaR models. We propose to replace earlier spectral VaR tests with the test based on the Anderson–Darling statistic. Based on assumptions relevant to VaR failure analysis, we experimentally prove that the Anderson–Darling spectral test displays strong power to reject inaccurate VaR. Its main advantage over the existing methods is the combination of two features: the lack of tendency to overreject properly predicted VaR and high sensitivity to limited evidence of incorrectness in VaR predictions. Thus, this test may play an important role in times of change in volatility dynamics, such as outbreaks of financial crises. We confirm this empirically, based on data starting before the subprime mortgage crisis, running through the COVID-19 pandemic, until the outbreak of the Russo–Ukrainian war. We give a number of examples when this method revealed the inaccuracy of VaR predictions not discovered by com- monly used tests. We also show that the proposed spectral test never failed at finding the models indicated as incorrect by other tests. [ABSTRACT FROM AUTHOR]

AbstractIn this paper, we study the estimation of Value-at-Risk (VaR) using GARCH models when the observed process is actually iid. Such an overfitting situation entails that the almost sure consistency of the quasi-maximum likelihood estimator (QMLE) is not ensured. Therefore, a simulation experiment is performed to shed some light on the consequences of such a poor parameters estimation on the VaR assessment. Since the GARCH specification is not identified when the ARCH and persistence parameters are equal to zero, then a constant volatility is predicted. As a consequence, it turns out that the VaR evaluation is not affected by the estimation drawbacks. [ABSTRACT FROM AUTHOR]

The dynamic landscape of modern financial analysis relies on the versatile instrument of copulas to unravel intricate interdependencies between variables. Value-at-risk (VAR) analysis, a crucial domain in risk assessment, seeks to navigate the complexities inherent in financial markets. Within portfolio management, risk minimization drives the selection of assets with diminished correlations. Copula models, particularly the symmetric Spearman ρ and Kendall τ, have traditionally underpinned VAR analysis. However, real-world financial assets exhibit asymmetric dependencies, necessitating a paradigm shift toward asymmetric copulas. This paper explores the potency of asymmetric copulas in VAR analysis for financial assets. Employing Monte Carlo simulations of copula functions, it juxtaposes nested Archimedean copulas with conventional symmetric counterparts. The study illuminates the role of asymmetric copulas in deciphering complex relationships inherent to financial variables, enriching the discourse on risk assessment and investment strategies. The paper's journey traverses methodology, empirical findings, and introspective analysis, bridging theory and practice. It demonstrates that meticulous copula model selection and skillful Monte Carlo simulation execution are pivotal for accurate VAR analysis. The application of asymmetric copulas, particularly nested Archimedean copulas, effectively captures intricate dependencies among financial assets, spotlighting their potential in risk management. This study's theoretical implications underscore the necessity of accurately modeling complex dependencies and tail events within portfolio risk management. Asymmetric copulas pave the way for dynamic models adaptable to evolving financial market dynamics. Managerially, the study guides risk managers in crafting tailored hedging and diversification strategies to enhance portfolio resilience. The study enhances risk management strategies by emphasizing sophisticated methodologies and nuanced risk assessment and contributes to stable financial outcomes. [ABSTRACT FROM AUTHOR]

In this work, a novel probability distribution is introduced and studied. Some characterizations are presented. Several financial risk indicators, such as the value-at-risk, tail-valueat-risk, tail variance, tail Mean-Variance, and mean excess loss function are considered under the maximum likelihood estimation, the ordinary least squares, the weighted least squares, and the Anderson Darling estimation methods. These four methods were applied for the actuarial evaluation under a simulation study and under an application to insurance claims data. For distributional validation under the complete data, the well-known Nikulin-Rao-Robson statistic is considered. The Nikulin-Rao-Robson test statistic is assessed under a simulation study and under three complete real data sets. For censored distributional validation, a new version of the Nikulin-Rao-Robson statistic is considered. The new Nikulin-Rao-Robson test statistic is assessed under a comprehensive simulation study and under three censored real data sets. [ABSTRACT FROM AUTHOR]

Accurate risk assessment is crucial for predicting potential financial losses. This paper introduces an innovative approach by employing expected risk models that utilize risk samples to capture comprehensive risk characteristics. The innovation lies in the integration of classical credibility theory with expected risk models, enhancing their stability and precision. In this study, two distinct expected risk models were developed, referred to as Model Type I and Model Type II. The Type I model involves independent and identically distributed random samples, while the Type II model incorporates time-varying stochastic processes, including heteroscedastic models like GARCH(p,q). However, these models often exhibit high variability and instability, which can undermine their effectiveness. To mitigate these issues, we applied classical credibility theory, resulting in credible expected risk models. These enhanced models aim to improve the accuracy of Value-at-Risk (VaR) forecasts, a key risk measure defined as the maximum potential loss over a specified period at a given confidence level. The credible expected risk models, referred to as CreVaR, provide more stable and precise VaR forecasts by incorporating credibility adjustments. The effectiveness of these models is evaluated through two complementary approaches: coverage probability, which assesses the accuracy of risk predictions; and scoring functions, which offer a more nuanced evaluation of prediction accuracy by comparing predicted risks with actual observed outcomes. Scoring functions are essential in further assessing the reliability of CreVaR forecasts by quantifying how closely the forecasts align with the actual data, thereby providing a more comprehensive measure of predictive performance. Our findings demonstrate that the CreVaR risk measure delivers more reliable and stable risk forecasts compared to conventional methods. This research contributes to quantitative risk management by offering a robust approach to financial risk prediction, thereby supporting better decision making for companies and financial institutions. [ABSTRACT FROM AUTHOR]

Effective risk exposure descriptions can be made using continuous distributions. To illustrate the level of exposure to a certain danger, it is better to use a single number, or at the very least, a small set of numbers. These risk exposure numbers, which are commonly referred to as significant risk indicators, are unquestionably the output of a particular model. In this regard, five key indicators are utilized to define the risk exposure in the reinsurance revenues data. For this specific purpose we introduce a new distribution called odd log-logistic XGamma model. We estimated the parameters using maximum-likelihood method, least squares method and Bayesian method. Monte Carlo simulation study is performed under a set of conditions and controls. The risk exposure under the reinsurance revenue data was also described using five important risk indicators, including value-at-risk, tail-value-at-risk, tail variance, tail mean-variance, and mean excess loss function. These statistical measures were developed for the proposed new model. [ABSTRACT FROM AUTHOR]

In this article, we calculate the value-at-risk (VaR) for large portfolios in intensity models, where the idiosyncratic and systematic risk exposures as well as the impact of past default losses are subsumed into the intensity processes. The adopted method is based on the theory of saddlepoint approximation for continuous-time Markov processes whose transition densities and distribution functions can be approximated in closed forms. A simple example with theoretical and numerical results is presented in the end. [ABSTRACT FROM AUTHOR]

This study presents a dynamic analysis framework called autoregressive conditional extreme value (AEV), designed for modeling the daily maximum drawdowns of commodity futures markets, using steel rebar futures as an illustrative example. The research demonstrates that AEV outperforms AR or generalized autoregressive conditional heteroskedasticity (GARCH)‐type benchmark models in terms of in‐sample fitting and out‐of‐sample forecasting accuracy. Notably, AEV's time‐varying shape parameter (tail index) sensitively captures the clustering nature of tail risk and differentiates between long‐ and short‐side markets. The study also presents theoretical findings regarding AEV‐based value at risk (VaR) and expected shortfall (ES), and empirically measures and predicts the tail risk of the steel rebar futures market. Moreover, the research extends the methodology to create a dynamic margin model for Chinese commodity futures, showing that the AEV‐based model effectively achieves the specified risk coverage targets and significantly reduces current exchange margin requirements. [ABSTRACT FROM AUTHOR]

This research incorporates realized volatility and overnight information into risk models, wherein the overnight return often contributes significantly to the total return volatility. Extending a semiparametric regression model based on asymmetric Laplace distribution, we propose a family of RES‐CAViaR‐oc models by adding overnight return and realized measures as a nowcasting technique for simultaneously forecasting Value‐at‐Risk (VaR) and expected shortfall (ES). We utilize Bayesian methods to estimate unknown parameters and forecast VaR and ES jointly for the proposed model family. We also conduct extensive backtests based on joint elicitability of the pair of VaR and ES during the out‐of‐sample period. Our empirical study on four international stock indices confirms that overnight return and realized volatility are vital in tail risk forecasting. [ABSTRACT FROM AUTHOR]

A significant amount of historical returns is needed for the generalized autoregressive conditional heteroscedasticity (GARCH) models to be calibrated. Newer cryptocurrencies, such as non-fungible tokens (NFTs), have relatively limited data to create robust parameter estimates. This study uses a newly developed method, the exponentially weighted moving average (EWMA) model, that takes into account the fat-tailed distributions of returns and volatility response to forecast Value-at-Risk (VaR) and Expected Shortfall (ES). We employ thorough back tests of daily VaR and ES forecasts, which are widely utilized for regulatory approval and are considered to be industry standards. We also use loss function ratios to select the best model. Our results indicate that simpler models are just as good as the complicated ones, provided the simpler models capture fat-tailed distributions of returns. The primary findings hold up through several tests.

The aim of this paper is to assess whether the availability of high-frequency data enhances the accuracy of extreme market risk estimation in comparison to low-frequency data by using Value-at-risk (VaR) and Expected shortfall (ES). The sample data used for analysis comprised the daily closing stock prices and 5-minute intraday stock prices of DJIA, FTSE100, BOVESPA, and MERVAL Index from 2014 to 2022. The data analysis was done to compare the performance of two-stages hybrid methods called conditional EVT that combined the GARCH, RV and HAR specification models with the EVT approach. To assess the accuracy of the VaR forecasts, out-of-sample VaR forecast was backtested by using unconditional coverage (UC) and conditional coverage (CC) tests. The VaR backtesting procedure also incorporated the utilization loss function which are the regulatory loss function (RLF) and the firm’s loss function (FLF). The accuracy of the forecasted ES was backtested by using the generalized breach indicator (GBI) method. The findings of this research emphasized that high-frequency conditional EVT, incorporating the HAR specification outperformed the low-frequency conditional EVT in predicting market risk during periods characterized by extreme returns. Based on the VaR and ES measure, the HAR-EVT typed models are the best performance model compared to the GARCH-EVT and RV-EVT typed models during both crisis and non-crisis periods. This research study contributes to the current literature on the forecasting ability of risk models by concentrating on the hybrid model of long-memory models (FIEGARCH, RV-FIEGARCH and HAR-FIEGARCH) for with the EVT approach.

The normality of the distribution of stock returns is one of the basic assumptions in financial mathematics. Empirical studies, however, undermine the validity of this assumption. In order to flexibly fit complex non-normal distributions, this article applies a Gaussian Mixture Model (GMM) in the context of Value-at-Risk (VaR) estimation. The study compares the forecasting ability of GMM with other widespread VaR approaches, scrutinizing the data on the daily log-returns for a wide range of “S&P 500” stocks in two periods: from 2006 to 2010 and from 2016 to 2021. The statistical and graphical analysis revealed that GMM quickly and adequately adjusts to significant and rapid stock market changes, although the remaining methods delay. The study also found that the ratio of short-term and long-term standard deviations significantly improves the GMM and other methods’ ability to predict VaR, reflecting the observed features of analyzed stock log-returns.

AbstractThis study estimates value-at-risk (VaR) to measure foreign exchange risk in Indonesia’s banking industry using quantile regression (QR) approach. Four large banks whose capital and assets were the biggest were observed, and their selection was based on their market share in the industry. To compute VaR, data on each bank’s day-to-day gain/loss between 1 January 2016 and 9 February 2021 were examined, and they involved records of all transactions involving six foreign currencies. According to results of a backtesting analysis using dynamic quantile (DQ) test at a 95% confidence level performed in this study, VaR estimation of each bank’s gain/loss on foreign currency transactions generated using QR regression approach demonstrates an excellent predictive performance, with an average of 95% accuracy level. The contribution of this article lies in the development of an internal model that produces better risk mea­surements, a model that has not yet gained widespread usage in empirical research within the context of Indonesia.

Abstract This study investigates the simplicity and adequacy of tail-based risk measures—value-at-risk (VaR) and expected shortfall (ES)—when applied to tail targeting of the extreme value (EV) model. We implement Lévy–VaR and ES risk measures as full density-based alternatives to the generalized Pareto VaR and the generalized Pareto ES of the tail-targeting EV model. Using data on futures contracts of S&P500, FTSE100, DAX, Hang Seng, and Nikkei 225 during the Global Financial Crisis of 2007–2008, we find that the simplicity of tail-based risk management with a tail-targeting EV model is more attractive. However, the performance of EV risk estimates is not necessarily superior to that of full density-based relatively complex Lévy risk estimates, which may not always give us more robust VaR and ES results, making the model inadequate from a practical perspective. There is randomness in the estimation performances under both approaches for different data ranges and coverage levels. Such mixed results imply that banks, financial institutions, and policymakers should find a way to compromise or trade-off between “simplicity” and user-defined “adequacy”.

Abstract.This article studies the joint value-at-risk (VaR) and expected shortfall (ES) regression for a wide class of location-scale time series models including autoregressive and moving average models with generalized autoregressive conditional heteroscedasticity errors. In contrast to the quasi-maximum likelihood estimation, we estimate the model parameters with the aim of more accurate VaR and ES estimation. Then, we show consistency and asymptotic normality for parameter estimators under weak regularity conditions. Finally, a simulation study and a real data analysis are shown to illustrate our results. [ABSTRACT FROM AUTHOR]

In this article, we use a deep quantile estimator, based on neural networks and their universal approximation property to examine a non-linear association between the conditional quantiles of a dependent variable and predictors. This methodology is versatile and allows both the use of different penalty functions, as well as high dimensional covariates. We present a Monte Carlo exercise where we examine the finite sample properties of the deep quantile estimator and show that it delivers good finite sample performance. We use the deep quantile estimator to forecast value-at-risk and find significant gains over linear quantile regression alternatives and other models, which are supported by various testing schemes. Further, we consider also an alternative architecture that allows the use of mixed frequency data in neural networks. This article also contributes to the interpretability of neural network output by making comparisons between the commonly used Shapley Additive Explanation values and an alternative method based on partial derivatives. [ABSTRACT FROM AUTHOR]

This study aims to jointly predict conditional quantiles and tail expectations for the returns of the most popular cryptocurrencies (Bitcoin, Ethereum, Ripple, Dogecoin and Litecoin) using financial and macroeconomic indicators as explanatory variables. We adopt a Monotone Composite Quantile Regression Neural Network (MCQRNN) model to make one- and five-steps-ahead predictions of Value-at-Risk (VaR) and Expected Shortfall (ES) based on a rolling window and compare the performance of our model against the Historical simulation and the standard ARMA(1,1)-GARCH(1,1) model used as benchmarks. The superior set of models is then chosen by backtesting VaR and ES using a Model Confidence Set procedure. Our results show that the MCQRNN performs better than both benchmark models for jointly predicting VaR and ES when considering daily data. Models with the implied volatility index, treasury yield spread and inflation expectations sharpen the extreme return predictions. The results are consistent for the two risk measures at the 1% and 5% level both, in the case of a long and short position and for all cryptocurrencies. [ABSTRACT FROM AUTHOR]

This paper aims to design a quadratic optimization model of an investment portfolio based on value-at-risk (VaR) by entering risk-free assets and company liabilities. The designed model develops Markowitz's investment portfolio optimization model with risk aversion. Model development was carried out using vector and matrix equations. The entry of risk-free assets and liabilities is essential. Risk-free assets reduce the loss risk, while liabilities accommodate a fundamental analysis of the company's condition. The model can be applied in various sectors of capital markets worldwide. This study applied the model to Indonesia's mining and energy sector. The application results show that risk aversion negatively correlates with the mean and VaR of the return of investment portfolios. Assuming that risk aversion is in the 5.1% to 8.2% interval, the maximum mean and VaR obtained for the next month are 0.0103316 and 0.0138270, respectively, while the minimum mean and VaR are 0.0102964 and 0.0137975, respectively. The finding of this study is that the vector equation for investment portfolio weights is obtained, which can facilitate calculating investment portfolio weight optimization. This study is expected to help investors control the quality of appropriate investment, especially in some stocks in Indonesia's mining and energy sector. [ABSTRACT FROM AUTHOR]

This study investigates the simplicity and adequacy of tail-based risk measures—value-at-risk (VaR) and expected shortfall (ES)—when applied to tail targeting of the extreme value (EV) model. We implement Lévy–VaR and ES risk measures as full density-based alternatives to the generalized Pareto VaR and the generalized Pareto ES of the tail-targeting EV model. Using data on futures contracts of S&P500, FTSE100, DAX, Hang Seng, and Nikkei 225 during the Global Financial Crisis of 2007–2008, we find that the simplicity of tail-based risk management with a tail-targeting EV model is more attractive. However, the performance of EV risk estimates is not necessarily superior to that of full density-based relatively complex Lévy risk estimates, which may not always give us more robust VaR and ES results, making the model inadequate from a practical perspective. There is randomness in the estimation performances under both approaches for different data ranges and coverage levels. Such mixed results imply that banks, financial institutions, and policymakers should find a way to compromise or trade-off between "simplicity" and user-defined "adequacy". [ABSTRACT FROM AUTHOR]

This paper proposes a new GARCH specification that adapts the architecture of a long-term short memory neural network (LSTM). It is shown that classical GARCH models generally give good results in financial modeling, where high volatility can be observed. In particular, their high value is often praised in Value-at-Risk. However, the lack of nonlinear structure in most approaches means that conditional variance is not adequately represented in the model. On the contrary, the recent rapid development of deep learning methods is able to describe any nonlinear relationship in a clear way. We propose GARCHNet, a nonlinear approach to conditional variance that combines LSTM neural networks with maximum likelihood estimators in GARCH. The variance distributions considered in the paper are normal, t and skewed t, but the approach allows extension to other distributions. To evaluate our model, we conducted an empirical study on the logarithmic returns of the WIG 20 (Warsaw Stock Exchange Index), S&P 500 (Standard & Poor's 500) and FTSE 100 (Financial Times Stock Exchange) indices over four different time periods from 2005 to 2021 with different levels of observed volatility. Our results confirm the validity of the solution, but we provide some directions for its further development. [ABSTRACT FROM AUTHOR]

This paper proposes the time‐heterogeneous Student's t autoregressive model as an alternative to the various volatility forecast models documented in the literature. The empirical results indicate that: (i) the proposed model has better forecasting performance than other commonly used models, and (ii) the problem of reliable risk measurement arises primarily from the model risk associated with risk forecast models rather than the particular risk measure for computing risk. Based on the results, the paper makes recommendations to regulators and practitioners. [ABSTRACT FROM AUTHOR]

This paper provides two specification tests for the system of spatial autoregressive model of order m. We derive the theoretical limit distributions and show in a detailed Monte Carlo simulation study that the tests result in reasonable sized testing procedures with large power. In the empirical application, we analyze Euro Stoxx 50 returns in two different time spans, looking for insights how well models with different specifications of the spatial weighting matrices (local, country, industry and country-industry specific dependencies including interaction effects) fit to the data. The analyzes also demonstrate the ability of the tests to detect inaccurate Value-at-Risk forecasts. [ABSTRACT FROM AUTHOR]

A new generalization of the extreme value distribution is presented with its density function, having a wide variety of density and tail shapes for modeling extreme value data. This generalized extreme value distribution will be referred to as the odd generalized extreme value distribution. It is derived by considering the distributions of the odds of the generalized extreme value distribution. Consequently, the new distribution is enlightened by not only having all six families of extreme value distributions; Gumbel, Fréchet, Weibull, reverse‐Gumbel, reverse‐Fréchet, and reverse‐Weibull as submodels but also convenient for modeling bimodal extreme value data that are frequently found in environmental sciences. Basic properties of the distribution, including tail behavior and tail heaviness, are studied. Also, quantile‐based aliases of the new distribution are illustrated using Galton's skewness and Moor's kurtosis plane. The adequacy of the new distribution is illustrated using well‐known goodness‐of‐fit measures. A simulation is performed to validate the estimated risk measures due to repeated data points frequently found in temperature data. The Grand Rapids and well‐known Wooster temperature data sets are analyzed and compared to nine different extreme value distributions to illustrate the new distribution's bimodality, flexibility, and overall fitness. [ABSTRACT FROM AUTHOR]

This study examines the relationship between financial decisions and the value-at-risk (VaR) of companies operating in the Turkish stock market. The study contains semi-annual data of non-financial BIST 100 Index companies spanning from January 2010 to June 2023. Companies’ VaR are calculated using Monte-Carlo simulation, bootstrap, delta-normal, and historical simulation methods and included in separate econometric models as dependent variables. Financial decisions are represented through financial ratios in line with the basic principles of corporate finance and included as explanatory variables in econometric models. The study employs a five-stage panel data methodology. Findings reveal that the impact of financial decisions regarding working capital management, capital structure, dividend pay-out, and growth policies on companies’ VaR differ according to the VaR calculation method. Notably, findings show that financial decisions explain the changes in VaR calculated by Bootstrap method with the highest success rate, aligning with existing finance literature. Prudent financing policies and flexible investment strategies in working capital management, enhanced profitability and financial performance, and sales growth exhibit dampening effects on VaR. Conversely, heightened leverage and long-term borrowings, decisions to pay-out dividends, and growth in foreign investments have increasing effects on VaR. Furthermore, the study identifies the Covid-19 pandemic as exerting a negative influence on VaR.