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We develop a novel multivariate semi-parametric framework for joint portfolio Value-at-Risk (VaR) and Expected Shortfall (ES) forecasting. Unlike existing univariate semi-parametric approaches, the proposed framework explicitly models the dependence structure among portfolio asset returns through a dynamic conditional correlation (DCC) parameterization. To estimate the model, a two-step procedure based on the minimization of a strictly consistent VaR and ES joint loss function is employed. This procedure allows to simultaneously estimate the DCC parameters and the portfolio risk factors. The performance of the proposed model in risk forecasting on various probability levels is evaluated by means of a forecasting study on the components of the Dow Jones index for an out-of-sample period from December 2016 to September 2021. The empirical results support effectiveness of the proposed framework compared to a variety of existing approaches. [ABSTRACT FROM AUTHOR]

This paper considers the Recursive Kernel Estimator (RKE) of the expectile-based conditional shortfall. The estimator is constructed under a functional structure based on the ergodicity assumption. More preciously, we assume that the input-variable is valued in a pseudo-metric space, output-variable is scalar and both are sampled from ergodic functional time series data. We establish the complete convergence rate of the RKE-estimator of the considered functional shortfall model using standard assumptions. We point out that the ergodicity assumption constitutes a relevant alternative structure to the mixing time series dependency. Thus, the results of this paper allows to cover a large class of functional time series for which the mixing assumption is failed to check. Moreover, the obtained results is established in a general way, allowing to particularize this convergence rate for many special situations including the kernel method, the independence case and the multivariate case. Finally, a simulation study is carried out to illustrate the finite sample performance of the RKE-estimator. In order to examine the feasibility of the recursive estimator in practice we consider a real data example based on financial time series data. [ABSTRACT FROM AUTHOR]

AbstractExpected shortfall (ES) has emerged as an important metric for characterizing the tail behavior of a random outcome, specifically associated with rarer events that entail severe consequences. In climate science, the threats of flooding and heatwaves loom large, impacting natural environments and human communities. In actuarial studies, a key observation in modeling insurance claim sizes is that features exhibit distinct effects in explaining small and large claims. This paper concerns nonparametric expected shortfall regression as a class of statistical methods for tail learning. These methods directly target upper/lower tail averages and will empower practitioners to address complex questions that are beyond the reach of mean regression-based approaches. Using kernel ridge regression, we introduce a two-step nonparametric ES estimator that involves a plugged-in quantile function estimate without sample-splitting. We provide non-asymptotic estimation and Gaussian approximation error bounds, depending explicitly on the effective dimension, sample size, regularization parameters, and quantile estimation error. To construct pointwise confidence bands, we propose a fast multiplier bootstrap procedure and establish its validity. We demonstrate the finite-sample performance of the proposed methods through numerical experiments and an empirical study aimed at examining the heterogeneous effects of different air pollutants and meteorological factors on average and high PM2.5 concentration. [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]

This paper explores backtesting Value-at-Risk (VaR) and Expected Shortfall (ES) considering ten standard and extended tests in the context of non-technical individual investors trading equities of twenty selected commercial banks listed at the Dhaka Stock Exchange (DSE) using their daily share prices for 11 years (from 2010 to 2020). Following a significant gap in the literature on investigating the efficacy of user-friendly models in quantifying the market risk of banks in emerging economies, this paper adopted four user-friendly models that are relatively straightforward to understand and interpret and are considered representatives of zero, -one, -two, and -three parametric families of all risk models in the literature specifically for the emerging economy of Bangladesh. The popular RiskMetrics™ risk forecast model of JPMorgan, sweeping the world as the most user-friendly conditional alternative to unconditional Gaussian risk forecasts under the framework of VaR, is found not to be adequate under the framework of ES that was recently recommended by Basel-III. The joint score value-based comparison finds the historical simulation (HS) model as the most appropriate model in Bangladesh when models are assessed under a practical user-friendly implementation design. Under this design the Trust Bank Ltd. (TBL), the bank managed and operated by Bangladesh Military, qualifies as the most investor-friendly bank in terms of causing the least frustration to its equity investors over 2010–2020. Overall, augmenting earlier studies in the literature that are mostly for developed markets and are mostly without any ES back-test, we find that the user-friendly model HS is still successful in quantifying market risk over the globe since its relative usefulness gets well established through recent back-tests of VaR and ES in emerging market too. [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]

This study uses a hybrid model of the exponential generalised auto-regressive conditional heteroscedasticity (eGARCH)-extreme value theory (EVT)-Gumbel copula model to investigate the dependence structure between Bitcoin and the South African Rand, and quantify the portfolio risk of an equally weighted portfolio. The Gumbel copula, an extreme value copula, is preferred due to its versatile ability to capture various tail dependence structures. To model marginals, firstly, the eGARCH(1, 1) model is fitted to the growth rate data. Secondly, a mixture model featuring the generalised Pareto distribution (GPD) and the Gaussian kernel is fitted to the standardised residuals from an eGARCH(1, 1) model. The GPD is fitted to the tails while the Gaussian kernel is used in the central parts of the data set. The Gumbel copula parameter is estimated to be α = 1.007 , implying that the two currencies are independent. At 90%, 95%, and 99% levels of confidence, the portfolio's diversification effects (DE) quantities using value at risk (VaR) and expected shortfall (ES) show that there is evidence of a reduction in losses (diversification benefits) in the portfolio compared to the risk of the simple sum of single assets. These results can be used by fund managers, risk practitioners, and investors to decide on diversification strategies that reduce their risk exposure. [ABSTRACT FROM AUTHOR]

Abstract This study introduces the dynamic Gerber model (DGC) and evaluates its performance in the prediction of Value at Risk (VaR) and Expected Shortfall (ES) compared to alternative parametric, non-parametric and semi-parametric methods for estimating the covariance matrix of returns. Based on ES backtests, the DGC method produces, overall, accurate ES forecasts. Furthermore, we use the Model Confidence Set procedure to identify the superior set of models (SSM). For all the portfolios and VaR/ES confidence levels we consider, the DGC is found to belong to the SSM.

Portfolio formation is one of the strategies that investors can do to get the best results Portfolio formation can use the Downside Deviation method. The optimal portfolio with this method uses downside deviation and sets the return below the benchmark as a measure of risk. Every optimal portfolio certainly cannot be separated from risk. To measure risk, you can use the Value at Risk (VaR) and Expected Shortfall values. This study aims to form an optimal portfolio using the Downside Deviation method and continued by comparing the possible losses that occur from the formed portfolio using the VaR and Expected Shortfall values. The data used in this study is the daily closing price data of LQ-45 Index stocks in the banking sector in the period February-June 2023. From the stock data, data selection is carried out by selecting stocks that have a positive expected return and are normally distributed. Then, the optimal portfolio formation stage is continued using the Downside Deviation method and comparing the possible risks formed with the VaR and Expected Shortfall values. The results of this study show that the optimal portfolio with the Downside Deviation method consists of four stocks, namely with the stock codes BRIS.JK, BBRI.JK, BBNI.JK, and BBCA.JK. This study uses a case example by investing capital of Rp100,000,000 with a one-day time period and three levels of confidence, namely 90%, 95%, and 99%. Based on the comparison of the risk value of the portfolio formed using VaR and Expected Shortfall, it is shown that the possible risk with the Expected Shortfall method is greater than the VaR value. Therefore, Expected Shortfall is better in estimating the maximum risk.

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]

The main aim of this paper is to consider a new risk metric that permits taking into account the spatial interactions of data. The considered risk metric explores the spatial tail-expectation of the data. Indeed, it is obtained by combining the ideas of expected shortfall regression with an expectile risk model. A spatio-functional Nadaraya–Watson estimator of the studied metric risk is constructed. The main asymptotic results of this work are the establishment of almost complete convergence under a mixed spatial structure. The claimed asymptotic result is obtained under standard assumptions covering the double functionality of the model as well as the data. The impact of the spatial interaction of the data in the proposed risk metric is evaluated using simulated data. A real experiment was conducted to measure the feasibility of the Spatio-Functional Expectile Shortfall Regression (SFESR) in practice. [ABSTRACT FROM AUTHOR]

Increasing rearrangement is a rewarding instrument in financial risk management. In practice, risks must be managed from different perspectives. A common example is the portfolio risk, which often can be seen from at least two perspectives: market value and book value. Different perspectives with different distributions can be coupled by increasing rearrangement. One distribution is regarded as underlying, and the other distribution can be expressed as an increasing rearrangement of the underlying distribution. Then, the risk measure for the latter can be expressed in terms of the underlying distribution. Our first objective is to introduce increasing rearrangement for application in financial risk management and to apply increasing rearrangement to the class of distortion risk measures. We derive formulae to compute risk measures in terms of the underlying distribution. Afterwards, we apply our results to a series of special distortion risk measures, namely the value at risk, expected shortfall, range value at risk, conditional value at risk, and Wang's risk measure. Finally, we present the connection of increasing rearrangement with inverse transform sampling, Monte Carlo simulation, and cost-efficient strategies. Butterfly options serve as an illustrative example of the method. [ABSTRACT FROM AUTHOR]

This paper treats the problem of risk management through a new conditional expected shortfall function. The new risk metric is defined by the expectile as the shortfall threshold. A nonparametric estimator based on the Nadaraya–Watson approach is constructed. The asymptotic property of the constructed estimator is established using a functional time-series structure. We adopt some concentration inequalities to fit this complex structure and to precisely determine the convergence rate of the estimator. The easy implantation of the new risk metric is shown through real and simulated data. Specifically, we show the feasibility of the new model as a risk tool by examining its sensitivity to the fluctuation in financial time-series data. Finally, a comparative study between the new shortfall and the standard one is conducted using real data. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the Bahadur type representation of a nonparametric expected shortfall estimator for α -mixing financial losses. Based on the Bahadur type representation, we further establish the Berry–Esseen bound of the nonparametric expected shortfall estimator. It is shown that the optimal rate can achieve nearly O (n - 1 / 8) under some appropriate conditions. We also carry out some numerical simulations and a real data example to support our theoretical results based on finite samples. [ABSTRACT FROM AUTHOR]

In recent years, the semiparametric methods for the joint estimation and prediction of value at risk (VaR) and expected shortfall (ES) have triggered great interests and attention. Compared to existing literature which usually incorporates realized volatility (RV) into the dynamic semiparametric risk models, this paper considers three more robust proxies (medRV, BPV, and RK) of intraday volatility in the models to verify whether high‐frequency information can improve the joint prediction ability of risk measures. To strengthen the persuasion of conclusions, four international stock indices (S&P500, Nikkei225, GDAXI, and DJIA) are applied to these models to estimate and forecast VaR and ES at different probability levels (1%, 2.5%, 5%, and 10%). Then, the predicted VaR and ES are backtested by several methods individually, and the popular score function FZ0 and MCS test are used to compare the effects of jointly predicting risk measures. Our results confirm that these semiparametric models containing intraday information outperform the benchmark models for four stocks and various probability levels, and medRV is the best volatility measure in improving the effects of models. [ABSTRACT FROM AUTHOR]

This study introduces the dynamic Gerber model (DGC) and evaluates its performance in the prediction of Value at Risk (VaR) and Expected Shortfall (ES) compared to alternative parametric, non-parametric and semi-parametric methods for estimating the covariance matrix of returns. Based on ES backtests, the DGC method produces, overall, accurate ES forecasts. Furthermore, we use the Model Confidence Set procedure to identify the superior set of models (SSM). For all the portfolios and VaR/ES confidence levels we consider, the DGC is found to belong to the SSM. [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]

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.

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.

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]

This paper deals with the problem of financial risk management using a new expected shortfall regression. The latter is based on the expectile model for financial risk-threshold. Unlike the VaR model, the expectile threshold is constructed by an asymmetric least square loss function. We construct an estimator of this new model using the k-nearest neighbors (kNN) smoothing approach. The mathematical properties of the constructed estimator are stated through the establishment of the pointwise complete convergence. Additionally, we prove that the constructed estimator is uniformly consistent over the nearest neighbors (UCNN). Such asymptotic results constitute a good mathematical support of the proposed financial risk process. Thus, we examine the easy implantation of this process through an artificial and real data. Our empirical analysis confirms the superiority of the kNN-approach over the kernel method as well as the superiority of the expectile over the quantile in financial risk analysis. [ABSTRACT FROM AUTHOR]

Since 2016, the Basel Committee on Banking Supervision has regulated banks to switch from a Value-at-Risk (VaR) to an Expected Shortfall (ES) approach to measuring the market risk and calculating the capital requirement. In the transition from VaR to ES, the major challenge faced by financial institutions is the lack of simple but powerful tools for evaluating ES forecasts (i.e., backtesting ES). This article first shows that the unconditional backtest is inconsistent in evaluating the most popular Historical Simulation (HS) and Filtered Historical Simulation (FHS) E S models, with power even less than the nominal level in large samples. To overcome this problem, we propose a new class of conditional backtests for E S that are powerful against a large class of alternatives. We establish the asymptotic properties of the tests, and investigate their finite sample performance through some Monte Carlo simulations. An empirical application to stock indices data highlights the merits of our method. [ABSTRACT FROM AUTHOR]

Modern portfolio theory has provided for decades the main framework for optimizing portfolios. Because of its sensitivity to small changes in input parameters, especially expected returns, the mean–variance framework proposed by Markowitz in 1952 has, however, been challenged by new construction methods that are purely based on risk. Among risk‐based methods, the most popular ones are Minimum Variance, Maximum Diversification, and Risk Budgeting (especially Equal Risk Contribution) portfolios. Despite some drawbacks, Risk Budgeting is particularly attracting because of its versatility: based on Euler's homogeneous function theorem, it can indeed be used with a wide range of risk measures. This paper presents mathematical results regarding the existence and the uniqueness of Risk Budgeting portfolios for a very wide spectrum of risk measures and shows that, for many of them, computing the weights of Risk Budgeting portfolios only requires a standard stochastic algorithm. [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]

In this study, we use daily gold log-returns to analyse the quality of forecasting expected shortfalls (ES) using volatility and models based on the extreme value theory (EVT). ES forecasts were calculated for conditional APARCH models formed on the entire distribution of returns, as well as for EVT models. The results of ES forecasts for each model were verified using the backtesting procedure proposed by Acerbi and Szekely. The results show that EVT models provide more accurate one-day ahead ES forecasts compared to the other models. Moreover, the asymmetric theoretical distributions for innovations of EVT models allow the improvement of the accuracy of ES forecasting. [ABSTRACT FROM AUTHOR]

Claims with high severity and low probability constitute a high risk for the insurance market. One tool to deal with this kind of event is the Extreme Value Theory (EVT). The main goal of this article is to apply the EVT to Actuarial Science using a different estimator for parameters, allowing the calculation of pure reinsurance premiums and the choice for the retention limit for insurance companies. The execution was split into two parts: (i) comparing the estimators through simulations, and; (ii) using data from 5 SUSEP lines of business with different natures, intending to estimate some extreme value statistics. In simulation studies, the Pickands estimator was very promising, but the limited amount of data resulted in a great variance when applied to real cases. Lastly, we concluded that the EVT is a powerful tool for insurance, capturing the behavior of extreme clams amount better than traditional models. [ABSTRACT FROM AUTHOR]

Co-moments of asset returns play a major role in financial contagion during crises. We study the properties of a particular specification of the generalized bivariate normal distribution which allows for co-volatility and co-skewness. With this probability distribution, formulae for single-name and exchange options can be evaluated quickly since they are based on one-dimensional integrals. We provide a very precise approximation formula for spread option prices and derive the corresponding greeks. We perform a day-to-day re-estimation of the probability distribution on a dataset of WTI vs Brent spread options, showing the ability of this specification to capture the salient empirical features observed in the market. Finally, we show the impact of co-movements on portfolio risk management. [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]

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To support the bankability of PV projects, PV manufacturers have been offering one of the longest warranties in the world, typically in the range of 25–30 years. During the warranty period, PV manufacturers guarantee that the degradation of PV modules will not exceed 0.4–0.6% each year, or the buyer can at any time make a claim to the manufacturer for replacement or compensation for the shortfall. Due to its popularity, the performance warranty terms have become more and more competitive each year. However, long-term PV operating data have been very limited and bankruptcy of PV manufacturers has been quite common. Without a proper methodology to assess the adequacy of PV manufacturer's warranty fund (WF) reserve, the 25-year performance warranty can become empty promises. To ensure sustainable development of the PV industry, this study develops a probability-weighted expected value method to determine the necessary WF reserve based on benchmark field degradation data and prevailing degradation cap of 0.55% per year. The simulation result shows that, unless the manufacturer's degradation pattern is significantly better than the benchmark degradation profile, 1.302% of the sales value is required for the WF reserve. To the best of our knowledge, this is the first study that provides WF reserve requirement estimation for 25-year PV performance warranty. The result will provide transparency for PV investors and motivation for PV manufacturers for continuous quality improvement as all such achievement can now be reflected in manufacturers' annual report result. [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]

PT Aneka Tambang Tbk (ANTAM) received an award as the most sought-after stock issuer in Indonesia in 2016. That stock continued to attract investors in 2022 due to a 105% increase in net profit and a 19% increase in sales from the previous year. Despite the upward trend, investors still had doubts due to the fluctuating movement of ANTAM's stock prices. Therefore, forecasting was needed to determine the future movement of stock prices. The Backpropagation Neural Network method had good capabilities for fluctuating data types. However, this method has the disadvantage of a lengthy iteration process. To handle this limitation, The Nguyen-Widrow weighted setting was applied to address this constraint. The expected Shortfall (ES) method used the forecasting results to measure investment risk. This research uses ANTAM stock closing price data from May 2, 2018, to May 31, 2023. Based on the analysis results, the best architecture was obtained with a configuration of 5-11-1, using Nguyen-Widrow weight initialization and a combination of a learning rate of 0.5 and momentum of 0.9. This architecture yielded a prediction error based on the Mean Absolute Percentage Error (MAPE) of 1.9947%. Risk measurement with the ES method based on the prediction for the next 60 periods showed that at a 95% confidence level, the risk value was 0.002181; at a 90% confidence level, it was 0.002165; at an 85% confidence level, it was 0.002148, and at an 80% confidence level, it was 0.002132.

There has been much work on the distribution of independent or dependent random variables. But we are not aware of any work giving exact results for the distribution of the sum of randomly weighted random variables. In this paper, we derive exact results for the randomly weighted sum of two dependent random variables. The derived expressions are for the cumulative distribution function, conditional expectation, moment generating function, value at risk, expected shortfall and the limiting tail behavior of the randomly weighted sum of two dependent random variables. Two numerical illustrations are given. [ABSTRACT FROM AUTHOR]

Guided by the extreme value theory, this study empirically investigates the impact of tail risk measures on financial distress of publicly traded bank holding companies (BHCs) in the United States. Our results show that tail risk measures namely, value‐at‐risk and expected shortfall, are significantly and positively related to banks distress risk. Implying that BHCs with more frequent extreme negative daily equity returns induce higher tail risks, thereby increasing their likelihood of experiencing financial distress. Our results also show that tail risk measures enhance the explanatory power of traditional models explaining banks distress risk based on accounting information. These results indicate that market discipline is generally beneficial in managing and regulating banks, bolstering claims of the importance of macro‐prudential supervision of financial institutions. [ABSTRACT FROM AUTHOR]

This paper aims at the role of accounting for time‐varying higher moments in conditional volatility models in emerging markets. In particular, we perform a comprehensive analysis of out‐of‐sample value at risk (VaR) and expected shortfall (ES) forecasts of eight generalized autoregressive conditional heteroskedasticity (GARCH) models with alternative distributions for 10 leading emerging markets. To evaluate the forecast accuracy, we employ a battery of absolute performance backtests and two alternative loss functions in the relative performance exercises. We find that the asymmetric GARCH models with time‐varying skewness and kurtosis significantly outperform traditional GARCH‐based forecasts across quantiles across quantile levels. In particular, we explore that the superior performance of the GARCH models with improved distributions is mainly driven by their performance during crisis periods, where the traditional GARCH specifications often underestimate the tail risk in the markets. [ABSTRACT FROM AUTHOR]

This paper introduces a non-Gaussian dynamic currency hedging strategy for globally diversified investors with ambiguity. It provides theoretical and empirical evidence that, under the stylized fact of non-Gaussianity of financial returns and for a given optimal portfolio, the investor-specific ambiguity can be estimated from historical asset returns without the need for additional exogenous information. Acknowledging non-Gaussianity, we compute an optimal ambiguity-adjusted mean-variance (dynamic) currency allocation. Next, we propose an extended filtered historical simulation that combines Monte Carlo simulation based on volatility clustering patterns with the semi-parametric non-normal return distribution from historical data. This simulation allows us to incorporate investor's ambiguity into a dynamic currency hedging strategy algorithm that can numerically optimize an arbitrary risk measure, such as the expected shortfall. The out-of-sample backtest demonstrates that, for globally diversified investors, the derived non-Gaussian dynamic currency hedging strategy is stable, robust, and highly risk reductive. It outperforms the benchmarks of constant hedging as well as static/dynamic hedging approaches with Gaussianity in terms of lower maximum drawdown and higher Sharpe and Sortino ratios, net of transaction costs. [ABSTRACT FROM AUTHOR]