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In this paper, the gamma test is used to determine the order of lag-k tail dependence existing in financial time series. Using standardized return series, statistical evidences based on the test results show that jumps in returns are not transient. New time series models which combine a specific class of max-stable processes, Markov processes, and GARCH processes are proposed and used to model tail dependencies within asset returns. Estimators for parameters in the models are developed and proved to be consistent and asymptotically joint normal. These new models are tested on simulation examples and some real data, the S&P 500.

Fat‐tailed distributions have been found in many financial and economic variables ranging from forecasting returns on financial assets to modeling recovery distributions in bankruptcies. They have also been found in numerous insurance applications such as catastrophic insurance claims and in value‐at‐risk measures employed by risk managers. Financial applications include:

The purpose of the paper is to back-test value-at-risk (VaR) models for conditional distributions belonging to a Generalized Hyperbolic (GH) family of Lévy processes – Variance Gamma, Normal Inverse Gaussian, Hyperbolic distribution and GH – and compare their risk-management features with a traditional unconditional extreme value (EV) approach using data from future contracts return data of S&P500, FTSE100, DAX, HangSeng and Nikkei 225 indices.

The authors apply tail-based and Lévy-based calibration to estimate the parameters of the models as part of the initial data analysis. While the authors utilize the peaks-over-threshold approach for generalized Pareto distribution, the conditional maximum likelihood method is followed in case of Lévy models. As the Lévy models do not have closed form expressions for VaR, the authors follow a bootstrap method to determine the VaR and the confidence intervals. Finally, for back-testing, they use both static calibration (on the entire data) and dynamic calibration (on a four-year rolling window) to test the unconditional, independence and conditional coverage hypotheses implemented with 95 and 99 per cent VaRs.

Both EV and Lévy models provide the authors with a conservative proportion of violation for VaR forecasts. A model targeting tail or fitting the entire distribution has little effect on either VaR calculation or a VaR model’s back-testing performance.

To the best of the authors’ knowledge, this is the first study to explore the back-testing performance of Lévy-based VaR models. The authors conduct various calibration and bootstrap techniques to test the unconditional, independence and conditional coverage hypotheses for the VaRs.

Application of financial risk models in the emerging markets poses special challenges. A fundamental challenge is to accurately model the return distributions which are particularly fat tailed and skewed. Value-at-Risk (VaR) measures based on the Extreme Value Theory (EVT) have been suggested, but typically data histories are limited, making it hard to test and apply EVT. The chapter addresses issues in (i) modeling the VaR measure in the presence of structural breaks in an economy, (ii) the choice of stable innovation distribution with volatility clustering effects, (iii) modeling the tails of the empirical distribution, and (iv) fixing the cut-off point for isolating extreme observations. Pakistan offers an instructive case since its equity market exhibits high volatility and incidence of extreme returns. The recent Global Financial Crisis has been another source of extreme returns. The confluence of the two sources of volatility provides us with a rich data set to test the VaR/EVT model rigorously and examine practical challenges in its application in an emerging market.

The last few years in the financial markets have shown great instability and high volatility. In order to capture the amount of risk a financial firm takes on in a single trading day, risk managers use a technology known as value‐at‐risk (VaR). There are many methodologies available to calculate VaR, and each has its limitations. Many past methods have included a normality assumption, which can often produce misleading figures as most financial returns are characterized by skewness (asymmetry) and leptokurtosis (fat‐tails). The purpose of this paper is to provide an overview of VaR and describe some of the most recent computational approaches.

This paper compares the Student‐t, autoregressive conditional heteroskedastic (ARCH) family of models, and extreme value theory (EVT) as a means of capturing the fat‐tailed nature of a returns distribution.

Recent research has utilized the third and fourth moments to estimate the shape index parameter of the tail. Other approaches, such as extreme value theory, focus on the extreme values to calculate the tail ends of a distribution. By highlighting benefits and limitations of the Student‐t, autoregressive conditional heteroskedastic (ARCH) family of models, and the extreme value theory, one can see that there is no one particular model that is best for computing VaR (although all of the models have proven to capture the fat‐tailed nature better than a normal distribution).

This paper details the basic advantages, disadvantages, and mathematics of current parametric methodologies used to assess value‐at‐risk (VaR), since accurate VaR measures reduce a firm's capital requirement and reassure creditors and investors of the firm's risk level.

The COVID-19 situation affected the whole landscape of retailing in India and around the world. However, some businesses have used the pandemic-related difficulties into opportunities. E-tailing is one of the ways that helped people in India to continue shopping their essential products and choosing their luxury products without making any physical visits during the lockdown. This research understands the current situation through an observation study and suggests the e-tailing model suitable during the COVID-19 and beyond.

We used secondary data to make the observational study. We also conducted two case studies and interviews with grocery shops and an automotive company.

This research suggests a simple collaborative e-tailing model combining all supply chain players to reduce people’s movement, timely delivery and enhanced service to meet customers demand during the lockdown period.

This paper has considered two real cases for discussion and also obtained information from public domain. The proposed model has been discussed with the case companies, and it hoped to support business planning for online services.

This paper aims to evaluate the accuracy of a quantile estimate. Especially when estimating high quantiles from a few data, the quantile estimator itself is a random number with its own distribution. This distribution is first determined and then it is shown how the accuracy of the quantile estimation can be assessed in practice.

The paper considers the situation that the parent distribution of the data is unknown, the tail is modeled with the generalized pareto distribution and the quantile is finally estimated using the fitted tail model. Based on well-known theoretical preliminary studies, the finite sample distribution of the quantile estimator is determined and the accuracy of the estimator is quantified.

In general, the algebraic representation of the finite sample distribution of the quantile estimator was found. With the distribution, all statistical quantities can be determined. In particular, the expected value, the variance and the bias of the quantile estimator are calculated to evaluate the accuracy of the estimation process. Scaling laws could be derived and it turns out that with a fat tail and few data, the bias and the variance increase massively.

Currently, the research is limited to the form of the tail, which is interesting for the financial sector. Future research might consider problems where the tail has a finite support or the tail is over-fat.

The ability to calculate error bands and the bias for the quantile estimator is equally important for financial institutions, as well as regulators and auditors.

Understanding the quantile estimator as a random variable and analyzing and evaluating it based on its distribution gives researchers, regulators, auditors and practitioners new opportunities to assess risk.

The paper aims to investigate the relative performance of the most popular value‐at‐risk (VaR) estimates with an emphasis on the extreme value theory (EVT) methodology for seven Middle East and North Africa (MENA) countries.

The paper calculates tails distributions of return series by EVT. This allows computing VaR and comparing the results with Variance‐Covariance method, Historical simulation, and ARCH‐type process with normal distribution, Student‐t distribution and skewed Student‐t distribution. The paper assesses the performance of the models, which are used in VaR estimations, based on their empirical failure rates.

The empirical results demonstrate that the return distributions of the MENA markets are characterized by fat tails which implies that VaR measures relies on the normal distribution will underestimate VaR. The results suggest that the extreme value approach, by modeling the tails of the return distributions, are more relevant to measure VaR in most of the MENA.

The results show that the use of conventional methodologies such as the normal distribution model to estimate the financial market risk in MENA countries may lead to faulty estimation of risk in the world of volatile markets.

The paper tried to fill the gap in the literature and perform an evaluation of the relative performance of the most popular VaR estimates with an emphasis on the EVT methodology in seven MENA emerging stock markets. A comparison of the performance between EVT and other VaR techniques should support the decision whether more or less sophisticated methods are appropriate in order to assess stock market risks in the MENA countries.

This paper aims to test empirically the performance of different models in measuring VaR and ES in the presence of heavy tails in returns using historical data.

Daily returns of popular indices (S&P500, DAX, CAC, Nikkei, TSE, and FTSE) and currencies (US dollar vs Euro, Yen, Pound, and Canadian dollar) for over ten years are modeled with empirical (or historical), Gaussian, Generalized Pareto (peak over threshold (POT) technique of extreme value theory (EVT)) and Stable Paretian distribution (both symmetric and non‐symmetric). Experimentation on different factors that affect modeling, e.g. rolling window size and confidence level, has been conducted.

In estimating VaR, the results show that models that capture rare events can predict risk more accurately than non‐fat‐tailed models. For ES estimation, the historical model (as expected) and POT method are proved to give more accurate estimations. Gaussian model underestimates ES, while Stable Paretian framework overestimates ES.

Research findings are useful to investors and the way they perceive market risk, risk managers and the way they measure risk and calibrate their models, e.g. shortcomings of VaR, and regulators in central banks.

A comparative, thorough empirical study on a number of financial time series (currencies, indices) that aims to reveal the pros and cons of Gaussian versus fat‐tailed models and Stable Paretian versus EVT, in estimating two popular risk measures (VaR and ES), in the presence of extreme events. The effects of model assumptions on different parameters have also been studied in the paper.

The purpose of this paper is to investigate how the selection of return distribution impacts estimated volatility in China’s stock market.

The authors use a Bayesian analysis of fat-tailed stochastic volatility (SV) model with Student’s t-distribution, and conduct an out-of-sample test with realized volatility.

Empirical analysis results indicate that fat-tailed SV model performs better in capturing the dynamics of daily returns. The authors find that asymmetry, holiday and day of the week effects are detected in estimated volatility. However, the out-of-sample comparison shows that fat-tailed SV models fail to outperform SV models with normal distribution in fitting and predicting realized volatility.

The contribution of this paper to existing literature is twofold. First, it proves that fat-tailed SV models with Student’s t-distribution perform better than normally distributed SV models in fitting daily returns of China’s stock market. Second, this paper takes asymmetry, holiday and day of the week effects into consideration at the same time in the fat-tailed SV model.