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The potential advantage of extreme value theory in modeling management phenomena is the central theme of this paper. The statistics of extremes have played only a very limited role in management studies despite the disproportionate emphasis on unusual events in the world of managers. An overview of this theory and related statistical models is presented, and illustrative empirical examples provided.

This study examines problems that may occur when conventional Value‐at‐Risk (VaR) estimators are used to quantify market risks in an agricultural context. For example, standard VaR methods, such as the variance‐covariance method or historical simulation, can fail when the return distribution is fat tailed. This problem is aggravated when long‐term VaR forecasts are desired. Extreme Value Theory (EVT) is proposed to overcome these problems. The application of EVT is illustrated by an example from the German hog market. Multi‐period VaR forecasts derived by EVT are found to deviate considerably from standard forecasts. We conclude that EVT is a useful complement to traditional VaR methods.

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 purpose of this paper is to investigate and compare the extreme behavior of securitized real estate and stock market returns as well as their value‐at‐risk (VaR) dynamics in international investing. Extreme value theory using the block maxima method is applied to ten securitized real estate and equity market indices representing Asian, European and North American markets.

The paper models the maxima and minima of all return series within the extreme value theory (EVT) framework and derive the VaR estimates. It then compares the VaR estimates derived from the EVT and the normal distribution and investigates the impact of clustered returns on the VaR estimates. Finally, both the conventional standard deviation measure and VaR method are conducted to evaluate and compare the impact of the Asian financial turmoil on the real estate and stock market risk profiles.

Evidence shows that Asian real estate and equity maxima and minima return series are characterized by a fat‐tailed Fréchet distribution. The frequency and severity of extreme Asian real estate returns are greater than their European and North American counterparts. Securitized real estate markets are riskier than the broader stock markets before and during the Asian financial turmoil. In contrast, many stock markets become riskier after the financial crisis with their VaRs higher than the equivalent VaR estimates for the real estate series.

Knowledge about real estate market returns exhibit extreme behavior can help investors and fund managers understand the distribution of real estate market returns better and obtain potentially more accurate real estate return forecasts.

International real estate portfolio risk management should include both extreme risks and standard deviations. Accordingly, global investors should be even more cautious in formulating their diversification strategies since gains from diversification can be reduced significantly by the severity of extreme return levels.

The paper characterizes the distribution of extreme returns for a broad spectrum of international securitized real estate markets from three continents. The extreme value investigation is also conducted for broader stock markets corresponding to the individual real estate markets. The July 1997 turmoil that occurred in Asian financial markets provides interesting exploratory opportunities within which this paper estimates and compares the extreme market risk with the conventional standard deviation measure.

This article investigates the effect of modeling extreme events on the calculation of minimum capital risk requirements for three LIFFE futures contracts. The use of internal models will be permitted under the European Community Capital Adequacy Directive II and will be widely adopted in the near future for determining capital adequacies. Close scrutiny of competing models is required to avoid a potentially costly misallocation of capital resources, to ensure the safety of the financial system. The authors propose a semi‐parametric approach, for which extreme risks are modeled using a generalized Pareto distribution, and smaller risks are characterized by the empirically observed distribution function. The primary finding of comparing the capital requirements based on this approach with those calculated from both the unconditional density and from a conditional density (a GARCH(1,1) model), is that for both in‐sample and out‐of‐sample tests, the extreme value approach yields superior results. This is attributable to the fact that the other two models do not explicitly model the tails of the return distribution.

Modern property investment allocation techniques are typically based on recognised measures of return and risk. Whilst these models work well in theory under stable conditions, they can fail when stable assumptions cease to hold and extreme volatility occurs. This is evident in commercial property markets which can experience extended stable periods followed by large concentrated negative price fluctuations as a result of major unpredictable events. This extreme volatility may not be fully reflected in traditional risk calculations and can lead to ruin. The paper aims to discuss these issues.

This research studies 28 years of quarterly Australian direct commercial property market performance data for normal distribution features and signs of extreme downside risk. For the extreme values, Power Law distribution models were examined as to provide a better probability measure of large negative price fluctuations.

The results show that the normal bell curve distribution underestimated actual extreme values both by frequency and extent, being by at least 30 per cent for the outermost data point. For the statistical outliers beyond 2 SD, a Power Law distribution can overcome many of the shortcomings of the standard deviation approach and therefore better measure the probability of ruin, being extreme downside risk.

In highlighting the challenges to measuring property market performance, analysis of extreme downside risk should be separated from traditional standard deviation risk calculations. In recognising these two different types of risk, extreme downside risk has a magnified domino effect with the tendency of bad news to come in crowds. Big price changes can lead to market crashes and financial ruin which is well beyond the standard deviation risk measure. This needs to be recognised and developed as there is evidence that extreme downside risk determinants are increasing by magnitude, frequency and impact.

Analysis of extreme downside risk should form a key part of the property decision process and be included in the property investment manager’s toolkit. Modelling techniques for estimating measures of tail risk provide challenges and have shown to be beyond traditional risk management practices, being too narrow and constraining a definition. Measuring extreme risk and the likelihood of ruin is the first step in analysing and dealing with risk in both an asset class and portfolio context.

From a regulatory point of view, as explained by Dimson and Marsh [1994, 1995], the amount of capital required by a financial institution to ensure an acceptably small probability of failure should depend on the risk associated with the assets detained in its portfolio. Dimson and Marsh [1994] conduct an empirical study on long and short equity trading books of securities firms acting as market makers. They consider different existing regulations: the comprehensive approach, as applied in the United States by the Securities and Exchange Commission; the building‐block approach, as proposed by the Basle Committee on Banking Supervision, and incorporated in the European Community [1992] Capital Adequacy Directive (CAD); and the portfolio approach, which in the U.K. forms part of the rules of the Securities and Futures Authority [1992]. All three methods are compared via the position risk requirement (PRR) that determines the amount of capital that financial institutions have to put aside. As shown by the authors in their empirical study, the methods proposed by the international regulators are barely related to the risk of the portfolios! Only for the national U.K. rules, the PRR and the risk of a portfolio show positive correlation.

Extreme value model is one of the most important models that are applicable in air pollution data. This paper aims at introducing a new model of extreme value that is more suitable in environmental studies.

The parameters of the new model have been estimated by method of maximum likelihood. In order to relate to air pollution impacts, the new extreme value model was used, applied to carbon monoxide (CO) in parts per million (ppm) at several places in Malaysia. The objective of this analysis is to fit the extreme values with a new model and to examine its performance. Comparison of the new model with others is shown to illustrate the applicability of this new model.

The results show that the new model is the best fit using the method of maximum likelihood. The new model gives a significant impact of CO data, which gives the smallest standard error and p‐values. The new extreme value model is able to identify significantly problems of air pollution. The results presented by the new extreme value model can be used as an air quality management tool by providing the decision makers means to determine the required reduction of source.

The new extreme value model has mostly been applied in environmental studies for the statistical treatment of air pollution. The results of the numerical and simulated CO data indicate that the new model both is easy to use and can achieve even higher accuracy compared with other models.

The purpose of this paper is to give a review of the standard approaches to extreme value theory. Special focus on the tail of the distribution is underlined, in particular concerning the fat‐tails phenomenon typical of financial returns. The core of the work is then represented by a survey of models which try to overtake some problems in determining the right shaping of extreme financial returns distribution.

The paper attempts to give a broad view of the theory about the Tail of distribution of financial market returns, with a special focus on bond returns. The aim of the core work is to find and explore via data, the best solution in order to give a right estimate of the higher moments of the distribution and of the Tail index associated with particular tail shape.

The EVT approach to VaR has certain advantages over traditional parametric and non‐parametric approaches to VaR. Parametric approaches estimate VaR by fitting some distribution to a set of observed returns while non‐parametric estimate VaR by reading off the VaR from an appropriate histogram of returns. Results show how EVT allows to overtake the problems of underestimation of risk typical of standard VaR measures. In particular the paper compares with historical simulation. The difference is quite evident showing a consistent improvement of the risk measurement performance.

It is necessary to underline how the result in the paper relies on very specific assumptions and dataset feature. Back to drawbacks of EVT, it is very important then to remind how the dataset is usually and necessarily limited to sporadic extreme events. Moreover, there is no mathematical safety of claiming robust result in the absence of normality.

Research on price extremes and overreactions as potential violations of market efficiency has a long tradition in investment literature. Arguably, very few studies to date have addressed this issue in cryptocurrencies trading. The purpose of this paper is to consider the extreme value modelling for forecasting COVID-19 effects on cryptocoin markets. Additionally, this paper examines the importance of technical trading indicators in predicting the extreme price behaviour of cryptocurrencies.

This paper decomposes the daily-time series returns of four cryptocurrency returns into potential maximum gains (PMGs) and potential maximum losses (PMLs) at first and then tests their lead–lag relations under an econometric framework. This paper also investigates the non-random properties of cryptocoins by computing the incremental explanatory power of PML–PMG modelling with technical trading indicators controlled. Besides, this paper executes an event study to identify significant changes caused by COVID-19-related events, which is capable of analysing the cryptocoin market overreactions.

The findings of this paper produce the evidence of both market overreactions and trend persistence in the potential gains and losses from coins trading. Extreme price behaviour explains volatility and price trends in crypto markets before and after the outbreak of a pandemic that substantiate the non-random walk behaviour of crypto returns. The presence of technical trading indicators as control variables in the extreme value regressions significantly improves the predictive power of models. COVID-19 crisis affects the market efficiency of cryptocurrencies that improves the usefulness of extreme value predictions with technical analysis.

This paper strongly supports for the robustness of technical trading strategies in cryptocurrency markets. However, the “beast is moving quick” and uncertainty as to the new normalcy about the post-COVID-19 world puts constraint on making best predictions.

The paper contributes substantially to our understanding of the pricing efficiency of cryptocurrency markets after the COVID-19 outbreak. The findings of continuing return predictability and price volatility during COVID-19 show that profitable investment opportunities for cryptocoin traders are prevailing in pandemic times.

The paper is unique to understand extreme return reversals behaviour of cryptocurrency markets regarding events related to COVID-19 breakout.