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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.

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.

Previous research suggests that monthly commodity futures returns are like equity returns and recommend long-only portfolio positions. A follow-up question is whether the distributions of daily returns on commodity futures are fat-tailed, just like equity returns. This question has important implication for commodity futures traders because futures trade positions are marked to the market daily. The Extreme Value Theory (EVT) is used to test whether the distributions of the commodity futures returns are fat-tailed with finite variance. The results suggest that not all commodity futures returns have a fat-tail distribution and the tails of the distributions of commodity futures returns generally are smaller than the tails of the distribution of equity returns.

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.

In this article we design an econometric test for monotone comparative statics (MCS) often found in models with multiple equilibria. Our test exploits the observable implications of the MCS prediction: that the extreme (high and low) conditiona l quantiles of the dependent variable increase monotonically with the explanatory variable. The main contribution of the article is to derive a likelihood-ratio test, which to the best of our knowledge is the first econometric test of MCS proposed in the literature. The test is an asymptotic “chi-bar squared” test for order restrictions on intermediate conditional quantiles. The key features of our approach are: (1) we do not need to estimate the underlying nonparametric model relating the dependent and explanatory variables to the latent disturbances; (2) we make few assumptions on the cardinality, location, or probabilities over equilibria. In particular, one can implement our test without assuming an equilibrium selection rule.

Heavy-tailed distributions present a tough setting for inference. They are also common in industrial applications, particularly with internet transaction datasets, and machine learners often analyze such data without considering the biases and risks associated with the misuse of standard tools. This chapter outlines a procedure for inference about the mean of a (possibly conditional) heavy-tailed distribution that combines nonparametric analysis for the bulk of the support with Bayesian parametric modeling – motivated from extreme value theory – for the heavy tail. The procedure is fast and massively scalable. The work should find application in settings wherever correct inference is important and reward tails are heavy; we illustrate the framework in causal inference for A/B experiments involving hundreds of millions of users of eBay.com.

In this paper, we search to evaluate the systemic risk of the Moroccan banking sector. Indeed, we concentrate on the analysis and the evaluation on transverse dimension of the systemic. From this point of view, two approaches were used. First is based on the estimate on value at risk conditional allowing to measure the systemic importance of each banking institution. In addition, the second approach uses the heteroscedasticity models in order to consider the conditional correlations, making it possible, to measure the dependence between the Moroccan banks and with the whole of the financial system. The results obtained with through these two approaches confirm that ATW, BMCI and the BMCE are the most systemic banks in Moroccan banking system and who can initiate a systemic crisis. On another register and by using the conditional correlations of each bank we built an index of systemic risk. Moreover, a macrofinancial model was developed, connecting the index of the systemic risk and the principal macroeconomic variables. This model affirmed that the contagion dimension of systemic risk is procyclical.

The variance targeting estimator (VTE) for generalized autoregressive conditionally heteroskedastic (GARCH) processes has been proposed as a computationally simpler and misspecification-robust alternative to the quasi-maximum likelihood estimator (QMLE). In this paper we investigate the asymptotic behavior of the VTE when the stationary distribution of the GARCH process has infinite fourth moment. Existing studies of historical asset returns indicate that this may be a case of empirical relevance. Under suitable technical conditions, we establish a stable limit theory for the VTE, with the rate of convergence determined by the tails of the stationary distribution. This rate is slower than that achieved by the QMLE. The limit distribution of the VTE is nondegenerate but singular. We investigate the use of subsampling techniques for inference, but find that finite sample performance is poor in empirically relevant scenarios.