Extreme Value Theory Approach Research Articles

Modelling Kenyan Foreign Exchange Risk Using Asymmetry Garch Models and Extreme Value Theory Approaches

The Foreign Exchange Market in developing countries, Kenya being one of them is a key driving force for the development of a country economic growth. In the last decade, world financial markets have been characterized by significant instabilities and the currency exchange rate market is not an exception. As a consequence of the significant instabilities in the financial markets, this paper models the tail risk associated with the Kenya Shilling against the leading currencies, especially the one day ahead Value-at-Risk forecast in risk control, by using the two leading alternatives, the two-stage GARCH-EVT approach and the asymmetry GARCH models. In practice by applying the conditional Extreme Value Theory, the tail behaviour of the daily returns is modelled and thus the VaR while by using the asymmetry GARCH models, one models the whole distribution of the returns and thereafter estimates the Value at Risk. In addition to modelling the value at risk, we further examine the performance of the two leading alternatives with the daily log returns of leading currencies in the Kenyan Foreign Exchange market (US dollar, Sterling Pound and Euro) foreign currencies from the period January 2005 – August 2017 for trading days excluding weekends and holidays. The backtesting result indicate that the conditional Extreme Value Theory does not completely dominate the asymmetry GARCH models in estimating the VaR especially in the Sterling Pound and Euro Exchange Rates.

Modeling operational risk depending on covariates: an empirical investigation

The importance of operational risk management in financial and commodity markets has increased significantly over the last few decades. This paper demonstrates the application of a nonhomogeneous Poisson model and dynamic extreme value theory (EVT) incorporating covariates on estimating frequency, severity and risk measures for operational risk. Compared with a classical EVT approach, the dynamic EVT gives a better performance with respect to the statistical fit and realism. It is also flexible enough to handle different types of empirical data. In our model, we include firm-specific covariates associated with internal control weaknesses (ICWs) and show empirically that firms with higher incidences of selected ICWs have higher time-varying severities for operational risk. Our methodology provides risk managers and regulators with a tool that uncovers the nonobvious patterns hidden in operational risk data.

An Application of Extreme Value Theory to Learning Analytics: Predicting Collaboration Outcome from Eye-tracking Data

The statistics used in education research are based on central trends such as the mean or standard deviation, discarding outliers. This paper adopts another viewpoint that has emerged in Statistics, called the Extreme Value Theory (EVT). EVT claims that the bulk of the normal distribution is mostly comprised of uninteresting variations while the most extreme values convey more information. We applied EVT to eye-tracking data collected during online collaborative problem solving with the aim of predicting the quality of collaboration. We compare our previous approach, based on central trends, with an EVT approach focused on extreme episodes of collaboration. The latter occurred to provide a better prediction of the quality of collaboration.

Estimating and forecasting portfolio’s Value-at-Risk with wavelet-based extreme value theory: Evidence from crude oil prices and US exchange rates

This article proposes a wavelet-based extreme value theory (W-EVT) approach to estimate and forecast portfolio’s Value-at-Risk (VaR) given the stylized facts and complex structure of financial data. Our empirical application to portfolios of crude oil prices and US dollar exchange rates shows that the W-EVT models provide an effective and powerful tool for gauging extreme moments and improving the accuracy of portfolio’s VaR estimates and forecasts after noise is removed from the original data.

Improved VaR forecasts using extreme value theory with the Realized GARCH model

PurposeThis study aims to forecast daily value-at-risk (VaR) for international stock indices by using the conditional extreme value theory (EVT) with the Realized GARCH (RGARCH) model. The predictive ability of this Realized GARCH-EVT (RG-EVT) model is compared with those of the standalone GARCH models and the conditional EVT specifications with standard GARCH models.Design/methodology/approachThe authors use daily data on returns and realized volatilities for 13 international stock indices for the period from 1 January 2003 to 8 October 2014. One-step-ahead VaR forecasts are generated using six forecasting models: GARCH, EGARCH, RGARCH, GARCH-EVT, EGARCH-EVT and RG-EVT. The EVT models are implemented using the two-stage conditional EVT framework of McNeil and Frey (2000). The forecasting performance is evaluated using multiple statistical tests to ensure the robustness of the results.FindingsThe authors find that regardless of the choice of the GARCH model, the two-stage conditional EVT approach provides significantly better out-of-sample performance than the standalone GARCH model. The standalone RGARCH model does not perform better than the GARCH and EGARCH models. However, using the RGARCH model in the first stage of the conditional EVT approach leads to a significant improvement in the VaR forecasting performance. Overall, among the six forecasting models, the RG-EVT model provides the best forecasts of daily VaR.Originality/valueTo the best of the authors’ knowledge, this is the earliest implementation of the RGARCH model within the conditional EVT framework. Additionally, the authors use a data set with a reasonably long sample period (around 11 years) in the context of high-frequency data-based forecasting studies. More significantly, the data set has a cross-sectional dimension that is rarely considered in the existing VaR forecasting literature. Therefore, the findings are likely to be widely applicable and are robust to the data snooping bias.

PRUDENT DECISIONS TO ESTIMATE THE RISK OF LOSS IN INSURANCE

The directive 2009/138/EC „Solvency II”, provides the determination of insurance capital requirements based either on a standard formula or an internal model built by the company and approved by the regulatory authority. The build of an internal model involves the determination of an extreme quantile from the empirical distribution of portfolio. An estimate of this quantile, with a 99.5% confidence level, requires a large number of simulations, each taking into account different scenarios as: insufficient reserves, unfavourable developments of financial assets, etc. The present paper proposes to argue the necessity of the extreme value theory approach in order to estimate the risk of loss for the insurance issue, in accordance with European Directive „Solvency II”, from the perspective of making prudent decisions for the assessment of insurance capital requirements.

Exchangeability, extreme returns and Value-at-Risk forecasts

In this paper, we propose a new approach to extreme value modelling for the forecasting of Value-at-Risk (VaR). In particular, the block maxima and the peaks-over-threshold methods are generalised to exchangeable random sequences. This caters for the dependencies, such as serial autocorrelation, of financial returns observed empirically. In addition, this approach allows for parameter variations within each VaR estimation window. Empirical prior distributions of the extreme value parameters are attained by using resampling procedures. We compare the results of our VaR forecasts to that of the unconditional extreme value theory (EVT) approach and the conditional GARCH-EVT model for robust conclusions.

A limit distribution of credit portfolio losses with low default probabilities

This paper employs a multivariate extreme value theory (EVT) approach to study the limit distribution of the loss of a general credit portfolio with low default probabilities. A latent variable model is employed to quantify the credit portfolio loss, where both heavy tails and tail dependence of the latent variables are realized via a multivariate regular variation (MRV) structure. An approximation formula to implement our main result numerically is obtained. Intensive simulation experiments are conducted, showing that this approximation formula is accurate for relatively small default probabilities, and that our approach is superior to a copula-based approach in reducing model risk.

Packet Error Rate Analysis of Uncoded Schemes in Block-Fading Channels Using Extreme Value Theory

We present a generic approximation of the packet error rate (PER) function of uncoded schemes in the AWGN channel using extreme value theory (EVT). The PER function can assume both the exponential and the Gaussian Q-function bit error rate (BER) forms. The EVT approach leads us to a best closed-form approximation, in terms of accuracy and computational efficiency, of the average PER in block-fading channels. The numerical analysis shows that the approximation holds tight for any value of SNR and packet length whereas the earlier studies approximate the average PER only at asymptotic SNRs and packet lengths.

Mortality and morbidity peaks modeling: An extreme value theory approach.

Hospitalizations and deaths belong to the most studied health variables in public health. Those variables are usually analyzed through mean events and trends, based on the whole dataset. However, this approach is not appropriate to comprehend health outcome peaks which are unusual events that strongly impact the health care network (e.g. overflow in hospital emergency rooms). Peaks can also be of interest in etiological research, for instance when analyzing relationships with extreme exposures (meteorological conditions, air pollution, social stress, etc.). Therefore, this paper aims at modeling health variables exclusively through the peaks, which is rarely done except over short periods. Establishing a rigorous and general methodology to identify peaks is another goal of this study. To this end, the extreme value theory appears adequate with statistical tools for selecting and modeling peaks. Selection and analysis for deaths and hospitalizations peaks using extreme value theory have not been applied in public health yet. Therefore, this study also has an exploratory goal. A declustering procedure is applied to the raw data in order to meet extreme value theory requirements. The application is done on hospitalization and death peaks for cardiovascular diseases, in the Montreal and Quebec metropolitan communities (Canada) for the period 1981-2011. The peak return levels are obtained from the modeling and can be useful in hospital management or planning future capacity needs for health care facilities, for example. This paper focuses on one class of diseases in two cities, but the methodology can be applied to any other health peaks series anywhere, as it is data driven.

An Application of Extreme Values Theory to Learning Analytics: Predicting Collaboration Quality from Eye-Tracking Data

The statistics used in education research are based on central trends such as the mean or standard deviation, discarding outliers. This paper adopts another viewpoint that has emerged in Statistics, called the Extreme Value Theory (EVT). EVT claims that the bulk of the normal distribution is mostly comprised of uninteresting variations while the most extreme values convey more information. We applied EVT to eye-tracking data collected during online collaborative problem solving with the aim of predicting the quality of collaboration. We compare our previous approach, based on central trends, with an EVT approach focused on extreme episodes of collaboration. The latter occurred to provide a better prediction of the quality of collaboration.

Zipf law: an extreme perspective

Extreme value theory (EVT) asserts that the Fréchet law emerges universally from linearly scaled maxima of collections of independent and identically distributed random variables that are positive-valued. Observations of many real-world sizes, e.g. city-sizes, give rise to the Zipf law: if we rank the sizes decreasingly, and plot the log-sizes versus the log-ranks, then an affine line emerges. In this paper we present an EVT approach to the Zipf law. Specifically, we establish that whenever the Fréchet law emerges from the EVT setting, then the Zipf law follows. The EVT generation of the Zipf law, its universality, and its associated phase transition, are analyzed and described in detail.

Realizing the extremes: Estimation of tail-risk measures from a high-frequency perspective

Abstract This article applies realized volatility forecasting to Extreme Value Theory (EVT). We propose a two-step approach where returns are first pre-whitened with a high-frequency based volatility model, and then an EVT based model is fitted to the tails of the standardized residuals. This realized EVT approach is compared to the conditional EVT of McNeil & Frey (2000). We assess both approaches' ability to filter the dependence in the extremes and to produce stable out-of-sample VaR and ES estimates for one-day and ten-day time horizons. The main finding is that GARCH-type models perform well in filtering the dependence, while the realized EVT approach seems preferable in forecasting, especially at longer time horizons.

Precipitation extremes in the Mediterranean region and associated upper-level synoptic-scale flow structures

A non-stationary analysis of daily precipitation extremes over the Mediterranean region and the associated upper-level atmospheric dynamics is presented for autumn, winter and spring. An Extreme Value Theory approach is applied to identify homogeneous areas in terms of precipitation extremes and to characterise the spatio-temporal behaviour of precipitation extremes. Results reveal a high spatial variability of extremes in the region as a whole, while the eastern Mediterranean shows a lower variability compared to the western part. The temporal variability of the estimated 5-year return levels also varies significantly across the basin especially in autumn. The synoptic-scale flow structures associated with these extreme events are then investigated. Significant upper-level flow anomalies in the form of troughs and cut-offs are found for all regions/seasons. Moreover, in many areas the associated low-level flow is directed against the local topography pointing to the relevant role of orographic lifting. Finally, significant precursor signals, 2–3 days before the events, are identified for most of the areas.

Density approximations and VaR computation for compound Poisson-lognormal distributions

ABSTRACTParametric approximations of the compound Poisson-lognormal distribution are developed and used to compute Value-at-Risk (VaR). As guidelines for finding an approximation, the skewness–kurtosis space and the tail behavior are considered. The Generalized Beta distribution of the second kind (GB2) and a mixture of lognormals are found to provide a good fit. In certain cases, the GB2 can be estimated by moment-matching, thus providing a simulation-free procedure for VaR computation. For confidence levels larger than 99%, extreme value theory approaches are developed. According to extensive Monte Carlo evidence, the proposed approximations are more efficient than crude Monte Carlo.

Intraday risk management in International stock markets: A conditional EVT approach

The study compares the predictive ability of various models in estimating intraday Value-at-Risk (VaR) and Expected Shortfall (ES) using high frequency share price index data from sixteen different countries across the world for a period of seven and half months from September 20, 2013 to May 07, 2014. The main emphasis of the study has been given to Extreme Value Theory (EVT) and to evaluate how well Conditional EVT model performs in modeling tails of distributions and in estimating and forecasting intraday VaR and ES measures. We have followed McNeil and Frey's (2000) two stage approach called Conditional EVT to estimate dynamic intraday VaR and ES. We have compared the accuracy of Conditional EVT approach to intraday VaR and ES estimation with other competing models. The best performing model is found to be the Conditional EVT in estimating both the quantiles for the entire sample. The study is useful for market participants (such as intraday traders and market makers) involved in frequent intraday trading in such equity markets.

Tail risk in emerging markets of Southeastern Europe

ABSTRACTThis article examines the left-tail behaviour of returns on stocks in Southeastern Europe (SEE). We apply conditional extreme value theory (EVT) approach on daily returns of six stock market indices from SEE between 2004 and 2013. Predictive performance of value-at-risk (VaR) and expected shortfall (ES) based on EVT is compared against several alternatives, such as historical simulation and analytical approach based on GARCH with a single conditional distribution. Model backtesting with daily returns shows that EVT-based models provide more reliable VaR and ES forecasts than the alternative models in all six markets. Unlike the alternatives, the EVT-based models cannot be rejected as VaR confidence level is increased. This emphasizes the importance of extreme events in SEE markets and indicates that the ability of a model to capture volatility clustering accurately is not sufficient for a correct assessment of risk in these markets.

Risk model validation for BRICS countries: a value-at-risk, expected shortfall and extreme value theory approach

In this paper, we employ value-at-risk (VaR) and expected shortfall (ES) as risk measures to assess the competency of several volatility models, based on the stock indexes of the BRICS countries (Brazil, Russia, India, China and South Africa) after the financial crisis. The aim is to determine the most appropriate model for each country and identify a set of common models for the BRICS countries. A family of generalized autoregressive conditional heteroscedasticity (GARCH) models, extreme value theory (EVT) and a dynamic bivariate technique are considered to demonstrate different volatility dynamics. Some models are ruled out under the presented backtesting operations, while the nonrejected models are ranked using two loss functions. In spite of returns displaying large kurtosis, the models with normal innovation generally prove to have better estimates ofVaR and ES. GARCH and fractionally integrated GARCH are preferred by Brazil and Russia, while India favors dual models and the Student t distribution. The Glosten, Jagannathan and Runkle GARCH-N is the best model for South Africa, which is the only country that rejects the stationary EVT approach. Despite these contrasting results, we find that it is possible to obtain more than one model that can be used to model all of the BRICS countries: these are the integrated GARCH-N and exponential GARCH-EVT approaches.

Using extreme value theory approaches to forecast the probability of outbreak of highly pathogenic influenza in Zhejiang, China.

BackgroundInfluenza is a contagious disease with high transmissibility to spread around the world with considerable morbidity and mortality and presents an enormous burden on worldwide public health. Few mathematical models can be used because influenza incidence data are generally not normally distributed. We developed a mathematical model using Extreme Value Theory (EVT) to forecast the probability of outbreak of highly pathogenic influenza.MethodsThe incidence data of highly pathogenic influenza in Zhejiang province from April 2009 to November 2013 were retrieved from the website of Health and Family Planning Commission of Zhejiang Province. MATLAB “VIEM” toolbox was used to analyze data and modelling. In the present work, we used the Peak Over Threshold (POT) model, assuming the frequency as a Poisson process and the intensity to be Pareto distributed, to characterize the temporal variability of the long-term extreme incidence of highly pathogenic influenza in Zhejiang, China.ResultsThe skewness and kurtosis of the incidence of highly pathogenic influenza in Zhejiang between April 2009 and November 2013 were 4.49 and 21.12, which indicated a “fat tail” distribution. A QQ plot and a mean excess plot were used to further validate the features of the distribution. After determining the threshold, we modeled the extremes and estimated the shape parameter and scale parameter by the maximum likelihood method. The results showed that months in which the incidence of highly pathogenic influenza is about 4462/2286/1311/487 are predicted to occur once every five/three/two/one year, respectively.ConclusionsDespite the simplicity, the present study successfully offers the sound modeling strategy and a methodological avenue to implement forecasting of an epidemic in the midst of its course.

Commodity market risk from 1995 to 2013: an extreme value theory approach

In this article we examine whether extreme risk has increased in the agricultural commodity market during the period 1995–2013. We add to the literature on food price volatility by analysing the tail segment of futures price return distributions. Food price variability is a concern for governments and regulators worldwide, as most nations trade in food. High food price variability can contribute to poverty and malnourishment, in particular for people in less economically developed economies. We find no indications of systematically increasing tail-risk for the commodities in our sample. Analysis of estimated shape-parameters of the Generalized Extreme Value distribution further supports the conclusion that there is no general systematic change in the extreme risk associated with these commodity investments.