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"Extreme Value Theory"
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Extreme Value Methods with Applications to Finance
Extreme value theory (EVT) provides tools for assessing risk of highly unusual developments, such as financial market crashes. This book presents a synthesis of recent research, with emphasis on dependent observations. It concentrates on modern topics, such as compound Poisson approximation, processes of exceedances, and nonparametric estimation methods, which have not been focused on in other books on extremes. Along with examples from finance and insurance that illustrate the methods, the book includes over 200 exercises, making it useful as a reference book, self-study tool, or comprehensive course text.
eBook
Evolution of extreme precipitation in Spain: contribution of atmospheric dynamics and long-term trends
The analysis of temporal changes in extreme event attributes, specifically magnitude and frequency, is hindered by the rarity and exceptional nature of the events being studied. The non-stationary extreme value theory (NSEVT) provides a well-established framework for assessing how extreme event probabilities vary as a function of one or more covariates. This study employs NSEVT to investigate the recent evolution and primary drivers of extreme precipitation in Spain, utilizing indices of three large-scale modes of atmospheric circulation and time as covariates. A non-stationary peaks-over-threshold model is applied to an observational network comprising 341 weather stations over the period 1951–2020. The results demonstrate that a multivariate model accounting for the influences of all covariates fits the data significantly better than simpler, univariate and stationary models in the majority of stations. The multivariate model effectively captures the spatial and temporal marginal influences of atmospheric dynamics on the magnitude-frequency relationship of different attributes of extreme precipitation events, including daily peak intensity and accumulated event precipitation. In contrast, the marginal influence of time is relatively small and sparse, lacking a spatially coherent pattern. Notably, the multivariate model reveals larger temporal influences than those inferred from the univariate model, with more stations displaying significant decreases than increases in extreme precipitation event attributes. These findings highlight the importance of considering multiple covariates and non-stationarity when analyzing temporal changes in extreme events.
Journal Article
Future projections of Indian summer monsoon rainfall extremes over India with statistical downscaling and its consistency with observed characteristics
Indian summer monsoon rainfall extremes and their changing characteristics under global warming have remained a potential area of research and a topic of scientific debate over the last decade. This partially attributes to multiple definitions of extremes reported in the past studies and poor understanding of the changing processes associated with extremes. The later one results into poor simulation of extremes by coarse resolution General Circulation Models under increased greenhouse gas emission which further deteriorates due to inadequate representation of monsoon processes in the models. Here we use transfer function based statistical downscaling model with non-parametric kernel regression for the projection of extremes and find such conventional regional modeling fails to simulate rainfall extremes over India. In this conjuncture, we modify the downscaling algorithm by applying a robust regression to the gridded extreme rainfall events. We observe, inclusion of robust regression to the downscaling algorithm improves the historical simulation of rainfall extremes at a 0.25° spatial resolution, as evaluated based on classical extreme value theory methods, viz., block maxima and peak over threshold. The future projections of extremes during 2081–2100, obtained with the developed algorithm show no change to slight increase in the spatial mean of extremes with dominance of spatial heterogeneity. These changing characteristics in future are consistent with the observed recent changes in extremes over India. The proposed methodology will be useful for assessing the impacts of climate change on extremes; specifically while spatially mapping the risk to rainfall extremes over India.
Journal Article
Estimating the Value-at-Risk (VaR) in stock investment of insurance companies: An application of the extreme value theory
As a capital market investment, stocks have risks that must be managed. Therefore, investors should consider the returns and risks of investment products. This study aims to estimate the risk of insurance companies' loss when investing. The method used to estimate the level of risk is Value at Risk (VaR) based on Extreme Value Theory (EVT). The data used is secondary data in the form of daily stock closing prices from two insurance companies, AXA General Insurance and BRI Insurance, from January 2016 to January 2022. The data were used to estimate the risk value according to the EVT principle. As a result, Insurance AXA General Insurance, with 5.91% liquidity, has the lowest VaR value with a 99% confidence level, while BRI Insurance has 5.04%. We concluded from these results that AXA General Insurance has a lower investment risk. It means that each company has a different risk value. Therefore, investors should know these risk factors when choosing a company.
Journal Article
Extreme events in finance : a handbook of extreme value theory and its applications
A guide to the growing importance of extreme value risk theory, methods, and applications in the financial sector Presenting a uniquely accessible guide, Extreme Events in Finance: A Handbook of Extreme Value Theory and Its Applications features a combination of the theory, methods, and applications of extreme value theory (EVT) in finance and a.
eBook
Analysis of Carbon Dioxide Value with Extreme Value Theory Using Generalized Extreme Value Distribution
Abstract-This paper applies the generalized extreme value (GEV) distribution using maximum likelihood estimates to analyze extreme carbon dioxide data collected by the Provincial Energy Office of Phitsanulok from 2010 to 2023. The study aims to model return levels for carbon dioxide emissions for the periods of 5, 25, 50, and 100 years, utilizing data from various fuels-Gasohol E85, Gasohol E20, Gasohol 91, Gasohol 95, ULG95, and LPG. By fitting the GEV distribution, this research not only categorizes the behavior of emissions data under different subclasses of the GEV distribution but also confirms the suitability of the GEV model for this dataset. The findings indicate a trend of increasing return levels, suggesting rising peaks in carbon dioxide emissions over time. This model provides a valuable tool for forecasting and managing environmental risks associated with high emission levels.
Journal Article
Probabilistic assessment of earthquake hazard in the Andaman–Nicobar–Sumatra region
The Andaman–Nicobar–Sumatra (ANS) region is a very hazardous area on the globe, which has witnessed a megathrust earthquake of Mw 9.2 on 26 December 2004 and several dozen large earthquakes in the past. We estimate earthquake hazard parameters (i.e. seismic a- and b-values, maximum expected earthquake magnitudes, mean return periods and probabilities of earthquakes) in 11 shallow and 4 intermediate to deep depth seismogenic zones of the ANS region using a uniform and comprehensive earthquake data for the duration 1906–2018. The earthquake hazard scenarios for all seismogenic zones are calculated using the Gutenberg–Richter frequency–magnitude relation and the Gumbel’s extreme value theory. The low b-values (< 1.0) for both types of zones in the entire region suggest that the region is very active, under high stress and capable to generate large to great earthquakes. The estimated maximum magnitudes in different time periods using the extreme value theory show that shallow–depth zones 7, 8 and 11 (west to the Sumatra) have capabilities to generate an earthquake of magnitude Mw ≥ 8.0 in the next 50 and 100 years, while all intermediate to deep zones can generate magnitude less than 8.0. The mean return periods of earthquakes of magnitude Mw 7.0 in shallow zones 4–9 and 11 (the Sumatra and Nicobar Islands) exhibit less than 25 years. It is less than 80 years in shallow zones 4–11 for magnitude Mw 7.5, while higher return periods have been observed in the intermediate to deep zones (except for zone 4). The high probabilities (> 0.90) for the earthquake of Mw 7.0 in the next 50 years and 100 years are observed in shallow zones 4–11 (the Sumatra and Nicobar Islands), while only intermediate to deep zone 4 (Sumatra) shows high probabilities. The low return periods (< 25 years) and high probabilities (> 0.90) for the earthquake of Mw 7.0 are observed in shallow zones 5–11 (the Nicobar Islands and Sumatra regions), which suggest high earthquake hazard in these zones. The spatial variations of earthquake hazard parameters from one zone to another suggest a large grade of crustal heterogeneity and seismotectonic complexity present in this area.
Journal Article
Modelling Extreme Losses in JSE Life Insurance Price Index Growth Rates Using the Generalised Extreme Value Distribution (GEVD) and the Generalised Pareto Distribution (GPD)
The life insurance sector plays a critical role in financial system stability but is inherently exposed to extreme market fluctuations due to long-term liabilities and asset–liability mismatches. This study investigates extreme losses in the growth rates of the JSE Life Insurance Price Index (LIPI) using the Generalised Extreme Value Distribution (GEVD) and the Generalised Pareto Distribution (GPD) under the Extreme Value Theory (EVT) framework. Monthly data from January 2000 to October 2023 were transformed into a loss series, and extreme events were captured using quarterly block maxima and a POT threshold at the 95th percentile. Model parameters were estimated through Maximum Likelihood Estimation, and downside risk was assessed using return levels, Value-at-Risk (VaR), and Tail Value-at-Risk (tVaR). The GEVD model produced a negative shape parameter, consistent with a bounded Weibull-type tail, while the GPD indicated a heavy-tailed distribution. Return level estimates show escalating loss magnitudes and widening uncertainty over longer horizons, reflecting the challenges of projecting rare events. Kupiec backtesting confirms the adequacy and reliability of the GEVD-based VaR across all confidence levels, whereas the GPD underestimates risk at lower thresholds. These findings indicate significant tail risk within the South African life insurance equity segment and underscore the importance of EVT-based risk measures for capital planning and regulatory oversight. The study contributes to financial risk modelling in the life insurance sector and offers practical insights for strengthening solvency assessment and enterprise risk management frameworks.
Journal Article
Generalized Pareto processes for simulating space-time extreme events: an application to precipitation reanalyses
To better manage the risks of destructive natural disasters, impact models can be fed with simulations of extreme scenarios to study the sensitivity to temporal and spatial variability. We propose a semi-parametric stochastic framework that enables simulations of realistic spatio-temporal extreme fields using a moderate number of observed extreme space-time episodes to generate an unlimited number of extreme scenarios of any magnitude. Our framework draws sound theoretical justification from extreme value theory, building on generalized Pareto limit processes arising as limits for event magnitudes exceeding a high threshold. Specifically, we exploit asymptotic stability properties by decomposing extreme event episodes into a scalar magnitude variable (that is resampled), and an empirical profile process representing space-time variability. For illustration on hourly gridded precipitation data in Mediterranean France, we calculate various risk measures using extreme event simulations for yet unobserved magnitudes, and we highlight contrasted behavior for different definitions of the magnitude variable.
Journal Article