Extreme Value Theory Approach Research Articles

VALUE AT RISK ESTIMATION USING EXTREME VALUE THEORY APPROACH IN INDONESIA STOCK EXCHANGE

Extreme Value Theory (EVT) is a method used to identify extreme cases in heavy tail data such as financial time series data. This research aimed to obtain an estimate of stock risk through the EVT approach and compare the accuracy of the two EVT approaches, Block Maxima (BM) and Peaks Over Threshold (POT). The method used to estimate stock risk is VaR with the BM and POT approaches, and the Z statistic is used to compare the accuracy. The data used, and the limitation in this research is daily closing price data for non-cyclical consumer stocks included in LQ45 for the period February 01, 2017, to January 31, 2023. Other research limitations are using weekly blocks or 5 working days in dividing BM blocks, using the percentage method in determining threshold values in the POT approach, and using Maximum Likelihood Estimation (MLE) to estimate EVT parameter estimates. The results of the VaR analysis show that the risk level generated by the POT method is greater than the risk level from BM. The results of backtesting between the two EVT approaches in estimating VaR values show that the POT approach is more accurate than the BM approach.

Forecasting VaRs via hybrid EVT with normal and non-normal filters: A comparative analysis from the Chinese stock market

This paper studies the performance of hybrid methods combining normal and non-normal GARCH-type filters with extreme value theory (EVT) in predicting Value-at-Risk (VaR) for four major stock indices in the Chinese stock market. Based on the out-of-sample VaR forecasts results over the 24 models considered, we find that the hybrid EVT approaches illustrate substantial advantage over the corresponding GARCH-type models with parametric distributions, especially in the lower tail and extremal VaR evaluations (1% and 0.5% VaRs). Overall, the hybrid EVT methods with heavy-tailed filters (std-EVT, sstd-EVT) perform the best, followed by the hybrid EVT approaches with light-tailed filters (norm-EVT, snorm-EVT), and then the GARCH-type models with skewed student-t distribution. The conditional normal, skewed normal and student-t models are rejected and excluded from the Model Confidence Set (MCS) in predicting extremal VaRs for most cases, particularly for the lower tail. Additionally, we find that the results for alternative models in predicting VaRs vary sharply among alternative innovation specifications, but present trivial differences across the volatility models. Furthermore, our results based on the MCS tests and comparative backtests also indicate that the scoring function effectively discriminates predictive performance across methods for the lower tail, in contrast to showing less disparity for the upper tail. This emphasizes the importance of model selection in VaR forecasting performance for the lower tail. The above findings are robust to alternative threshold selections and the rolling-step chosen to update parameters. Similar analyses concerning the out-of-sample performance of the 24 models in predicting the Expected Shortfall (ES) show consistent results overall.

Modeling of Machine Learning-Based Extreme Value Theory in Stock Investment Risk Prediction: A Systematic Literature Review.

The stock market is heavily influenced by global sentiment, which is full of uncertainty and is characterized by extreme values and linear and nonlinear variables. High-frequency data generally refer to data that are collected at a very fast rate based on days, hours, minutes, and even seconds. Stock prices fluctuate rapidly and even at extremes along with changes in the variables that affect stock fluctuations. Research on investment risk estimation in the stock market that can identify extreme values is nonlinear, reliable in multivariate cases, and uses high-frequency data that are very important. The extreme value theory (EVT) approach can detect extreme values. This method is reliable in univariate cases and very complicated in multivariate cases. The purpose of this research was to collect, characterize, and analyze the investment risk estimation literature to identify research gaps. The literature used was selected by applying the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) and sourced from Sciencedirect.com and Scopus databases. A total of 1107 articles were produced from the search at the identification stage, reduced to 236 in the eligibility stage, and 90 articles in the included studies set. The bibliometric networks were visualized using the VOSviewer software, and the main keyword used as the search criteria is "VaR." The visualization showed that EVT, the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models, and historical simulation are models often used to estimate the investment risk; the application of the machine learning (ML)-based investment risk estimation model is low. There has been no research using a combination of EVT and ML to estimate the investment risk. The results showed that the hybrid model produced better Value-at-Risk (VaR) accuracy under uncertainty and nonlinear conditions. Generally, models only use daily return data as model input. Based on research gaps, a hybrid model framework for estimating risk measures is proposed using a combination of EVT and ML, using multivariable and high-frequency data to identify extreme values in the distribution of data. The goal is to produce an accurate and flexible estimated risk value against extreme changes and shocks in the stock market. Mathematics Subject Classification: 60G25; 62M20; 6245; 62P05; 91G70.

Extreme Value Theory Modelling of the Behaviour of Johannesburg Stock Exchange Financial Market Data

Financial market data are abundant with outliers, and the search for an appropriate extreme value theory (EVT) approach to apply is an endless debate in the statistics of extremes research. This paper uses EVT methods to model the five-year daily all-share total return index (ALSTRI) and the daily United States dollar (USD) against the South African rand (ZAR) exchange rate of the Johannesburg stock exchange (JSE). The study compares the block maxima approach and the peaks-over-threshold (POT) approach in terms of their ability to model financial market data. The 100-year return levels for the block maxima approach were found to be almost equal to the maximum observations of the financial markets of 10,860 and R18.99 for the ALSTRI and the USD–ZAR, respectively. For the peaks-over-threshold (POT) approach, the results show that the ALSTRI and the USD–ZAR exchange rate will surpass 17,501.63 and R23.72, respectively, at least once in 100 years. The findings in this study reveal a clear distinction between block maxima and POT return level estimates. The POT approach return level estimates were comparably higher than the block maxima estimates. The study further revealed that the blended generalised extreme value (bGEVD) is more suitable for relatively short-term forecasting, since it cuts off at the 50-year return level. Therefore, this study will add value to the literature and knowledge of statistics and econometrics. In the future, more studies on bGEVD, vine copulas, and the r-largest-order bGEVD can be conducted in the financial markets.

Before-after safety evaluation of part-time protected right-turn signals: An extreme value theory approach by applying artificial intelligence-based video analytics

Extreme value theory models have opened doors for before-after safety evaluation of engineering treatments using traffic conflict techniques. Recent advancements in automated conflict extraction technologies have further expedited conflict-based safety evaluation as a potential alternative to traditional crash-based methods. However, the suitability of extreme value theory models in the before-after evaluation of engineering treatments needs to be rigorously tested. As such, this study proposes a traffic conflict-based before-after evaluation of a novel part-time protected right-turn signal strategy for right-turn or opposing-through crashes at signalised intersections. A part-time protected right-turn signal strategy refers to a signal arrangement where permissive and fully protected right-turn phasings are operated during peak and off-peak hours, respectively. A deep neural network-based computer vision technique was applied to extract the conflicts from a total of 654 h of video recordings (before period: 266 h and after period: 388 h) over seven treated approaches, and four matching control approaches at five signalised intersections in the city of Cairns, Australia. Using post encroachment time and post-collision velocity difference as traffic conflict measures, non-stationary bivariate generalised extreme value models were developed to estimate the severe and non-severe opposing-through crashes at signal cycle levels. The odds ratio analysis of model-predicted crash risks suggests that part-time protected right-turn signals reduce 67% and 81% of severe and non-severe opposing-through crashes at signalised intersections, respectively. Part-time protected right-turn signal strategy offers a good safety solution without precipitating need for capacity upgrades to accommodate queued right turners at signalised intersections.

A comparison of pedestrian behavior in interactions with autonomous and human-driven vehicles: An extreme value theory approach

Autonomous Vehicle (AV) technologies are expected to result in significant safety and mobility benefits to the road system. However, one of the most important issues that autonomous vehicle technology faces is ensuring safe interactions with active road users such as pedestrians who can have unpredictable behavior. Moreover, road user behavior varies considerably across different traffic environments, which might represent a challenge to implementing AVs as they lack the intuition common in human-driven vehicles (HDV). This study proposes an approach to evaluate crash risk in vehicle–pedestrian interactions. An Extreme Value Theory (EVT) Peak Over Threshold (POT) model is used to compare the crash risk of AV-pedestrian and HDV-pedestrian interactions in four different cities, namely Boston, Las Vegas, Pittsburgh, and Singapore. A Bayesian hierarchical structure is used to incorporate the effect of several behavioral covariates, which enables estimating the crash risk of each interaction. Results show that the risk varies considerably depending on the type of interaction and the environment. For example, the impact of behavioral covariates (i.e., minimum distance between road users and maximum pedestrian speed) on the risk of AV-pedestrian interactions is greater when compared to the risk of HDV-pedestrian interactions in Boston, Las Vegas, and Singapore. This might indicate that, in busy and congested environments, road users may not be entirely comfortable with the presence of AVs. In addition, Singapore presented a higher percentage of riskier AV-pedestrian interactions when compared to the other cities. Finally, this study offers significant insights into the challenges of introducing AVs in diverse environments as behavior plays a crucial role in traffic and can influence conflict occurrence.

Estimating fractal dimensions: A comparative review and open source implementations.

The fractal dimension is a central quantity in nonlinear dynamics and can be estimated via several different numerical techniques. In this review paper, we present a self-contained and comprehensive introduction to the fractal dimension. We collect and present various numerical estimators and focus on the three most promising ones: generalized entropy, correlation sum, and extreme value theory. We then perform an extensive quantitative evaluation of these estimators, comparing their performance and precision using different datasets and comparing the impact of features like length, noise, embedding dimension, and falsify-ability, among many others. Our analysis shows that for synthetic noiseless data, the correlation sum is the best estimator with extreme value theory following closely. For real experimental data, we found the correlation sum to be more strongly affected by noise vs the entropy and extreme value theory. The recent extreme value theory estimator seems powerful as it has some of the advantages of both alternative methods. However, using four different ways for checking for significance, we found that the method yielded "significant" low-dimensional results for inappropriate data like stock market timeseries. This fact, combined with some ambiguities we found in the literature of the method applications, has implications for both previous and future real-world applications using the extreme value theory approach, as, for example, the argument for small effective dimensionality in the data cannot come from the method itself. All algorithms discussed are implemented as performant and easy to use open source code via the DynamicalSystems.jl library.

Assessing a Connected Environment’s Safety Impact During Mandatory Lane-Changing: A Block Maxima Approach

Previous studies have mostly hypothesised or provided preliminary evidence that crash risk during mandatory lane-changing manoeuvres in a connected environment would be reduced. However, the unavailability of crash data for a connected environment makes it challenging to confirm such a hypothesis. To this end, this study has adopted an Extreme Value Theory approach to estimate and compare crash risk using traffic conflicts during mandatory lane-changing manoeuvres in the traditional and connected environments. Using the CARRS-Q advanced driving simulator, seventy-eight participants performed mandatory lane-changing manoeuvres in three randomised driving conditions: baseline (without driving aids), connected environment with perfect communication (PC), and connected environment with communication delay (CD). Driving-related factors obtained from the driving simulator data such as speeds, spacings, lag gaps, and remaining distances were used as input to a block maximum (or generalised extreme value, GEV) model. The characteristics of the estimated GEV distributions and relative crash risk were employed as an indicator of safety. Results reveal that in the connected environment driving conditions, the mandatory lane-changing crash risk is significantly reduced compared to the baseline, with the highest reduction observed in the PC condition. The crash risk is found to be higher in the CD condition compared with the PC condition. Findings of this study confirm (i) that the connected environment has the potential to reduce the crash risk substantially by assisting drivers during mandatory lane-changing manoeuvres, and (ii) the efficacy of GEV models to quantify crash risk by using conflict data when crash records are unavailable.

Intraday Risk Management of Cryptocurrency Returns During 2020–2021 Upsurge: A Conditional EVT Approach

The cryptocurrency market is characterized by extremely high volatility. In the present study, we show the predictive ability of conditional EVT models in the cryptocurrency market during the price upsurge of 2020–2021. Taking high-frequency intraday data of four popular cryptocurrencies, Bitcoin, Ethereum, Litecoin, and Binance coin, we compare the accuracy of different competing models in estimating intraday value at risk (VaR) and expected shortfall (ES). The present study focuses on the extreme value theory (EVT) for modeling the tail of the distribution to forecast the measures of intraday VaR and ES. The study confirms the fat-tailed behavior of intraday returns of all four cryptocurrencies. Further, the study shows the magnitudes of high negative shocks are more than the positive ones for the returns of all four cryptocurrencies. The study uses suitable GARCH-family models such as apARCH, EGARCH, and CGARCH in the ARMA-GARCH framework. Using a two-stage approach the study shows how GARCH-EVT models with skewed student’s— t distribution outperform the predictability of conditional EVT with standard normal distribution as well as the unconditional EVT models in predicting intraday VaR and ES. The result of the study is useful for risk managers, day traders, and also for machine-based algorithmic trading.

An analysis of the return–volume relationship in decentralised finance (DeFi)

The decentralised finance sector has recently experienced a surge in popularity, and has emerged from the shadows of the cryptocurrency space. Although the purposes of the currencies used in this new sector differ from traditional cryptocurrencies, they still possess monetary value and can be traded using fiat currencies on specialised decentralised exchanges. This paper investigates the dynamic volume–return relationship of the five largest decentralised finance tokens, to better understand this relationship given the similarities with cryptocurrencies and the possible benefits for traders and practitioners. We implement the quantile-on-quantile regression and an extreme value theory approach to examine the relationship between the daily returns of the prices and trading volumes of decentralised finance tokens at varying quantiles and at the extreme tails. Our results suggest that when trading volume is experiencing large increases, the returns of the prices of tokens appear to be significantly positive for some cases but negative for others. The extreme volume-return dependence is found to be asymmetric in the extreme negative and positive tails of the distributions, where the dependence below extreme negative thresholds is essentially non-existent but above extreme positive thresholds it is significant. This asymmetric extreme dependence between returns and volume may be beneficial for developing trading strategies that incorporate trading volume data, and may indicate an inefficient market.

Characterizing changes in extreme ozone levels under 2050s climate conditions: An extreme-value analysis in California

Ground-level ozone has a well established climate penalty associated with changing meteorological conditions under future climate change, but most existing research focuses exclusively on ozone-temperature relationships defined at specific locations. Using an extreme-value theory approach, we model relationships between temperature, humidity, and vapor pressure deficit and maximum daily 8 h ozone concentrations (MDA8) across California using a combination of ozone station network data and Community Multiscale Air Quality Modeling System (CMAQ) model output from 2008 to 2017. We use a spatial regression with time varying bias coefficients to fuse station observations and modeled output into a spatially explicit gridded ozone dataset at 12 km resolution, then fit independent Point Process models to every grid cell to estimate 5, 20, and 50 year ozone return-levels across California. We evaluate the impact of climate change on ozone return levels and episode days under RCP4.5 conditions using an ensemble of 18 downscaled CMIP5 climate models, finding changes of -6t to 8 ppb in effective return levels and −8 to 16 episode days, Our results further strengthen the evidence for anozone climate penalty in California and show the advantages of considering multiple climate variables when modeling ground-level ozone. • Extreme ozone levels are affected by multiple meteorological variables, including temperature, relative humidity, and vapor pressure deficit. • Climate change increases extreme ozone levels across most of California. • Extreme value theory model fits are improved with meteorological covariates.

A Conflict Measures-Based Extreme Value Theory Approach to Predicting Truck Collisions and Identifying High-Risk Scenes on Two-Lane Rural Highways

Collision risk identification and prediction is an effective means to prevent truck accidents. However, most existing studies focus only on highways, not on two-lane rural highways. To predict truck collision probabilities and identify high-risk scenes on two-lane rural highways, this study first calculated time to collision and post-encroachment time using high-precision trajectory data and combined them with extreme value theory to predict the truck collision probability. Subsequently, a traffic feature parameter system was constructed with the driving behavior risk parameter. Furthermore, machine learning algorithms were used to identify critical feature parameters that affect truck collision risk. Eventually, extreme value theory based on time to collision and post-encroachment time incorporated a machine learning algorithm to identify high-risk truck driving scenes. The experiments showed that bivariate extreme value theory integrates the applicability of time to collision and post-encroachment time for different driving trajectories of trucks, resulting in significantly better prediction performances than univariate extreme value theory. Additionally, the horizontal curve radius has the most critical impact on truck collision; when a truck is driving on two-lane rural highways with a horizontal curve radius of 227 m or less, the frequency and probability of collision will be higher, and deceleration devices and central guardrail barriers can be installed to reduce risk. Second is the driving behavior risk: the driving behavior of truck drivers on two-lane rural highways has high-risk, and we recommend the installation of speed cameras on two-lane rural roads to control the driving speed of trucks and thus avoid dangerous driving behaviors. This study extends the evaluation method of truck collisions on two-lane rural highways from univariate to bivariate and provides a basis for the design of two-lane rural highways and the development of real-time dynamic warning systems and enforcement for trucks, which will help prevent and control truck collisions and alleviate safety problems on two-lane rural highways.

An Empirical Study for Comparison of Estimation Methods for Value at Risk, Tail Value at Risk, and Adjusted Tail Value at Risk Using Extreme Value Theory Approach to Stock Market Index

Risk management helps the financial industry to manage and estimate the risks that may occur by using risk measures. Financial series data mostly have a heavy tail distribution which causes the probability of extreme values to occur. To overcome these extreme values, it is necessary to apply a mathematical model in calculating risk estimates in financial data combined with the Extreme Value Theory approach. The Adjusted-TVaR model is a measure of the risk of modification of the TVaR model to eliminate outliers in the tail of the distribution. The purpose of this study is to measure the accuracy of the Value at Risk, Tail Value at Risk, and Adjusted Tail Value at Risk using the Peak Over Thresholdapproach in Extreme Value Theory Models.The results of the risk estimation research using the POT approach method, show that the higher the level of confidence and the chosen constant, the higher the value of Adj-TVaR presented. This value represents that the potential loss will be higher. The estimation results obtained that the VaR value is smaller than Adj-TVaR and Adj-TVaR is smaller than TVaR. This shows that Adj-TVaR is more efficient to use in terms of predicting risk value when compared to TVaR with the Peak Over Threshold approach

Comparison of extreme value theory approaches in temperature frequency analysis (case study: Arak plain in Iran)

Comparison of extreme value theory approaches in temperature frequency analysis (case study: Arak plain in Iran)

Evaluating the safety of autonomous vehicle–pedestrian interactions: An extreme value theory approach

With the increasing advancements in autonomous vehicle (AV) technologies, the forecasts of AV market shares seem to follow an ever-growing trend. This leads to the inherent need for proactive safety evaluations of AV impacts on other road users. To that end, this study proposes a modeling framework for the proactive assessment of pedestrian safety in AV environments. The proposed framework relies on the Extreme Value Theory (EVT), with the peak over threshold modeling technique, to develop an estimate of AV-pedestrian collisions using AV-pedestrian conflicts. The proposed framework was applied to two AV datasets, collected from three locations in the US and Singapore, using the operating AV fleets of two developers, Motional and Lyft. Both datasets included trajectory data for the subject AV, as well as LiDAR point clouds and annotated video data from AV cameras to capture the trajectories of surrounding road users. The datasets were processed to extract the AV-pedestrian conflicts along with the corresponding conflict indicators, mainly the post-encroachment time (PET) and time-to-collision (TTC). Relevant covariates were introduced to the proposed models to enhance their performance and prediction accuracy, including turning movements and conflict speeds. The results indicate an alarming risk to pedestrians when interacting with AVs, especially at the early stages of AV adoption. The expected number of collisions ranged from 4 to 5.5 per million vehicle kilometers travelled (VKT) of the AVs. With the addition of the covariates, the expected number of collisions went down to a range of 2.3–3.7 per million VKT, but with a narrower confidence interval of the resulting estimate and a better fit. The introduced approach shows promising prospects for the application of EVT methods to address AV safety impacts. It also invites future applications to address issues of concern for pedestrian safety in different conditions of urban traffic.

Network Analysis of SIFIs Based on Tail Systemic Linkage

This article applies several distinct methods including the systemic linkage method and network analysis to address intranational systemic risk interdependencies. Specifically, we initially quantify dynamic systemic linkages among US and Chinese systemically important financial institutions through time-varying adjacency matrices related to an extreme value theory (EVT) approach and then visualize them using network analysis. Numerical and graphical results show that intranational systemic linkages are obviously enhancive under extreme scenarios such as large negative shocks in the financial system. In addition, we apply a tail event-driven network quantile regression (TENQR) model to address the interdependence and dynamics of the entire network. The estimation results show that the network factors respond more strongly when the market suffers extreme stress.

Modeling of the air temperature using the Extreme Value Theory for selected biomes in Mato Grosso do Sul (Brazil).

This paper aims to find probabilities of extreme values of the air temperature for the Cerrado, Pantanal and Atlantic Forest biomes in Mato Grosso do Sul in Brazil. In this case a maximum likelihood estimation was employed for the probability distributions fitting the extreme monthly air temperatures for 2007–2018. Using the Extreme Value Theory approach this work estimates three probability distributions: the Generalized Distribution of Extreme Values (GEV), the Gumbel (GUM) and the Log-Normal (LN). The Kolmogorov–Smirnov test, the corrected Akaike criterion AICc, the Bayesian information criterion BIC, the root of the mean square error RMSE and the determination coefficient R2 were applied to measure the goodness-of-fit. The estimated distributions were used to calculate the probabilities of occurrence of maximum monthly air temperatures over 28–32 °C. Temperature predictions were done for the 2-, 5-, 10-, 30-, 50- and 100-year return periods. The GEV and GUM distributions are recommended to be used in the warmer months. In the coldest months, the LN distribution gave a better fit to a series of extreme air temperatures. Deforestation, combustion and extensive fires, and the related aerosol emissions contribute, alongside climate change, to the generation of extreme air temperatures in the studied biomes.Supplementary InformationThe online version contains supplementary material available at 10.1007/s00477-022-02206-1.

ON THE APPLICATION OF THE EXTREME VALUE THEORY IN SHIP’S STRENGTH CALCULATIONS

A procedure is proposed for application of the extreme value theory (EVT) approach considering not only the maximal value of the corresponding random variable but also its probability of exceedance. It substantially reduces the probability of exceedance of any given limit value used in the case when traditional EVT is applied. Examples are provided to illustrate its application when records of the random process are available.

An Extreme Value Theory approach to estimate crash risk during mandatory lane-changing in a connected environment

Examining crash risk in the highly anticipated connected environment is hindered by its novelty and the consequent scarcity of relevant data. This study proposes an Extreme Value Theory approach to examine and quantify mandatory lane-changing crash risk in the traditional and connected environments using traffic conflict techniques. The CARRS-Q advanced driving simulator was utilised to collect trajectory data of 78 participants performing mandatory lane-changing manoeuvres in three randomised driving conditions: baseline (without driving aids), connected environment with perfect communication, and connected environment with communication delay. Using the exceedance statistics theory (also known as a Peak Over Threshold approach corresponding to Generalised Pareto distribution), three separate models corresponding to each driving condition were developed. Driving-related factors obtained from the driving simulator data, such as speeds, spacings, lag gaps, and remaining distances, as well as driver demographics, were used as input variables to these models. Relative crash risk analysis and characteristics of the fitted Generalised Pareto distributions were employed as indicators of safety. The findings suggest that the connected environment significantly reduces mandatory lane-changing crash risk compared with the baseline condition, with the highest risk reduction observed in the perfect communication condition. While the crash risk of the communication delay condition is higher than that of the perfect communication condition, it is lower than the baseline condition. Furthermore, a comparison of the developed model to its counterpart (i.e., Block Maxima approach) showed the better performance of the adopted approach. The findings of this study provide insights into the positive impact of the connected environment on the safety of mandatory lane-changing manoeuvres as well as confirm the veracity of Peak Over Threshold models in estimating crash risk using traffic conflict data.

An extreme value analysis of the tail relationships between returns and volumes for high frequency cryptocurrencies

This paper investigates both the extreme dependence and correlation between high frequency cryptocurrency (Bitcoin and Ethereum, versus the Euro and US Dollar) returns and transaction volumes, at the extreme tails associated with booms and busts in the cryptocurrency markets. We apply an extreme value theory (EVT) approach, and highlight how these results assist traders and practitioners who rely on such technical indicators in their trading strategies – especially in times of extreme market turbulence or irrational market exuberance. Our findings contradict the belief in Wall Street that volume can significantly influence price levels and from an economic perspective our model reveals weak positive correlation between return and volume at the tails, which suggests that a misinterpretation among market participants can cause cryptocurrency markets to be relatively illiquid, thus leading to extreme price movements. Relating our statistical findings to economic models, we find that our empirical results are consistent with the explanation of market crashes based on trade misinterpretation.