Extreme Value Theory

Economic uncertainty and exchange rates linkage revisited: modelling tail dependence with high frequency data ArXiv ID: 2511.05315 “View on arXiv” Authors: Nourhaine Nefzi, Abir Abid Abstract The aim of this paper is to dig deeper into understanding the exchange rates and uncertainty dependence. Using the novel Baker et al. (2020)’s daily Twitter Uncertainty Index and BRICS exchange rates, we investigate their extreme tail dependence within an original time-varying copula framework. Our analysis makes several noteworthy results. Evidence for Indian, Russian and South African currencies indicates an elliptical copulas’ dominance implying neither asymmetric features nor extreme movements in their dependence structure with the global economic uncertainty. Importantly, Brazilian and Chinese currencies tail dependence is upward trending suggesting a safe-haven role in times of high global economic uncertainty including the recent COVID-19 pandemic. In such circumstances, these markets offer opportunities to significant gains through portfolio diversification. ...

Systemic Risk Management via Maximum Independent Set in Extremal Dependence Networks ArXiv ID: 2503.15534 “View on arXiv” Authors: Unknown Abstract The failure of key financial institutions may accelerate risk contagion due to their interconnections within the system. In this paper, we propose a robust portfolio strategy to mitigate systemic risks during extreme events. We use the stock returns of key financial institutions as an indicator of their performance, apply extreme value theory to assess the extremal dependence among stocks of financial institutions, and construct a network model based on a threshold approach that captures extremal dependence. Our analysis reveals different dependence structures in the Chinese and U.S. financial systems. By applying the maximum independent set (MIS) from graph theory, we identify a subset of institutions with minimal extremal dependence, facilitating the construction of diversified portfolios resilient to risk contagion. We also compare the performance of our proposed portfolios with that of the market portfolios in the two economies. ...

Mitigating Extremal Risks: A Network-Based Portfolio Strategy ArXiv ID: 2409.12208 “View on arXiv” Authors: Unknown Abstract In financial markets marked by inherent volatility, extreme events can result in substantial investor losses. This paper proposes a portfolio strategy designed to mitigate extremal risks. By applying extreme value theory, we evaluate the extremal dependence between stocks and develop a network model reflecting these dependencies. We use a threshold-based approach to construct this complex network and analyze its structural properties. To improve risk diversification, we utilize the concept of the maximum independent set from graph theory to develop suitable portfolio strategies. Since finding the maximum independent set in a given graph is NP-hard, we further partition the network using either sector-based or community-based approaches. Additionally, we use value at risk and expected shortfall as specific risk measures and compare the performance of the proposed portfolios with that of the market portfolio. ...

The Efficient Tail Hypothesis: An Extreme Value Perspective on Market Efficiency ArXiv ID: 2408.06661 “View on arXiv” Authors: Unknown Abstract In econometrics, the Efficient Market Hypothesis posits that asset prices reflect all available information in the market. Several empirical investigations show that market efficiency drops when it undergoes extreme events. Many models for multivariate extremes focus on positive dependence, making them unsuitable for studying extremal dependence in financial markets where data often exhibit both positive and negative extremal dependence. To this end, we construct regular variation models on the entirety of $\mathbb{“R”}^d$ and develop a bivariate measure for asymmetry in the strength of extremal dependence between adjacent orthants. Our directional tail dependence (DTD) measure allows us to define the Efficient Tail Hypothesis (ETH) – an analogue of the Efficient Market Hypothesis – for the extremal behaviour of the market. Asymptotic results for estimators of DTD are described, and we discuss testing of the ETH via permutation-based methods and present novel tools for visualization. Empirical study of China’s futures market leads to a rejection of the ETH and we identify potential profitable investment opportunities. To promote the research of microstructure in China’s derivatives market, we open-source our high-frequency data, which are being collected continuously from multiple derivative exchanges. ...

Estimation of tail risk measures in finance: Approaches to extreme value mixture modeling ArXiv ID: 2407.05933 “View on arXiv” Authors: Unknown Abstract This thesis evaluates most of the extreme mixture models and methods that have appended in the literature and implements them in the context of finance and insurance. The paper also reviews and studies extreme value theory, time series, volatility clustering, and risk measurement methods in detail. Comparing the performance of extreme mixture models and methods on different simulated distributions shows that the method based on kernel density estimation does not have an absolute superior or close to the best performance, especially for the estimation of the extreme upper or lower tail of the distribution. Preprocessing time series data using a generalized autoregressive conditional heteroskedasticity model (GARCH) and applying extreme value mixture models on extracted residuals from GARCH can improve the goodness of fit and the estimation of the tail distribution. ...

Jump detection in high-frequency order prices ArXiv ID: 2403.00819 “View on arXiv” Authors: Unknown Abstract We propose methods to infer jumps of a semi-martingale, which describes long-term price dynamics, based on discrete, noisy, high-frequency observations. Different to the classical model of additive, centered market microstructure noise, we consider one-sided microstructure noise for order prices in a limit order book. We develop methods to estimate, locate and test for jumps using local minima of best ask quotes. We provide a local jump test and show that we can consistently estimate jump sizes and jump times. One main contribution is a global test for jumps. We establish the asymptotic properties and optimality of this test. We derive the asymptotic distribution of a maximum statistic under the null hypothesis of no jumps based on extreme value theory. We prove consistency under the alternative hypothesis. The rate of convergence for local alternatives is determined and shown to be much faster than optimal rates for the standard market microstructure noise model. This allows the identification of smaller jumps. In the process, we establish uniform consistency for spot volatility estimation under one-sided noise. Online jump detection based on the new approach is shown to achieve a speed advantage compared to standard methods applied to mid quotes. A simulation study sheds light on the finite-sample implementation and properties of the new approach and draws a comparison to a popular method for market microstructure noise. We showcase how our new approach helps to improve jump detection in an empirical analysis of intra-daily limit order book data. ...

Simulation of a Lévy process, its extremum, and hitting time of the extremum via characteristic functions ArXiv ID: 2312.03929 “View on arXiv” Authors: Unknown Abstract We suggest a general framework for simulation of the triplet $(X_T,\bar X_ T,τ_T)$ (Lévy process, its extremum, and hitting time of the extremum), and, separately, $X_T,\bar X_ T$ and pairs $(X_T,\bar X_ T)$, $(\bar X_ T,τ_T)$, $(\bar X_ T-X_T,τ_T)$, via characteristic functions and conditional characteristic functions. The conformal deformations technique allows one to evaluate probability distributions, joint probability distributions and conditional probability distributions accurately and fast. For simulations in the far tails of the distribution, we precalculate and store the values of the (conditional) characteristic functions on multi-grids on appropriate surfaces in $C^n$, and use these values to calculate the quantiles in the tails. For simulation in the central part of a distribution, we precalculate the values of the cumulative distribution at points of a non-uniform (multi-)grid, and use interpolation to calculate quantiles. ...