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In risk management, tail risks are of crucial importance. The quality of a tail model, which is determined by data from an unknown distribution, depends critically on the subset of data used to model the tail. Based on a suitably weighted…
Multivariate dynamic time series models are widely encountered in practical studies, e.g., modelling policy transmission mechanism and measuring connectedness between economic agents. To better capture the dynamics, this paper proposes a…
In this paper we estimate the conditional value-at-risk by fitting different multivariate parametric models capturing some stylized facts about multivariate financial time series of equity returns: heavy tails, negative skew, asymmetric…
Determining contributions by sub-portfolios or single exposures to portfolio-wide economic capital for credit risk is an important risk measurement task. Often economic capital is measured as Value-at-Risk (VaR) of the portfolio loss…
Extreme values and the tail behavior of probability distributions are essential for quantifying and mitigating risk in complex systems of all kinds. In multivariate settings, accounting for correlations is crucial. Although extreme value…
Accurately defining, measuring and mitigating risk is a cornerstone of financial risk management, especially in the presence of financial contagion. Traditional correlation-based risk assessment methods often struggle under volatile market…
In this paper we discuss a general methodology to compute the market risk measure over long time horizons and at extreme percentiles, which are the typical conditions needed for estimating Economic Capital. The proposed approach extends the…
Basel II and Solvency 2 both use the Value-at-Risk (VaR) as the risk measure to compute the Capital Requirements. In practice, to calibrate the VaR, a normal approximation is often chosen for the unknown distribution of the yearly log…
The proper design and architecture of testing machine learning models, especially in their application to quantitative finance problems, is crucial. The most important aspect of this process is selecting an adequate loss function for…
The limitations of the traditional mean-variance (MV) efficient frontier, as introduced by Markowitz (1952), have been extensively documented in the literature. Specifically, the assumptions of normally distributed returns or quadratic…
We show how to reduce the problem of computing VaR and CVaR with Student T return distributions to evaluation of analytical functions of the moments. This allows an analysis of the risk properties of systems to be carefully attributed…
Regular variation is often used as the starting point for modeling multivariate heavy-tailed data. A random vector is regularly varying if and only if its radial part $R$ is regularly varying and is asymptotically independent of the angular…
Extreme Value Theory (EVT) is one of the most commonly used approaches in finance for measuring the downside risk of investment portfolios, especially during financial crises. In this paper, we propose a novel approach based on EVT called…
The role of cryptocurrencies within the financial systems has been expanding rapidly in recent years among investors and institutions. It is therefore crucial to investigate the phenomena and develop statistical methods able to capture…
This paper introduces a novel approach to financial risk assessment by incorporating topological data analysis (TDA), specifically cohomology groups, into the evaluation of equities portfolios. The study aims to go beyond traditional risk…
This paper considers the specification of covariance structures with tail estimates. We focus on two aspects: (i) the estimation of the VaR-CoVaR risk matrix in the case of larger number of time series observations than assets in a…
In multivariate time series, the estimation of the covariance matrix of the observation innovations plays an important role in forecasting as it enables the computation of the standardized forecast error vectors as well as it enables the…
This study introduces a new analytical framework for quantifying multivariate risk measures. Using the Wishart process, which is a stochastic process with values in the space of positive definite matrices, we derive several conditional tail…
Accurately estimating high quantiles beyond the largest observed value is crucial for risk assessment and devising effective adaptation strategies to prevent a greater disaster. The generalized extreme value distribution is widely used for…
Conditional value-at-risk (CVaR) is a prominent risk measure in financial engineering, energy systems, and supply chain management. In these domains, Markov decision processes (MDPs) with a long-run CVaR criterion effectively mitigate cost…