Related papers: Measuring Tail Risks
Capital allocation is a procedure used to assess the risk contributions of individual risk components to the total risk of a portfolio. While the conditional tail expectation (CTE)-based capital allocation is arguably the most popular…
The entropic risk measure is widely used in high-stakes decision-making across economics, management science, finance, and safety-critical control systems because it captures tail risks associated with uncertain losses. However, when data…
We consider random-design linear prediction and related questions on the lower tail of random matrices. It is known that, under boundedness constraints, the minimax risk is of order $d/n$ in dimension $d$ with $n$ samples. Here, we study…
Under Solvency II, the Value-at-Risk (VaR) is applied, although there is broad consensus that the Expected Shortfall (ES) constitutes a more appropriate risk measure. Moving towards ES would necessitate specifying the corresponding ES…
In this paper, we generalize the parametric delta-VaR method from portfolios with normally distributed risk factors to portfolios with elliptically distributed ones. We treat both the expected shortfall and the Value-at-Risk of such…
This paper measures and compares the tail risks of limit and market orders using Extreme Value Theory. The analysis examines realised tail outcomes using the Dealing 2000-2 electronic broking system based on completed transactions rather…
We propose a novel framework of estimating systemic risk measures and risk allocations based on Markov chain Monte Carlo (MCMC) methods. We consider a class of allocations whose jth component can be written as some risk measure of the jth…
Value at risk and expected shortfall are increasingly popular tail risk measures in the financial risk management field. Both academia and financial institutions are working to improve tail risk forecasts in order to meet the requirements…
Accurate forecasting of risk is the key to successful risk management techniques. Using the largest stock index futures from twelve European bourses, this paper presents VaR measures based on their unconditional and conditional…
The Lambda Value-at-Risk (Lambda-VaR) is a generalization of the Value-at-Risk (VaR), which has been actively studied in quantitative finance. Over the past two decades, the Expected Shortfall (ES) has become one of the most important risk…
Statistical analysis of extremes can be used to predict the probability of future extreme events, such as large rainfalls or devastating windstorms. The quality of these forecasts can be measured through scoring rules. Locally scale…
This paper presents a novel semiparametric method to study the effects of extreme events on binary outcomes and subsequently forecast future outcomes. Our approach, based on Bayes' theorem and regularly varying (RV) functions, facilitates a…
In financial risk management, Value at Risk (VaR) is widely used to estimate potential portfolio losses. VaR's limitation is its inability to account for the magnitude of losses beyond a certain threshold. Expected Shortfall (ES) addresses…
Renewable energy (RE) generation exhibits pronounced seasonality and variability, and neglecting these features can lead to significant underestimation of long-term power system risks in power supply. While long-term dispatch strategies are…
Estimation of tail quantities, such as expected shortfall or Value at Risk, is a difficult problem. We show how the theory of nonlinear expectations, in particular the Data-robust expectation introduced in [5], can assist in the…
We analyze the performance of RiskMetrics, a widely used methodology for measuring market risk. Based on the assumption of normally distributed returns, the RiskMetrics model completely ignores the presence of fat tails in the distribution…
The extreme value theory is very popular in applied sciences including Finance, economics, hydrology and many other disciplines. In univariate extreme value theory, we model the data by a suitable distribution from the general max-domain of…
The Value-at-Risk (VaR) of comonotonic sums can be decomposed into marginal VaR's at the same level. This additivity property allows to derive useful decompositions for other risk measures. In particular, the Tail Value-at-Risk (TVaR) and…
Estimating the probability of extreme events involving multiple risk factors is a critical challenge in fields such as finance and climate science. This paper proposes a semi-parametric approach to estimate the probability that a…
We review recent progress in modeling credit risk for correlated assets. We start from the Merton model which default events and losses are derived from the asset values at maturity. To estimate the time development of the asset values, the…