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In this paper we provide a review of copula theory with applications to finance. We illustrate the idea on the bivariate framework and discuss the simple, elliptical and Archimedean classes of copulae. Since the copulae model the dependency structure between random variables, next we explain the...
Persistent link: https://www.econbiz.de/10003727552
In this article, we present new ideas concerning Non-Gaussian Component Analysis (NGCA). We use the structural assumption that a high-dimensional random vector X can be represented as a sum of two components - a lowdimensional signal S and a noise component N. We show that this assumption...
Persistent link: https://www.econbiz.de/10003973622
An intensive and still growing body of research focuses on estimating a portfolio’s Value-at-Risk.Depending on both the degree of non-linearity of the instruments comprised in the portfolio and thewillingness to make restrictive assumptions on the underlying statistical distributions, a...
Persistent link: https://www.econbiz.de/10011301159
Complex phenomena in environmental sciences can be conveniently represented by several inter-dependent random variables. In order to describe such situations, copula-based models have been studied during the last year. In this paper, we consider a novel family of bivariate copulas, called...
Persistent link: https://www.econbiz.de/10010238359
Portfolio selection and risk management are very actively studied topics in quantitative finance and applied statistics. They are closely related to the dependency structure of portfolio assets or risk factors. The correlation structure across assets and opposite tail movements are essential to...
Persistent link: https://www.econbiz.de/10010365113
Time series of financial asset values exhibit well known statistical features such as heavy tails and volatility clustering. Strongly present in some series, nonstationarity is a feature that has been somewhat overlooked. This may however be a highly relevant feature when estimating extreme...
Persistent link: https://www.econbiz.de/10009273102
Considerable literature has been devoted to developing statistical inferential results for risk measures, especially for those that are of the form of L-functionals. However, practical and theoretical considerations have highlighted quite a number of risk measures that are of the form of ratios,...
Persistent link: https://www.econbiz.de/10013124424
The catastrophic failures of risk management systems in 2008 bring to the forefront the need for accurate and flexible estimators of market risk. Despite advances in the theory and practice of evaluating risk, existing measures are notoriously poor predictors of loss in high-quantile events. To...
Persistent link: https://www.econbiz.de/10013100621
We describe characteristics of various risk measures (Value-at-Risk, Expected Shortfall, etc.) that are used to analyze and quantify the tail risk exposure, and discuss their relative strengths and weaknesses. Emphasis is placed on presenting and comparing methodologies to compute and backtest...
Persistent link: https://www.econbiz.de/10013053188
This paper proposes methods for estimation and inference in multivariate, multi-quantile models. The theory can simultaneously accommodate models with multiple random variables, multiple confidence levels, and multiple lags of the associated quantiles. The proposed framework can be conveniently...
Persistent link: https://www.econbiz.de/10013020592