Value-at-Risk Bounds with Variance Constraints - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Value-at-Risk Bounds with Variance Constraints write by Carole Bernard. This book was released on 2015. Value-at-Risk Bounds with Variance Constraints available in PDF, EPUB and Kindle. Recent literature deals with bounds on the Value-at-Risk (VaR) of risky portfolios when only the marginal distributions of the components are known. In this paper we study Value-at-Risk bounds when the variance of the portfolio sum is also known, a situation that is of considerable interest in risk management.We provide easy to calculate Value-at-Risk bounds with and without variance constraint and show that the improvement due to the variance constraint can be quite substantial. We discuss when the bounds are sharp (attainable) and point out the close connections between the study of VaR bounds and convex ordering of aggregate risk. This connection leads to the construction of a new practical algorithm, called Extended Rearrangement Algorithm (ERA), that allows to approximate sharp VaR bounds. We test the stability and the quality of the algorithm in several numerical examples.We apply the results to the case of credit risk portfolio models and verify that adding the variance constraint gives rise to significantly tighter bounds in all situations of interest. However, model risk remains a concern and we criticize regulatory frameworks that allow financial institutions to use internal models for computing the portfolio VaR at high confidence levels (e.g., 99.5%) as the basis for setting capital requirements.
Reduction of Value-at-Risk Bounds Via Independence and Variance Information
Reduction of Value-at-Risk Bounds Via Independence and Variance Information - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Reduction of Value-at-Risk Bounds Via Independence and Variance Information write by Giovanni Puccetti. This book was released on 2015. Reduction of Value-at-Risk Bounds Via Independence and Variance Information available in PDF, EPUB and Kindle. We derive lower and upper bounds for the Value-at-Risk of a portfolio of losses when the marginal distributions are known and independence among (some) subgroups of the marginal components is assumed. We provide several actuarial examples showing that the newly proposed bounds strongly improve those available in the literature that are based on the sole knowledge of the marginal distributions. When the variance of the joint portfolio loss is small enough, further improvements can be obtained.
A Comparison of VAR and Cvar Constraints on Portfolio Selection with the Mean-Variance Model
A Comparison of VAR and Cvar Constraints on Portfolio Selection with the Mean-Variance Model - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Comparison of VAR and Cvar Constraints on Portfolio Selection with the Mean-Variance Model write by Gordon J. Alexander. This book was released on 2006. A Comparison of VAR and Cvar Constraints on Portfolio Selection with the Mean-Variance Model available in PDF, EPUB and Kindle. In this paper, we analyze the portfolio selection implications arising from imposing a value-at-risk (VaR) constraint on the mean-variance model, and compare them with those arising from the imposition of a conditional value-at-risk (CVaR) constraint. We show that for a given confidence level, a CVaR constraint is tighter than a VaR constraint if the CVaR and VaR bounds coincide. Consequently, a CVaR constraint is more effective than a VaR constraint as a tool to control slightly risk-averse agents, but in the absence of a risk-free security, has a perverse effect in that it is more likely to force highly risk-averse agents to select portfolios with larger standard deviations. However, when the CVaR bound is appropriately larger than the VaR bound or when a risk-free security is present, a CVaR constraint "dominates" a VaR constraint as a risk management tool.
Model Risk Management
Model Risk Management - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Model Risk Management write by Ludger Rüschendorf. This book was released on 2023-12-31. Model Risk Management available in PDF, EPUB and Kindle. This book provides the first systematic treatment of model risk, outlining the tools needed to quantify model uncertainty, to study its effects, and, in particular, to determine the best upper and lower risk bounds for various risk aggregation functionals of interest. Drawing on both numerical and analytical examples, this is a thorough reference work for actuaries, risk managers, and regulators. Supervisory authorities can use the methods discussed to challenge the models used by banks and insurers, and banks and insurers can use them to prioritize the activities on model development, identifying which ones require more attention than others. In sum, it is essential reading for all those working in portfolio theory and the theory of financial and engineering risk, as well as for practitioners in these areas. It can also be used as a textbook for graduate courses on risk bounds and model uncertainty.
VaR Bounds for Joint Portfolios with Dependence Constraints
VaR Bounds for Joint Portfolios with Dependence Constraints - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook VaR Bounds for Joint Portfolios with Dependence Constraints write by Giovanni Puccetti. This book was released on 2016. VaR Bounds for Joint Portfolios with Dependence Constraints available in PDF, EPUB and Kindle. Based on a novel extension of classical Hoeffding-Fréchet bounds, we provide an upper VaR bound for joint risk portfolios with fixed marginal distributions and positive dependence information. The positive dependence information can be assumed to hold in the tails, in some central part, or on a general subset of the domain of the distribution function of a risk portfolio. The newly provided VaR bound can be interpreted as a comonotonic VaR computed at a distorted confidence level and its quality is illustrated in a series of examples of practical interest.
