1 Introduction -- 2 Motivation -- Part I MEASURES -- 3 Basic Terms and Notation -- 4 Historical Value-at-Risk -- 5 Sensitivities -- 6 Stress Tests -- 7 Analytical Value-at-Risk -- 8 Expected Shortfall -- 9 Model Choices -- 10 A Monte Carlo Modi cation -- 11 Support Measures -- Part II OPERATIONS...

Historical VaR, CVaR and ES (Expected Shortfall) to LIQUIDATION Software is a model characterized by its straightforwardness, allowing regulators measure risk using a standard database of primitive factors and portfolio positions only, leaving little error margin in comparing market risk for...

Bonds historical returns cannot be used directly to compute VaR because the maturities of returns implied by the historical prices do not have the relevant maturities to compute VaR. Given the so-called pull-to-par in bonds, with return volatilities necessarily decreasing with diminishing...

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...

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 between choices of risk function (e.g. VaR vs CVaR); choice...

Assuming a Constant Elasticity of Variance (CEV) model for the asset price, that is a defaultable asset showing the so called leverage effect (high volatility when the asset price is low), a VaR constraint reevaluated over time induces an agent more risk averse than a logarithmic utility to take...