Risk diversification is the basis of insurance and investment. It is thus crucial to study the effects that could limit it. One of them is the existence of systemic risk that affects all the policies at the same time. We introduce here a probabilistic approach to examine the consequences of its...

Expected Shortfall (ES) has been widely accepted as a risk measure that is conceptually superior to Value-at-Risk (VaR). At the same time, however, it has been criticized for issues relating to backtesting. In particular, ES has been found not to be elicitable which means that backtesting for ES...

Using a new dataset of bid and offer quotes for credit default swaps, we investigate the relationship between theoretical determinants of default risk and actual market premia using cross sectional regressions. These theoretical determinants are variance risk premia, implied volatility and the...

Through a long-period analysis of the inter-temporal relations between the French markets for credit default swaps (CDS), shares and bonds between 2001 and 2008, this article shows how a financial innovation like CDS could heighten financial instability. After describing the operating principles...

Results from portfolio models for credit risk tell us that loan concentration in certain industry sectors can substantially increase the value-at-risk (VaR). The purpose of this paper is to analyze whether a tractable "infection model" can provide a meaningful estimate of the impact of...

In this paper we propose a new tool for backtesting that examines the quality of Value-at- Risk (VaR) forecasts. To date, the most distinguished regression-based backtest, proposed by Engle and Manganelli (2004), relies on a linear model. However, in view of the di- chotomic character of the...

This paper proposes a new test of Value at Risk (VaR) validation. Our test exploits the idea that the sequence of VaR violations (Hit function) - taking value 1-α, if there is a violation, and -α otherwise - for a nominal coverage rate α verifies the properties of a martingale difference if...

Adaptive Polar Sampling (APS) is proposed as a Markov chain Monte Carlomethod for Bayesian analysis of models with ill-behaved posteriordistributions. In order to sample efficiently from such a distribution,a location-scale transformation and a transformation to polarcoordinates are used. After...

Risk managers use portfolios to diversify away the unpriced risk of individual securities. In this article we compare the benefits of portfolio diversification for downside risk in case returns are normally distributed with the case of fat-tailed distributed returns. The downside risk of a...