We present several estimates of measures of risk amongst the most well-known, using both high and low frequency data. The aim of the article is to show which lower frequency measures can be an acceptable substitute to the high precision measures, when transaction data is unavailable for a long...

"Constant proportion portfolio insurance" (CPPI) is nowadays one of the most popular techniques for portfolio insurance strategies. It simply consists of reallocating the risky part of a portfolio with respect to market conditions, via a leverage parameter - called the multiple - guaranteeing a...

A drawback of available portfolio credit risk models is that they fail to allow for default risk dependency across loans other than through common risk factors. Thereby, thesemodels ignore that close ties can exist between companies due to legal, financial and business relations. In this paper,...

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...

It is widely known that the small but looming possibility of default renders the expected return distribution for financial products containing credit risk to be highly skewed and fat tailed. In this paper we apply recent techniques developed for incorporating the additional risk faced by...

In this paper portfolio problems with linear loss functions and multivariate elliptical distributed returns are studied. We consider two risk measures, Value-at-Risk and Conditional-Value-at-Risk, and two types of decision makers, risk neutral and risk averse. For Value-at-Risk, we show that the...

In this paper we examine the usefulness of multivariate semi-parametric GARCH models for evaluating the Value-at-Risk (VaR) of a portfolio with arbitrary weights. We specify and estimate several alternative multivariate GARCH models for daily returns on the S&P 500 and Nasdaq indexes. Examining...

This article proposes omnibus specification tests of parametric dynamic quantile models. Contrary to the existing procedures, we allow for a flexible specification, where a possibly continuum of quantiles are simultaneously specified under fairly weak conditions on the serial dependence in the...

Basel II and Solvency 2 both use the Value-at Risk (VaR) as the risk measure to compute the Capital Requirements. In practice, to calibrate the VaR, a normal approximation is often chosen for the unknown distribution of the yearly log returns of financial assets. This is usually justified by the...

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...