We develop robust models for optimization of the VaR and CVaR risk measures with a minimum expected return constraint under joint ambiguity in distribution, mean returns, and covariance matrix. We formulate models for ellipsoidal, polytopic, and interval ambiguity sets of the means and...

This paper considers a multivariate t version of the Gaussian dynamic conditional correlation (DCC) model proposed by Engle (2002), and suggests the use of devolatized returns computed as returns standardized by realized volatilities rather than by GARCH type volatility estimates. The t-DCC...

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...

Since Value-at-Risk (VaR) disregards tail losses beyond the VaR boundary, the expected shortfall (ES), which measures the average loss when a VaR is exceeded, and the tail-risk-of-VaR (TR), which sums the sizes of tail losses, are used to investigate risks at the tails of distributions for major...

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...

VaR_Delta-Normal fails in two counts: subadditivity and potentially producing losses larger than its portfolio value. This paper solves the second inconsistency developing formulas derived from a put option, named PVaR_Delta-Normal and Put_Expected_Shortfall, PSF_Delta-Normal; the latter also...

Our data, relating to a period of extreme market turmoil, show typical leptokurtosis and skewness, leading us to consider the skewed exponential power distribution of Fernández et al. (1995), referred to as the SEP3. We demonstrate that the conditional forecasting of VaR and CVaR, made up of a...

We demonstrate how a mixture of two SEP3 densities (skewed exponential power distribution of Fernández et al., 1995) can model the conditional forecasting of VaR and CVaR to efficiently cover market risk at regulatory levels of 1% and 2.5%, as well as at the additional 5% level. Our data...