Title: VaR modeling: Conditional quantile dependence approaches
Authors: Giorgia Rivieccio - Parthenope University (Italy) [presenting]
stefania Corsaro - Parthenope University (Italy)
Giovanni De Luca - University of Naples Parthenope (Italy)
Javier Ojea Ferreiro - Comision Nacional del Mercado de Valores (Spain)
Abstract: Risk Management typically focuses on the Value-at-Risk (VaR) as the main risk measure. VaR is financially interpreted as the worst expected loss of a portfolio over a specified holding period at a given confidence level (generally 1\% or 5\%) over one day. Statistically, the estimate of the VaR corresponds to the estimate of a tail quantile of the conditional distribution of future portfolio returns. Its measurement is a highly challenging statistical problem. The classical approaches have been partly overcome by the Multivariate Conditional AutoRegressive specification for VaR (MCAViaR) which directly estimates the dynamics of the quantiles without modeling the distribution of returns. Such an approach considers possible spillovers on the VaRs, assuming a linear model for bivariate conditional quantiles. However, the assumption of linearity is also its limit. We then propose alternative copula-based approaches, specifying both a static and a dynamic dependence structure. To measure the performance in estimating the VaR of a portfolio of financial returns, we have compared three models: the MCAViaR model, a copula-VaR model and a time-varying regime switching copula model.