Aggregational Effects in Extreme Value and Generalized Hyperbolic Models for Value-At-Risk Estimation: Evidence From the NYSE, FTSE, KRX and TWSE

The accurate estimation of Value-at-Risk (VaR) has become central to the measurement and management of financial risk - in particular, the financial risk inherent in investing in stock markets. While the Gaussian distribution is known to provide an unsuitable depiction of daily asset returns, it is a well-established fact that returns taken weekly, monthly or quarterly exhibits (progressively) more Gaussian behaviour. This paper examines such aggregational effect in using two popular families of distributions, namely extreme value models and generalized hyperbolic models, for VaR estimation and contrasts their behaviours against the corresponding Gaussian estimates. The data sets used are returns of indices extracted from the NYSE, FTSE, KRX and TWSE.