In this paper we model Value-at-Risk (VaR) for daily stock index returns using a collection of parametric models of the ARCH family based on the skewed Student distribution. We show that models that rely on a symmetric density distribution for the error term underperform with respect to skewed density models when the left and right tails of the distribution of returns must be modelled. Thus, Va...

Methods to computing value-at-risk gradients with respect to portfolio positions have many applications. They include calculation of capital/reward efficient frontiers, hedging of derivative portfolios and optimal replication. We present a new algorithm for computing value-at-risk and its gradients. If the return can be decomposed as a sum of independent portfolio marginals, the pay-off distrib...

Ait-Sahalia and Lo (2000) and Panigirtzoglou and Skiadopoulos (2004) have argued that Economic VaR (E-VaR), calculated under the option market implied risk neutral density is a more relevant measure of risk than historically based VaR. As industry practice requires VaR at high confidence level of 99%, we propose Extreme Economic Value at Risk (EE-VaR) as a new risk measure, based on the General...

This chapter reviews the role of various species in the genesis, persistence and spread of Asianlineage H5N1 HPAI viruses. Special attention is paid to the domestic duck (Anas platyrhynchos var. domesticus), which is considered to have played a key role in these processes. An understanding of the role of domestic ducks in the maintenance and spread of these viruses helps to explain why the curr...