I don't explain these. The market is not log-normal. It may even follow a diffusion law where no moment exist and sigma is moot or infinite. That does not undermine the VaR concept. It does mean that the common MC VaR computed with a set of normally distributed shocks is an optimistic approximation of the market risk. It does not preclude the use of MC VaR with a set of Levy-distributed or fractal shocks (although practical calibration issues have so far precluded real-life adoption, banks R&D are still working on it, guys next door to me).

It does degrade the accuracy of VaR through prices and/or greeks used in VaR and derived by means of log-normal resolution of stochastic equations, or MC diffusions. For equities, volatility smiles etc are some sort of built-in-pricer fixes, though ugly. Younger derivatives markets (CDS anyone ?) may have a bigger accuracy problem. Although nothing impossible to overcome.

My feeling is, these present short-comings are (quite) well understood in (some) (french) risk management. The US do seem to have a huge problem with it. Presently writing an article on this, but it will be company-copyrighted material ("you address the shortcomings faster if you buy my consulting", no shit).

Pierre