Calculate the losses associated with VaR forecasts.
LossVaR(realized, evaluated, which = 'asymmetricLoss', type = 'normal',
delta = 25, tau)a vector of returns realization
a vector or a matrix of VaR forecasts
The chosen VaR loss function. Only which = 'asymmetricLoss' is available.
if which = 'asymmetricLoss' the type of the asymmetric loss function of Gonzalez-Riviera et.al. (2004).
Possible choices are type = 'normal' which reports the quantile loss function used for example in Koenker and Bassett (1978)
and type = 'differentiable' for the differentiable version of Gonzalez-Riviera et.al. (2004).
if type = 'differentiable' the delta parameter controls the smoothness of the function.
the VaR confidence level
A matrix with the VaR losses
Koenker, R., Bassett, G. (1978). Regression quantiles. Econometrica, 46(1), 33-50.
Gonzalez-Rivera G, Lee TH, Mishra S (2004). Forecasting volatility: A reality check based on option pricing, utility function, value-at-risk, and predictive likelihood.' International Journal of Forecasting, 20(4), 629-645. ISSN 0169-2070. URL http://www.sciencedirect.com/science/article/pii/S0169207003001420.