LossVaR {MCS}

Loss Function for VaR forecasts

Description

Calculate the losses associated with VaR forecasts.

Usage

LossVaR(realized, evaluated, which = 'asymmetricLoss', type = 'normal',
  delta = 25, tau)

Arguments

realized

a vector of returns realization

evaluated

a vector or a matrix of VaR forecasts

which

The chosen VaR loss function. Only which = 'asymmetricLoss' is available.

type

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).

delta

if type = 'differentiable' the delta parameter controls the smoothness of the function.

tau

the VaR confidence level

Value

A matrix with the VaR losses

Author(s)

Leopoldo Catania & Mauro Bernardi

References

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.