VaR {OCA}

Value at Risk

Description

Analytical approach for calculating VaR based on Variance-Covariance Method based on both normal and t-student distribution.

Usage

VaR(
  variance,
  alpha = 0.95,
  weights = NULL,
  model = c("normal", "t-student", "both"),
  df = NULL,
  percentage = FALSE
)

Arguments

variance

It could be either a scalar or a matrix containing the variances and covariances of the losses. Provide a covariance matrix when analyzing correlated losses or a scalar when dealing with a single loss.

alpha

The confidence level at which either the VaR will be computed, by default alpha is set to 0.95.

weights

A vector of weights of size N for weighting the variance of losses. When weights=NULL, variances used to compute VaR are the original values supplied to variance with no weighting scheme.

model

A character string indicating which probability model has to be used for computing the risk measures, it could be a normal distribution or a t-student distribution with \(v\) degrees of freedom. The normal distibution is the default model for this funcion. model also allows the user to set 'both' if she wishes both normal and t-student VaR or ES depending on what she choses in measure. See example below.

df

An integer (df>2) denoting the degrees of freedom, only required if model='t-student'. Otherwise it has to be NULL.

percentage

Logical indicating whether the file names in the VaR table should be presented in percentage or decimal.

Value

A data.frame containing the VaR at its corresponding confidence level.

Author(s)

Jilber Urbina

References

Dhaene J., Tsanakas A., Valdez E. and Vanduffel S. (2011). Optimal Capital Allocation Principles. The Journal of Risk and Insurance. Vol. 00, No. 0, 1-28.

Urbina, J. (2013) Quantifying Optimal Capital Allocation Principles based on Risk Measures. Master Thesis, Universitat Politècnica de Catalunya.

Urbina, J. and Guillén, M. (2014). An application of capital allocation principles to operational risk and the cost of fraud. Expert Systems with Applications. 41(16):7023-7031.

See Also

Risk, ES

Examples

# Reproducing VaR from Table 2.1 in page 47 of
# McNeal A., Frey R. and Embrechts P (2005).

alpha <- c(.90, .95, .975, .99, .995)
VaR(variance=(10000*0.2/sqrt(250))^2, alpha=alpha, model='both', df=4)

# only normal VaR results
VaR(variance=(10000*0.2/sqrt(250))^2, alpha=alpha)