hap {OCA}

Haircut Allocation Principle

Description

Capital allocation based on the Haircut Allocation Principle.

Usage

hap(Loss, Capital, alpha = 0.95, model = "normal", df = NULL)

Arguments

Loss

Either a scalar or a vector of size N containing the mean losses.

Capital

A scalar representing the capital to be allocated to each loss.

alpha

A numeric value (either a single one or a vector) consisting of the significance level at which ES has to be computed, it can either be a single numeric value or a vector of numeric values.

model

A character string indicating which distribution is to be used for computing the VaR underlying the Haircut Allocation Principle (HAP), the default value is the normal distribution, the other alternative is t-student distribution with υ degrees of freedom. When model='both' 'normal' as well as 't-student' are used when computing the HAP, see examples.

df

An integer indicating the degrees of freedom for the t-student distribution when setting model='t-student' and model='both'. df must be greater than 2.

Details

This function computes the capital allocation based on the so-called Haircut Allocation Principle whose expression is as follows:

\[K_{i} = \frac{K}{\sum_{j=1}^{n} F_{X_{j}}^{-1}(p)} F_{X_{i}}^{-1}(p)\]

For \(i=1,\dots,n\), where \(K_i\) represents the optimal capital to be allocated to each individual loss for the i-th business unit, K is the total capital to be allocated, \(F_{X_{i}}^{-1}(p)\) is the quantile function (VaR) for the i-th loss.

Value

A vector containing the optimal capital allocation, if Capital is set to 1, then the returned matrix will consist of the proportions of capital each individual loss needs to be optimally faced.

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.

McNeil, A. J.; Frey, R. & Embrechts, P. Quantitative risk management: concepts, techniques and tools. Princeton University Press, 2005.

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

Overbeck2, cap

Examples

data(dat1, dat2)
Loss <- cbind(Loss1=dat1[1:400, ], Loss2=unname(dat2))
# Proportions of capital to be allocated to each bussines unit
hap(Loss, Capital=1)

# Capital allocation,
# capital is determined as the empirical VaR of the losses at 99\%
K <- quantile(rowSums(Loss),  probs = 0.99)
hap(Loss, Capital=K)