Calculation of Value-at-Risk Bounds using Rearrangement Algorithm

Abstract

For financial institutions, risk aggregation to calculate total economic capital is one of the main issue on integrated risk management. On risk aggregation, modeling association among marginal risks is quite important since they are strongly related. However, due to its complexity and lack of reliable data, it often has much of difficulty and uncertainty. Value-at-risk(VaR) is the most popular risk measure, but Embrechts et al. (2015) suggested that VaR is not robust to such uncertainty of dependence. For these reasons, it is beneficial to capture the model risk quantitatively by measuring fluctuation of total economic capital due to the dependence uncertainty. Rearrangement Algorithm(RA), proposed by Embrechts et al. (2013) enables us to calculate approximate upper and lower bounds of the aggregated risk capital among any dependence structures. On applying RA, it is sometimes required to discretize conditional tail distribution of marginals finely enough. This places considerable computational complexity on a real application of RA to integrated risk models. In this paper, we first show an integrated risk model which reduces the computational load on applying RA. Then calculate the bounds of total economic capital using RA. Lastly, we give some examinations and warnings based on our numerical results.