Appendix A
Economic Capital Allocation Approaches
Assume a loss distribution defined by L and a certain quantile α. The credit value at risk (CVaR) associated with the quantile is defined respectively as:
Below we will define approaches using standard risk measures that are largely used in practice for allocating economic capital. Assume the conglomerate is comprised of n subportfolios whose allocations we want to determine. Below we show some of the different approaches used for ECAP allocation with some comments on the differences:
1. VaR / Covar. Although largely used by practitioners, this approach is typical for Gaussian loss distribution. The allocated capital of a certain subportfolio is given by:
where Li and L are the losses of the subportfolio i and the total portfolio respectively. ECAPT(α) and361are the total ECAP of the portfolio at the quantile α, and the total portfolio loss variance respectively.
2. Pro-rata CVaR. In this approach one uses the stand-alone CVaRα of each sub-portfolio as a weight in the allocation of the total risk:3
3. Basel II. In this approach ...

Get The Art of Credit Derivatives: Demystifying the Black Swan now with the O’Reilly learning platform.

O’Reilly members experience live online training, plus books, videos, and digital content from nearly 200 publishers.