Within the Internal Ratings-Based (IRB) approach of Basel II it is assumed that idiosyncratic risk has been fully diversified away. The impact of undiversified idiosyncratic risk on portfolio Value-at-Risk can be quantified via a granularity adjustment (GA). We provide an analytic formula for the GA in an extended single-factor Credit Risk setting incorporating double default effects. It accounts for guarantees and their effect of reducing credit risk in the portfolio. Our general GA very well suits for application under Pillar 2 of Basel II as the data inputs are drawn from quantities already required for the calculation of IRB capital charges.
In the portfolio risk-factor frameworks that underpin both industry models of credit Value-at-Risk (VaR) and the Internal Ratings-Based (IRB) risk weights of Basel II, credit risk in a portfolio arises from two sources, systematic and idiosyn cratic. Idiosyncratic risk represents the effects of risks that are particular to individual borrowers. Under the Asymptotic Single Risk Factor (ASRF) framework on which the IRB approach is based, it is assumed that bank portfolios are perfectly fine-grained in the sense that the largest individual exposures account for an infinitely small share of total portfolio exposure. In such a portfolio idiosyncratic risk is fully diversified away, so that economic capital depends only on systematic risk. Real-world portfolios are not, of course, perfectly fine-grained. The asymptotic assumption might be approximately valid for some of the largest bank portfolios, but clearly would be much less satisfactory for portfolios of smaller or more specialized institutions. When there are material name concentrations, there will be a residual of undiversified idiosyncratic risk in the portfolio. The IRB formula omits the contribution of this residual to the required economic capital.
I hope all of you have had an enjoyable summer, and had an opportunity to enjoy the simple pleasures this season brings—iced tea, backyard hammocks, sand castles, watermelon, and great novels, to name a few! With this issue, you will notice an important addition to our readings.
With the increasing availability of high frequency financial data, the development of realized variance (RV) has made tremendous progress both on the theoretical front and in empirical applications, (see for instance Andersen and Bollerslev, 1998; Andersen, Bollerslev, Diebold, and Labys, 2001, 2003; Barndorff Nielsen and Shephard, 2004a). The focus of this literature is the construction of a flexible model-free measure of integrated variance for asset returns.
