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Concentration and contagion risk on credit portfolios have been studied for many
years with different methodologies and approaches. Such risks can be seen as departures
from the Asymptotic Single-Risk Factor (ASRF) paradigm, which underlies the IRB
approaches of Basel II (Basel Committee on Banking Supervision, 2006). Basic hypothesis of
this model includes the homogeneity of the underlying portfolio and a common factor
driving systematic risk.
In this framework, concentration risk represents a violation of the ASRF model
and can be decomposed into two parts – an idiosyncratic part, single name or
imperfect granularity risk, due to the small size of the portfolio or due to the presence of
large exposures associated to single obligors, and a systematic term, sectoral concentration,
due to imperfect diversification across sectoral factors. Many portfolio models have
been developed in order to deal with concentration risk (e.g., CreditMetrics – Gupton et al., 1997; CreditPortfolioView – Wilson, 1998; and PortfolioManager– Kealhofer and Bohn, 2001) and some of them rely on computationally heavy Monte-Carlo simulations.
A different solution to the problem of calculating economic capital exploits
an approximated analytical technique which applies to one-factor Merton-type models.
This method, originally introduced by Vasicek (Vasicek, 1991), consists of replacing the
original portfolio loss distribution with an asymptotic one, whose Value at Risk (VaR) can be computed analytically. The difference between the true and the asymptotic
VaR can also be computed analytically through a
second-order approximation (Gourieroux et
al., 2000). Many steps have been taken in this direction, extending the original Vasicek result
for homogeneous portfolios to include granularity risk (Wilde, 2001; Martin and Wilde,
2002; Emmer and Tasche, 2005; and Gordy, 2003) and sectoral concentration risk
(Pykhtin, 2004). |
