once we fix the value of M, the defaults of the n entities are (conditionally on M) mutually independent. As of 2010, the OFGC is the basis for credit risk management in Basel II. The benefits of the model are simplicity and intuition. One of the main shortcomings of the model is that traders when pricing CDOs randomly alter the correlation parameter for different CDO tranches to achieve desired tranche spreads. However conceptually, the correlation parameter should be identical for the whole portfolio. Contagion default modeling Contagion default modeling can be viewed as a variation of CID modeling. As discussed in section 2.3, in the CID framework, correlation is modeled by conditioning on a common market factor M, which impacts all entities to the same degree. The lower the random drawing for M, the higher is the default intensity of all entities (unless ρ = 0). Hence CID modeling can elucidate default clustering. In contrast, contagion approaches model the default intensity of an entity as a function of the default of another entity. Hence contagion default modeling incorporates counterparty risk, i.e. the direct impact of a defaulting entity on the default intensity of another entity. In particular, after a default of a particular entity, the default intensity of all assets in the portfolio increases. This default contagion then typically fades exponentially to non-contagious default intensity levels. See the papers of Davis and Lo (2001) and Jarrow and Yu (2001), who pioneered contagion default modeling. Top–down correlation approaches Within the credit correlation modeling framework, a fairly new correlation approach is top–down modeling. Here the evolution of the portfolio intensity distribution is derived directly, i.e. abstracting from the default intensities of individual entities. Top-down models are typically applied in practice if: The default intensities of the individual entities are unavailable or unreliable. The default intensities of the individual entities are unnecessary. This may be the case when evaluating a homogeneous portfolio such as an index of homogeneous entities. The sheer size of a portfolio makes the modeling of individual default intensities problematic. Top–down models are typically more parsimonious, computationally efficient and can often be calibrated better to market prices than bottom–up models. Although seemingly important information such as the default intensities of individual entities is disregarded, a top-down model can typically better capture properties of the portfolio such as volatility or correlation smiles. In addition, the default information of individual entities can