Valuation of synthetic CDOs with affine jump-diffusion processes involving Lévy stable distributions

Noticing the heavy tail dependence phenomenon in the Collateralised Debt Obligation (CDO) markets, we utilize affine jump-diffusion processes involving Lévy stable distributions to model the systematic and idiosyncratic risk factors under the setting of intensity-based models. We further derive explicit formulae for the expected loss of CDO tranches under this modelling framework.