A Factor Model of Securitisation of Sovereign Debt in the European Union

This paper investigates the risk implications of securitizing the Eurozone sovereign debt as collateralised debt obligations (CDO). The proposal of creating asset-backed securities underpinned by Eurozone sovereign bonds has gained traction since the Eurozone Sovereign Debt Crisis of 2009-2012, and particularly in the aftermath of the Covid-19 pandemic. It is being seriously considered by the European Union as an alternative to Eurobonds, which are strongly opposed by Eurozone members that reject the mutualisation of sovereign debt. Under these proposals, the senior tranche of the CDO would have the risk profile of a sovereign bond.This paper constructs a structural model of a synthetic CDO where the underlying comprises the government bonds of all the 19 Eurozone countries, weighted by their respective countries’ GDP. The default correlation structure of the portfolio loss is modelled as a Bernoulli mixture where default risk depends on several stochastic common factors. As default probabilities of Eurozone sovereigns cannot be assumed to be equal and independent, the portfolio loss distribution must thus be that of the sum of non-iid Bernoulli random variables. Obtaining the expected tranche losses of CDOs for the sum of non-iid Bernoulli distributions is computationally intractable even for a relatively small number of assets, but can be accurately calculated by saddlepoint approximations. Numerical experiments show that in a Gaussian copula model only a very high subordination level, where the junior tranche absorbs 30\% of portfolio losses, ensures that the senior tranche does not default. Morever under the Student t copula model, which implies higher probabilities for extreme events, even high levels of subordination cannot shield ESBies from default losses. Our findings suggest that Sovereign Bond-Backed Securities are unlikely to be substitutes of safe assets such as Eurobonds