Abstract
The stability of the financial system is associated with systemic risk factors such as the concurrent default of numerous small obligors. Hence, it is of utmost importance to study the mutual dependence of losses for different creditors in the case of large, overlapping credit portfolios. We analytically calculate the multivariate joint loss distribution of several credit portfolios on a non-stationary market. To take fluctuating asset correlations into account, we use an random matrix approach which preserves, as a much appreciated side effect, analytical tractability and drastically reduces the number of parameters. We show that, for two disjoint credit portfolios, diversification does not work in a correlated market. Additionally, we find large concurrent portfolio losses to be rather likely. We show that significant correlations of the losses emerge not only for large portfolios with thousands of credit contracts, but also for small portfolios consisting of a few credit contracts only. Furthermore, we include subordination levels, which were established in collateralized debt obligations to protect the more senior tranches from high losses. We analytically corroborate the observation that an extreme loss of the subordinated creditor is likely to also yield a large loss of the senior creditor.
Highlights
The subprime crisis 2007–2009 had a drastic influence on the world economy, due to the almost concurrent default of many small debtors (Hull 2009)
Most of the credit contracts where bundled into credit portfolios in the form of collateralized debt obligations (CDOs)
The portfolio loss correlation is a monotonic function of the asset correlation c and, for a fixed asset correlation, we find with increasing K an increasing portfolio loss correlation
Summary
The subprime crisis 2007–2009 had a drastic influence on the world economy, due to the almost concurrent default of many small debtors (Hull 2009). To describe this non-stationarity, we use an random matrix approach that was recently introduced (Chetalova et al 2015); for a comprehensive review, see (Mühlbacher and Guhr 2018) It results in a multivariate asset return distribution averaged over the fluctuating correlation matrices. The senior creditor is paid out first and the junior subordinated creditor is only paid out if the senior creditor regained the full promised payment This is related to CDO tranches and gives further information on to multivariate credit risk DVk g (V | Σ ) , where we split the Vk integrals in three parts We will use this expression later on, but we first need to specify the multivariate distribution of the correlated asset values g(V |Σ). We will argue that this is achieved by properly averaging the multivariate distribution g(V |Σ), resulting in h gi(V |Σ)
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