Welcome to the third issue of our eleventh volume. In this issue we have four research papers.
The first paper, "Hermite approximations in credit portfolio modeling with probability of default-loss given default correlation", is by Anthony Owen, James Bryers and Francois Buet-Golfouse. In this paper the authors present a multifactor analytical framework for credit portfolio modeling that incorporates the impact of correlation between probability of default and loss given default. The authors restrict their model to application to a highly diversified portfolio of loans. Due to the linear scaling of risk contribution to value-at-risk and expected shortfall calculations with respect to the number of borrowers, the authors' approach is extremely quick even with large portfolios consisting of millions of loans.
In our second paper, "Time series models for credit default swap premiums", Márton Eifert analyzes the theoretical properties and statistical behavior of credit default swap (CDS) premiums over time. The basic variable of interest - the continuously payed par premium of a CDS contract - is mathematically derived in a risk-neutral setting, and this leads to a simple yet idealized credit triangle approximation. The demonstration of the continuous-time autoregressive moving-average (CARMA) estimation shows that most CDS entities out of a large set of European and US corporate reference entities can be appropriately described by a single-factor Ornstein-Uhlenbeck model driven by Lévy processes. Non-Lévy cases occur for the banking, energy and electricity sectors.
Nicholas M. Kiefer and C. Erik Larson, in their paper "Counting processes for retail default modeling", analyze defaults at the loan level using an approach based on statistical counting processes. Empirically, the authors consider default experience in a sample of home mortgages. They generally confirm that, after controlling for various factors, mortgages with second lien loans have experienced higher lifetime rates of severe delinquency than first lien insured mortgages. The authors use statistical methods of survival analysis based on counting processes.
The fourth and final paper in this issue is "Credit risk: taking fluctuating asset correlations into account" by Thilo A. Schmitt, Rudi Schäfer and Thomas Guhr. Here the authors view asset correlations as fluctuating quantities for which they choose the average correlation to be homogeneous. They reduce the number of parameters to two: the average correlation between assets and the strength of the fluctuations around this average value. The authors derive the loss distribution of a credit portfolio taking fluctuating correlations between asset values into account, while also deriving an analytical expression in the case of a homogeneous portfolio.
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Hermite approximations in credit portfolio modeling with probability of default–loss given default correlation
The authors present an analytic framework for credit portfolio modeling using Hermite expansions.
This paper analyzes the theoretical properties and statistical behavior of credit default swap (CDS) premiums over time.
The article discusses the use of counting processes for retail (mortgage) default modeling.
This paper puts forward an ensemble approach for asset correlations.