Jan-Frederik Mai, Matthias Scherer, Rudi Zagst

Portfolio default models based on a conditionally independence assumption are popular due to their analytical viability. Most models in this regard, however, use as common factor a static random variable (corresponding to, e.g., the one-factor Gaussian copula, the extendible Archimedean copula). In order to obtain a dynamic model, we use as common factor a stochastic process. Starting as our base case with a Lévy subordinator (see [1], corresponding to a Marshall-Olkin dependence structure), we generalize the model in different directions and investigate the resulting dependence structures (see [2]). Moreover, we show how popular portfolio credit derivatives can efficiently be evaluated in such a framework and present some calibration results.

**References:**

[1] J.-F. Mai, M. Scherer, A tractable multivariate default model based on a stochastic time-change, International Journal of Theoretical and Applied Finance 12:2 (2009) pp. 227-249.

[2] J.-F. Mai, M. Scherer, R. Zagst, CIID default models and implied copulas, working paper (2010).

**Keywords:** Portfolio credit derivative; De Finetti's theorem; Large-homogeneous portfolio approximation; Lévy-frailty model

**Biography:** Matthias Scherer is professor at the “HVB-Institute for Mathematical Finance” at the “Technische Universität München”. He holds a Master's degree in mathematics from “Syracuse University” and a Diploma as well as a PhD in “Wirtschaftsmathematik” from “Ulm University”. His research focus lies on multivariate stochastic models with applications to various fields.