Browsing by Author "Schmidt, Thorsten"
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- CDOs in the light of the current crisisPublication . Gaspar, Raquel M.; Schmidt, ThorstenThis paper proposes a top-down model for pricing Collateralized Debt Obligation (CDOs). Our proposal is both treatable and realistic, in the sense we are able to obtain closed-form solutions to single tranche CDOs and capturing extreme credit events. We use as key ingredients the so-called (T, x)-bonds, as proposed in Filipovic, Overbeck, and Schmidt (2008), but generalize their affine specificationby including shot-noise processes. Our claim is that affine diffusions combined with shot-noise processes lead to an improved modeling of CDO spreads in comparison to existing affine jump-diffusion models. The proposed approach allows in particular for better capturing the possibility of extreme events, like the ones underlying the current crisis. We illustrate our results with a very concrete (simple) instance of our class of models. Finally, we identify the connections between the top-down and bottom-up approaches for modeling credit risk, within our class of models. Concretely, we show that even when taking a bottom-up approach the aggregate loss process would be a process of affine shot-noise type.
- On the pricing of CDOsPublication . Gaspar, Raquel M.; Schmidt, ThorstenThis chapter addresses the pricing of two popular portfolio credit derivatives: first-to-default swaps and collateralized debt obligations (CDOs). We use the recent model of Gaspar and Schmidt (2007) for the pricing of theses portfolio credit derivatives. This approach combines general quadratic models for term structures with shot-noise models and therefore naturally solves a number of important issues in credit portfolio risk. First, resulting pricing formulas are in closed form and therefore the model implementation is straightforward. Second, this class of models is able to incorporate well-known features of credit risky markets: realistic default correlations, default clustering and correlation between short-rate and credit spreads. Third, the recent turbulence in credit spreads caused by the U.S. subprime mortgage turmoil can be captured well.
- Quadratic models for portfolio credit risk with shot-noise effectsPublication . Gaspar, Raquel M.; Schmidt, ThorstenWe propose a reduced form model for default that allows us to derive closed-form solutions to all the key ingredients in credit risk modeling: risk-free bond prices, defaultable bond prices (with and without stochastic recovery) and probabilities of survival. We show that all these quantities can be represented in general exponential quadratic forms, despite the fact that the intensity is allowed to jump producing shot-noise effects. In addition, we show how to price defaultable digital puts, CDSs and options on defaultable bonds. Further on, we study a model for portfolio credit risk where we consider both firm specific and systematic risks. The model generalizes the attempt from Duffie and Garleanu (2001). We find that the model produces realistic default correlation and clustering of defaults. Then, we show how to price first-to-default swaps, CDOs, and draw the link to currently proposed credit indices.
- Term structure models with shot-noise effectsPublication . Gaspar, Raquel M.; Schmidt, ThorstenThis work proposes term structure models consisting of two parts: a part which can be represented in exponential quadratic form and a shot noise part. These term structure models allow for explicit expressions of various derivatives. In particular, they are very well suited for credit risk models. The goal of the paper is twofold. First, a number of key building blocks useful in term structure modelling are derived in closed-form. Second, these building blocks are applied to single and portfolio credit risk. This approach generalizes Duffie & Garleanu (2001) and is able to produce realistic default correlation and default clustering. We conclude with a specific model where all key building blocks are computed explicitly.