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http://hdl.handle.net/10419/40190
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| Title: | | Credit dynamics in a first passage time model with jumps  |
| Authors: | | Packham, Natalie Schlögl, Lutz Schmidt, Wolfgang M. |
| Issue Date: | | 2009 |
| Series/Report no.: | | CPQF Working Paper Series 21 |
| Abstract: | | The payoff of many credit derivatives depends on the level of credit spreads. In particular, the payoff of credit derivatives with a leverage component is sensitive to jumps in the underlying credit spreads. In the framework of first passage time models we extend the model introduced in [Overbeck and Schmidt, 2005] to address these issues. In the extended a model, a credit quality process is driven by an Itô integral with respect to a Brownian motion with stochastic volatility. Using a representation of the credit quality process as a time-changed Brownian motion, we derive formulas for conditional default probabilities and credit spreads. An example for a volatility process is the square root of a Lévy-driven Ornstein-Uhlenbeck process. We show that jumps in the volatility translate into jumps in credit spreads. We examine the dynamics of the OS-model and the extended model and provide examples. |
| Subjects: | | gap risk credit spreads credit dynamics first passage time models Lévy processes general Ornstein-Uhlenbeck processes |
| JEL: | | G12 G13 G24 C69 |
| Document Type: | | Working Paper |
| Appears in Collections: | | CPQF Working Paper Series, Frankfurt School of Finance and Management
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