@techreport{Packham2009Credit,
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 It\^{o} 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 L\'{e}vy-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.},
address = {Frankfurt, M.},
author = {Natalie Packham and Lutz Schl\"{o}gl and Wolfgang M. Schmidt},
copyright = {http://www.econstor.eu/dspace/Nutzungsbedingungen},
keywords = {G12; G13; G24; C69; 330; gap risk; credit spreads; credit dynamics; first passage time models; L\'{e}vy processes; general Ornstein-Uhlenbeck processes; Finanzderivat; Zins; Risikopr\"{a}mie; Volatilit\"{a}t; Stochastischer Prozess; Theorie},
language = {eng},
number = {21},
publisher = {Frankfurt School of Finance & Management},
title = {Credit dynamics in a first passage time model with jumps},
type = {CPQF Working Paper Series},
url = {http://hdl.handle.net/10419/40190},
year = {2009}
}
