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Credit dynamics in a first passage time model with jumps

Author

Listed:
  • Packham, Natalie
  • Schlögl, Lutz
  • Schmidt, Wolfgang M.
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.

Suggested Citation

  • Packham, Natalie & Schlögl, Lutz & Schmidt, Wolfgang M., 2009. "Credit dynamics in a first passage time model with jumps," CPQF Working Paper Series 21, Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF).
    • Handle: RePEc:zbw:cpqfwp:21
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    More about this item

    Keywords

    gap risk; credit spreads; credit dynamics; first passage time models; Lévy processes; general Ornstein-Uhlenbeck processes;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G24 - Financial Economics - - Financial Institutions and Services - - - Investment Banking; Venture Capital; Brokerage
    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other

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