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Credit dynamics in a first passage time model with jumps

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

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.

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Paper provided by Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF) in its series CPQF Working Paper Series with number 21.

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Date of creation: 2009
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Handle: RePEc:zbw:cpqfwp:21
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  1. Ansgar Belke & Thorsten Polleit, 2005. "(How) Do Stock Market Returns React to Monetary Policy? - An ARDL Cointegration Analysis for Germany," Diskussionspapiere aus dem Institut für Volkswirtschaftslehre der Universität Hohenheim 253/2005, Department of Economics, University of Hohenheim, Germany.
  2. Ansgar Belke & Thorsten Polleit, 2007. "How the ECB and the US Fed set interest rates," Applied Economics, Taylor & Francis Journals, vol. 39(17), pages 2197-2209.
  3. Bannier, Christina E., 2007. "Heterogeneous multiple bank financing: does it reduce inefficient credit-renegotation incidences?," Frankfurt School - Working Paper Series 83, Frankfurt School of Finance and Management.
  4. Christina E. Bannier, 2010. "Is there a Holdup Benefit in Heterogeneous Multiple Bank Financing?," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 166(4), pages 641-661, December.
  5. Schalast, Christoph & Ockens, Klaas & Jobe, Clemens J. & Safran, Robert, 2006. "Work-out und Servicing von notleidenden Krediten: Berichte und Referate des HfB-NPL Servicing Forums 2006," Frankfurt School - Working Paper Series 76, Frankfurt School of Finance and Management.
  6. Schanz, Kay-Michael & Richard, Jörg & Schalast, Christoph, 2004. "Unternehmen im Prime Standard staying public oder going private? Nutzenanalyse der Börsennotiz," Frankfurt School - Working Paper Series 60, Frankfurt School of Finance and Management.
  7. Anders, Dietmar & Binder, Andreas & Hesdahl, Ralf & Schalast, Christoph & Thöne, Thomas, 2004. "Aktuelle Fragen des Bank- und Kapitalmarktrechts I: Non-Performing-Loans/Faule Kredite - Handel, Work-Out, Outsourcing und Securitisation," Frankfurt School - Working Paper Series 54, Frankfurt School of Finance and Management.
  8. Demidova-Menzel, Nadeshda & Heidorn, Thomas, 2007. "Gold in the investment portfolio," Frankfurt School - Working Paper Series 87, Frankfurt School of Finance and Management.
  9. Bannier, Christina E. & Hänsel, Dennis N., 2007. "Determinants of banks' engagement in loan securitization," Frankfurt School - Working Paper Series 85, Frankfurt School of Finance and Management.
  10. Heidorn, Thomas & Siragusano, Tindaro, 2004. "Die Anwendbarkeit der Behavioral Finance im Devisenmarkt," Frankfurt School - Working Paper Series 52, Frankfurt School of Finance and Management.
  11. Hirsch, Christian & Bannier, Christina E., 2007. "The economics of rating watchlists: evidence from rating changes," Frankfurt School - Working Paper Series 88, Frankfurt School of Finance and Management.
  12. Wollersheim, Jutta & Barthel, Erich, 2008. "Kulturunterschiede bei Mergers & Acquisitions: Entwicklung eines Konzeptes zur Durchführung einer Cultural Due Diligence," Frankfurt School - Working Paper Series 94, Frankfurt School of Finance and Management.
  13. Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, vol. 106(1), pages 27-65, January.
  14. Heidorn, Thomas & Schmaltz, Christian & Kunze, Wolfgang, 2008. "Liquiditätsmodellierung von Kreditzusagen (term facilities and revolver)," Frankfurt School - Working Paper Series 93, Frankfurt School of Finance and Management.
  15. Schanz, Kay-Michael & Schalast, Christoph, 2006. "Wertpapierprospekte: Markteinführungspublizität nach EU-Prospektverordnung und Wertpapierprospektgesetz 2005," Frankfurt School - Working Paper Series 74, Frankfurt School of Finance and Management.
  16. Hankir, Yassin & Rauch, Christian & Umber, Marc P., 2009. "It's the market power, stupid! Stock return patterns in international bank M&A," Frankfurt School - Working Paper Series 129, Frankfurt School of Finance and Management.
  17. Roßbach, Peter, 2009. "Die Rolle des Internets als Informationsbeschaffungsmedium in Banken," Frankfurt School - Working Paper Series 120, Frankfurt School of Finance and Management.
  18. Roßbach, Peter & Gießamer, Dirk, 2009. "Ein eLearning-System zur Unterstützung der Wissensvermittlung von Web-Entwicklern in Sicherheitsthemen," Frankfurt School - Working Paper Series 116, Frankfurt School of Finance and Management.
  19. Schalast, Christoph & Tiemann, Marcel & Tuppi, Pascal, 2009. "Staatsfonds - neue Akteure an den Finanzmärkten?," Frankfurt School - Working Paper Series 114, Frankfurt School of Finance and Management.
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