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Credit gap risk in a first passage time model with jumps

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

Abstract

The payoff of many credit derivatives depends on the level of credit spreads. In particular, credit derivatives with a leverage component are subject to gap risk, a risk associated with the occurrence of jumps in the underlying credit default swaps. In the framework of first passage time models, we consider a model that addresses these issues. The principal idea is to model a credit quality process as an Itô integral with respect to a Brownian motion with a stochastic volatility. Using a representation of the credit quality process as a time-changed Brownian motion, one can 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. The model can be implemented efficiently using a technique called Panjer recursion. Calibration to a wide range of dynamics is supported. We illustrate the effectiveness of the model by valuing a leveraged credit-linked note.

Suggested Citation

  • Packham, Natalie & Schlögl, Lutz & Schmidt, Wolfgang M., 2009. "Credit gap risk in a first passage time model with jumps," CPQF Working Paper Series 22, Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF).
  • Handle: RePEc:zbw:cpqfwp:22
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    References listed on IDEAS

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    1. Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, vol. 106(1), pages 27-65, January.
    2. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, vol. 31(2), pages 351-367, May.
    3. 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.
    4. Duffie, Darrell & Lando, David, 2001. "Term Structures of Credit Spreads with Incomplete Accounting Information," Econometrica, Econometric Society, vol. 69(3), pages 633-664, May.
    5. 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.
    6. Schneider, Paul & Sögner, Leopold & Veža, Tanja, 2010. "The Economic Role of Jumps and Recovery Rates in the Market for Corporate Default Risk," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 45(6), pages 1517-1547, December.
    7. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
    8. Qiang Dai & Kenneth Singleton, 2003. "Term Structure Dynamics in Theory and Reality," Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 631-678, July.
    9. Hirsch, Christian & Bannier, Christina E., 2007. "The economics of rating watchlists: Evidence from rating changes," CFS Working Paper Series 2008/02, Center for Financial Studies (CFS).
    10. Robert A. Jarrow & Stuart M. Turnbull, 2008. "Pricing Derivatives on Financial Securities Subject to Credit Risk," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 17, pages 377-409, World Scientific Publishing Co. Pte. Ltd..
    11. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    12. Longstaff, Francis A & Schwartz, Eduardo S, 1995. "A Simple Approach to Valuing Risky Fixed and Floating Rate Debt," Journal of Finance, American Finance Association, vol. 50(3), pages 789-819, July.
    13. Christina E. Bannier & Patrick Behr & Andre Güttler, 2010. "Rating opaque borrowers: why are unsolicited ratings lower?," Review of Finance, European Finance Association, vol. 14(2), pages 263-294.
    14. 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.
    15. Bannier, Christina E. & Hirsch, Christian W., 2010. "The economic function of credit rating agencies - What does the watchlist tell us?," Journal of Banking & Finance, Elsevier, vol. 34(12), pages 3037-3049, December.
    16. 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.
    17. 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.
    18. Benjamin Yibin Zhang & Hao Zhou & Haibin Zhu, 2009. "Explaining Credit Default Swap Spreads with the Equity Volatility and Jump Risks of Individual Firms," Review of Financial Studies, Society for Financial Studies, vol. 22(12), pages 5099-5131, December.
    19. Roßbach, Peter, 2009. "Die Rolle des Internets als Informationsbeschaffungsmedium in Banken," Frankfurt School - Working Paper Series 120, Frankfurt School of Finance and Management.
    20. 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.
    21. Zhou, Chunsheng, 2001. "The term structure of credit spreads with jump risk," Journal of Banking & Finance, Elsevier, vol. 25(11), pages 2015-2040, November.
    22. 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.
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    Cited by:

    1. Inklaar, Robert & Koetter, Michael & Noth, Felix, 2012. "Who's afraid of big bad banks? Bank competition, SME, and industry growth," Frankfurt School - Working Paper Series 197, Frankfurt School of Finance and Management.
    2. Dietmar Harhoff & Elisabeth Mueller & John Van Reenen, 2014. "What are the Channels for Technology Sourcing? Panel Data Evidence from German Companies," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 23(1), pages 204-224, March.
    3. Boeing, Philipp & Mueller, Elisabeth & Sandner, Philipp, 2012. "What makes Chinese firms productive? Learning from indigenous and foreign sources of knowledge," Frankfurt School - Working Paper Series 196, Frankfurt School of Finance and Management.
    4. Martin Hellmich & Stefan Kassberger & Wolfgang M. Schmidt, 2013. "Credit Modeling Under Jump Diffusions With Exponentially Distributed Jumps — Stable Calibration, Dynamics And Gap Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(04), pages 1-26.
    5. Jessen, Cathrine & Lando, David, 2015. "Robustness of distance-to-default," Journal of Banking & Finance, Elsevier, vol. 50(C), pages 493-505.
    6. Kostka, Genia & Moslener, Ulf & Andreas, Jan G., 2011. "Barriers to energy efficiency improvement: Empirical evidence from small-and-medium sized enterprises in China," Frankfurt School - Working Paper Series 178, Frankfurt School of Finance and Management.
    7. Alexander Libman & Vladimir Kozlov & André Schultz, 2012. "Roving Bandits in Action: Outside Option and Governmental Predation in Autocracies," Kyklos, Wiley Blackwell, vol. 65(4), pages 526-562, November.
    8. Yu, Xiaofan, 2011. "A spatial interpretation of the persistency of China's provincial inequality," Frankfurt School - Working Paper Series 171, Frankfurt School of Finance and Management.
    9. Böing, Philipp & Müller, Elisabeth, 2012. "Technological Capabilities of Chinese Enterprises: Who is Going to Compete Abroad?," Annual Conference 2012 (Goettingen): New Approaches and Challenges for the Labor Market of the 21st Century 62081, Verein für Socialpolitik / German Economic Association.
    10. Cantia, Catalin & Tunaru, Radu, 2017. "A factor model for joint default probabilities. Pricing of CDS, index swaps and index tranches," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 21-35.

    More about this item

    Keywords

    gap risk; credit spreads; credit dynamics; first passage time models; stochastic volatility; general Ornstein-Uhlenbeck processes;

    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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