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Credit Modeling Under Jump Diffusions With Exponentially Distributed Jumps — Stable Calibration, Dynamics And Gap Risk

Author

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  • MARTIN HELLMICH

    (Frankfurt School of Finance and Management, Sonnemannstr. 9-11, 60314 Frankfurt, Germany)

  • STEFAN KASSBERGER

    (Frankfurt School of Finance and Management, Sonnemannstr. 9-11, 60314 Frankfurt, Germany)

  • WOLFGANG M. SCHMIDT

    (Frankfurt School of Finance and Management, Sonnemannstr. 9-11, 60314 Frankfurt, Germany)

Abstract

This paper investigates a structural credit default model that is based on a hyper-exponential jump diffusion process for the value of the firm. For credit default swap prices and other quantities of interest, explicit expressions for the corresponding Laplace transforms are derived. The time-dynamics of the model are studied, particularly the jumps in credit spreads, the understanding of which is crucial e.g. for the pricing of gap risk. As an application of our findings, the model is calibrated to credit default swap spreads observed in the market.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:16:y:2013:i:04:n:s0219024913500210
    DOI: 10.1142/S0219024913500210
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    References listed on IDEAS

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    1. Natalie Packham & Lutz Schloegl & Wolfgang M. Schmidt, 2013. "Credit gap risk in a first passage time model with jumps," Quantitative Finance, Taylor & Francis Journals, vol. 13(12), pages 1871-1889, December.
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    Cited by:

    1. Leippold, Markus & Vasiljević, Nikola, 2017. "Pricing and disentanglement of American puts in the hyper-exponential jump-diffusion model," Journal of Banking & Finance, Elsevier, vol. 77(C), pages 78-94.
    2. Valeriane Jokhadze & Wolfgang M. Schmidt, 2020. "Measuring Model Risk In Financial Risk Management And Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(02), pages 1-37, April.

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