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Credit derivatives pricing with default density term structure modelled by Lévy random fields

Author

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  • Lijun Bo

    (Department of Mathematics, Xidian University - Xidian University)

  • Ying Jiao

    (Laboratoire de Sciences Actuarielle et Financière)

  • Xuewei Yang

    (School of Mathematical Sciences, Nankai University - Nankai University, 94 Weijin Road, Nankai District, Tianjin 300071 China)

Abstract

We model the term structure of the forward default intensity and the default density by using Lévy random fields, which allow us to consider the credit derivatives with an after-default recovery payment. As applications, we study the pricing of a defaultable bond and represent the pricing kernel as the unique solution of a parabolic integro-differential equation. Finally, we illustrate by numerical examples the impact of the contagious jump risks on the defaultable bond price in our model.

Suggested Citation

  • Lijun Bo & Ying Jiao & Xuewei Yang, 2014. "Credit derivatives pricing with default density term structure modelled by Lévy random fields," Post-Print hal-00651397, HAL.
    • Handle: RePEc:hal:journl:hal-00651397
    Note: View the original document on HAL open archive server: https://hal.science/hal-00651397
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    References listed on IDEAS

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    3. D. P. Kennedy, 1994. "The Term Structure Of Interest Rates As A Gaussian Random Field," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 247-258, July.
    4. Damir Filipović & Stefan Tappe, 2008. "Existence of Lévy term structure models," Finance and Stochastics, Springer, vol. 12(1), pages 83-115, January.
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    6. El Karoui, Nicole & Jeanblanc, Monique & Jiao, Ying, 2010. "What happens after a default: The conditional density approach," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1011-1032, July.
    7. D. P. Kennedy, 1997. "Characterizing Gaussian Models of the Term Structure of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 107-118, April.
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