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Interacting Default Intensity with Hidden Markov Process

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  • Feng-Hui Yu
  • Wai-Ki Ching
  • Jia-Wen Gu
  • Tak-Kuen Siu

Abstract

In this paper we consider a reduced-form intensity-based credit risk model with a hidden Markov state process. A filtering method is proposed for extracting the underlying state given the observation processes. The method may be applied to a wide range of problems. Based on this model, we derive the joint distribution of multiple default times without imposing stringent assumptions on the form of default intensities. Closed-form formulas for the distribution of default times are obtained which are then applied to solve a number of practical problems such as hedging and pricing credit derivatives. The method and numerical algorithms presented may be applicable to various forms of default intensities.

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  • Feng-Hui Yu & Wai-Ki Ching & Jia-Wen Gu & Tak-Kuen Siu, 2016. "Interacting Default Intensity with Hidden Markov Process," Papers 1603.02902, arXiv.org.
    • Handle: RePEc:arx:papers:1603.02902
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    1. Duffie, Darrell & Saita, Leandro & Wang, Ke, 2007. "Multi-period corporate default prediction with stochastic covariates," Journal of Financial Economics, Elsevier, vol. 83(3), pages 635-665, March.
    2. Fan Yu, 2007. "Correlated Defaults In Intensity‐Based Models," Mathematical Finance, Wiley Blackwell, vol. 17(2), pages 155-173, April.
    3. Robert Elliott & Jia Shen, 2015. "Credit risk and contagion via self-exciting default intensity," Annals of Finance, Springer, vol. 11(3), pages 319-344, November.
    4. Robert Elliott & Jia Shen, 2015. "Dynamic optimal capital structure with regime switching," Annals of Finance, Springer, vol. 11(2), pages 199-220, May.
    5. 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..
    6. Harry Zheng & Lishang Jiang, 2009. "Basket CDS pricing with interacting intensities," Finance and Stochastics, Springer, vol. 13(3), pages 445-469, September.
    7. 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.
    8. Rüdiger Frey & Wolfgang Runggaldier, 2010. "Pricing credit derivatives under incomplete information: a nonlinear-filtering approach," Finance and Stochastics, Springer, vol. 14(4), pages 495-526, December.
    9. Kay Giesecke & Lisa R. Goldberg & Xiaowei Ding, 2011. "A Top-Down Approach to Multiname Credit," Operations Research, INFORMS, vol. 59(2), pages 283-300, April.
    10. Rama Cont, 2008. "Frontiers in Quantitative Finance: credit risk and volatility modeling," Post-Print hal-00437588, HAL.
    11. Shaked, Moshe & George Shanthikumar, J., 1987. "The multivariate hazard construction," Stochastic Processes and their Applications, Elsevier, vol. 24(2), pages 241-258, May.
    12. R. J. Elliott & M. Jeanblanc & M. Yor, 2000. "On Models of Default Risk," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 179-195, April.
    13. Francis A. Longstaff & Arvind Rajan, 2008. "An Empirical Analysis of the Pricing of Collateralized Debt Obligations," Journal of Finance, American Finance Association, vol. 63(2), pages 529-563, April.
    14. Robert A. Jarrow & Fan Yu, 2008. "Counterparty Risk and the Pricing of Defaultable Securities," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 20, pages 481-515, World Scientific Publishing Co. Pte. Ltd..
    15. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    16. Jia-Wen Gu & Wai-Ki Ching & Tak-Kuen Siu & Harry Zheng, 2013. "On pricing basket credit default swaps," Quantitative Finance, Taylor & Francis Journals, vol. 13(12), pages 1845-1854, December.
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    Cited by:

    1. Puneet Pasricha & Dharmaraja Selvamuthu & Guglielmo D’Amico & Raimondo Manca, 2020. "Portfolio optimization of credit risky bonds: a semi-Markov process approach," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 6(1), pages 1-14, December.
    2. Feng-Hui Yu & Jiejun Lu & Jia-Wen Gu & Wai-Ki Ching, 2019. "Modeling Credit Risk with Hidden Markov Default Intensity," Computational Economics, Springer;Society for Computational Economics, vol. 54(3), pages 1213-1229, October.

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