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Pricing Options with Credit Risk in Markovian Regime‐Switching Markets

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Listed:
  • Jinzhi Li
  • Shixia Ma

Abstract

This paper investigates the valuation of European option with credit risk in a reduced form model when the stock price is driven by the so‐called Markov‐modulated jump‐diffusion process, in which the arrival rate of rare events and the volatility rate of stock are controlled by a continuous‐time Markov chain. We also assume that the interest rate and the default intensity follow the Vasicek models whose parameters are governed by the same Markov chain. We study the pricing of European option and present numerical illustrations.

Suggested Citation

  • Jinzhi Li & Shixia Ma, 2013. "Pricing Options with Credit Risk in Markovian Regime‐Switching Markets," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:621371
    DOI: 10.1155/2013/621371
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    References listed on IDEAS

    as
    1. Robert Elliott & Carlton-James Osakwe, 2006. "Option Pricing for Pure Jump Processes with Markov Switching Compensators," Finance and Stochastics, Springer, vol. 10(2), pages 250-275, April.
    2. 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.
    3. Robert J. Elliott & Carlton-James U. Osakwe, 2006. "Option Pricing for Pure Jump Processes with Markov Switching Compensators," Finance and Stochastics, Springer, vol. 10(2), pages 250-275, April.
    4. Robert J. Elliott & Leunglung Chan & Tak Kuen Siu, 2005. "Option pricing and Esscher transform under regime switching," Annals of Finance, Springer, vol. 1(4), pages 423-432, October.
    5. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
    6. Darrell Duffie & Nicolae Gârleanu, 2001. "Risk and Valuation of Collateralized Debt Obligations," Financial Analysts Journal, Taylor & Francis Journals, vol. 57(1), pages 41-59, January.
    7. Robert J. Elliott & William C. Hunter & Barbara M. Jamieson, 2001. "Financial Signal Processing: A Self Calibrating Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(04), pages 567-584.
    8. Philippe Artzner & Freddy Delbaen, 1995. "Default Risk Insurance And Incomplete Markets1," Mathematical Finance, Wiley Blackwell, vol. 5(3), pages 187-195, July.
    9. Klein, Peter & Inglis, Michael, 2001. "Pricing vulnerable European options when the option's payoff can increase the risk of financial distress," Journal of Banking & Finance, Elsevier, vol. 25(5), pages 993-1012, May.
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    Cited by:

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