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Market Models of Forward CDS Spreads

  • Libo Li
  • Marek Rutkowski
Conference paper
Part of the Progress in Probability book series (PRPR, volume 65)

Abstract

The paper re-examines and generalizes the construction of several variants of market models for forward CDS spreads, as first presented by Brigo [10]. We compute explicitly the joint dynamics for some families of forward CDS spreads under a common probability measure. We first examine this problem for single-period CDS spreads under certain simplifying assumptions. Subsequently, we derive, without any restrictions, the joint dynamics under a common probability measure for the family of one- and two-period forward CDS spreads, as well as for the family of one-period and co-terminal forward CDS spreads. For the sake of generality, we work throughout within a general semimartingale framework.

Keywords

Credit default swap market model LIBOR 

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References

  1. 1.
    T.R. Bielecki and M. Rutkowski: Credit Risk: Modeling, Valuation and Hedging. Springer-Verlag, Berlin Heidelberg New York, 2002.Google Scholar
  2. 2.
    T.R. Bielecki, M. Jeanblanc and M. Rutkowski: Pricing and trading credit default swaps in a hazard process model. Annals of Applied Probability 18 (2008), 2495–2529.MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    T.R. Bielecki, M. Jeanblanc and M. Rutkowski: Hedging of a credit default swaption in the CIR default intensity model. Forthcoming in Finance and Stochastics.Google Scholar
  4. 4.
    T.R. Bielecki, M. Jeanblanc and M. Rutkowski: Credit Risk Modeling. Osaka University, CSFI Lecture Notes Series 02, Osaka University Press, 2009.Google Scholar
  5. 5.
    A. Brace: Engineering BGM. Chapman and Hall/CRC, Financial Mathematics Series, 2008.Google Scholar
  6. 6.
    A. Brace, D. G,atarek, and M. Musiela: The market model of interest rate dynamics. Mathematical Finance 7 (1997), 127–154.Google Scholar
  7. 7.
    P. Brémaud and M. Yor: Changes of filtrations and of probability measures. Z. für Wahrscheinlichkeitstheorie verw. Gebiete 45 (1978), 269–295.Google Scholar
  8. 8.
    D. Brigo: Market models for CDS options and callable floaters. Risk Magazine January (2005) (reprinted in: Derivatives Trading and Option Pricing, N. Dunbar, ed., Risk Books, 2005).Google Scholar
  9. 9.
    D. Brigo: Constant maturity CDS valuation with market models. Risk Magazine June (2006).Google Scholar
  10. 10.
    D. Brigo: CDS options through candidate market models and the CDS-calibrated CIR++ stochastic intensity model. In: Credit Risk: Models, Derivatives and Management, N. Wagner, ed., Chapman & Hall/CRC Financial Mathematics Series, 2008Google Scholar
  11. 11.
    pp. 393–426.Google Scholar
  12. 12.
    D. Brigo and M. Morini: CDS market formulas and models. Working paper, Banca IMI, 2005.Google Scholar
  13. 13.
    D. Brigo and F. Mercurio: Interest Rate Models. Theory and Practice – with Smile, Inflation and Credit. Second Edition. Springer-Verlag, Berlin Heidelberg New York, 2006.Google Scholar
  14. 14.
    T. Choulli, L. Krawczyk, and C. Stricker: E -martingales and their applications in mathematical finance. Annals of Probability 26 (1998), 853–876.MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    S. Galluccio, J.-M. Ly, Z. Huang, and O. Scaillet: Theory and calibration of swap market models. Mathematical Finance 17 (2007), 111–141.MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    J. Jacod and M. Yor: Etude des solutions extrémales et représentation intégrale des solutions pour certains probl`emes de martingales. Zeitschrift für Wahrscheinlichkeitstheorie und vervandte Gebiete 38 (1977), 83–125.Google Scholar
  17. 17.
    F. Jamshidian: LIBOR and swap market models and measures. Finance and Stochastics 1 (1997), 293–330.zbMATHCrossRefGoogle Scholar
  18. 18.
    F. Jamshidian: LIBOR market model with semimartingales. Working paper, NetAnalytic Limited, 1999.Google Scholar
  19. 19.
    F. Jamshidian: Valuation of credit default swaps and swaptions. Finance and Stochastics 8 (2004), 343–371.MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    M. Jeanblanc, M. Yor, and M. Chesney: Mathematical Methods for Financial Markets. Springer-Verlag, Berlin Heidelberg New York, 2009.Google Scholar
  21. 21.
    C. Lotz and L. Schlögl: Default risk in a market model. Journal of Banking and Finance 24 (2000), 301–327.Google Scholar
  22. 22.
    L. Li and M. Rutkowski: Admissibility of generic market models of forward swap rates. Working paper, University of Sydney, 2009.Google Scholar
  23. 23.
    M. Morini and D. Brigo: No-armageddon arbitrage-free equivalent measure for index options in a credit crisis. Forthcoming in Mathematical Finance.Google Scholar
  24. 24.
    M. Musiela and M. Rutkowski: Continuous-time term structure models: forward measure approach. Finance and Stochastics 1 (1997), 261–291.zbMATHCrossRefGoogle Scholar
  25. 25.
    M. Musiela and M. Rutkowski: Martingale Methods in Financial Modelling. Second Edition. Corrected 2nd printing. Springer-Verlag, Berlin Heidelberg New York, 2007.Google Scholar
  26. 26.
    R. Pietersz and M. van Regenmortel: Generic market models. Finance and Stochastics 10 (2006), 507–528.MathSciNetzbMATHCrossRefGoogle Scholar
  27. 27.
    M. Rutkowski: Models of forward Libor and swap rates. Applied Mathematical Finance 6 (1999), 1–32.MathSciNetCrossRefGoogle Scholar
  28. 28.
    Options on credit default swaps and credit default indexes. In: Credit Risk Frontiers: Subprime Crisis, Pricing and Hedging, CVA, MBS, Ratings and Liquidity, T.R. Bielecki, D. Brigo and F. Patras, eds., J. Wiley, 2010, 219–282.Google Scholar
  29. 29.
    M. Rutkowski and A. Armstrong: Valuation of credit default swaptions and credit default index swaptions. International Journal of Theoretical and Applied Finance 12 (2009), 1027–1053. [29] L. Schlögl: Note on CDS market models. Working paper, 2007.Google Scholar
  30. 30.
    P.J. Schönbucher: A Libor market model with default risk.Working paper, University of Bonn, 2000.Google Scholar
  31. 31.
    A.N. Shiryaev and A.S. Cherny: Vector stochastic integrals and the fundamental theorems of asset pricing. Proceedings of the Steklov Institute of Mathematics 237 (2002), 6–49.Google Scholar

Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUniversity of SydneySydneyAustralia

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