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A Markovian Defaultable Term Structure Model With State Dependent Volatilities

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  • CARL CHIARELLA

    ()
    (School of Finance and Economics, University of Technology, Sydney, PO Box 123, Broadway, NSW 2007, Australia)

  • CHRISTINA NIKITOPOULOS SKLIBOSIOS

    ()
    (School of Finance and Economics, University of Technology, Sydney, PO Box 123, Broadway, NSW 2007, Australia)

  • ERIK SCHLÖGL

    ()
    (School of Finance and Economics, University of Technology, Sydney, PO Box 123, Broadway, NSW 2007, Australia)

Abstract

The defaultable forward rate is modelled as a jump diffusion process within the Schönbucher [26,27] general Heath, Jarrow and Morton [20] framework where jumps in the defaultable term structure fd(t,T) cause jumps and defaults to the defaultable bond prices Pd(t,T). Within this framework, we investigate an appropriate forward rate volatility structure that results in Markovian defaultable spot rate dynamics. In particular, we consider state dependent Wiener volatility functions and time dependent Poisson volatility functions. The corresponding term structures of interest rates are expressed as finite dimensional affine realizations in terms of benchmark defaultable forward rates. In addition, we extend this model to incorporate stochastic spreads by allowing jump intensities to follow a square-root diffusion process. In that case the dynamics become non-Markovian and to restore path independence we propose either an approximate Markovian scheme or, alternatively, constant Poisson volatility functions. We also conduct some numerical simulations to gauge the effect of the stochastic intensity and the distributional implications of various volatility specifications.

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Bibliographic Info

Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

Volume (Year): 10 (2007)
Issue (Month): 01 ()
Pages: 155-202

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Handle: RePEc:wsi:ijtafx:v:10:y:2007:i:01:p:155-202

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Related research

Keywords: Defaultable HJM model; stochastic credit spreads; defaultable bond prices;

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References

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  1. Byström, Hans & Kwon, Oh Kang, 2003. "A Simple Continuous Measure of Credit Risk," Working Papers 2003:14, Lund University, Department of Economics, revised 18 Jan 2005.
  2. Carl Chiarella & Christina Sklibosios, 2003. "A Class of Jump-Diffusion Bond Pricing Models within the HJM Framework," Asia-Pacific Financial Markets, Springer, vol. 10(2), pages 87-127, September.
  3. Prigent, J.-L. & Renault, O. & Scaillet, O., 2000. "An Empirical Investigation in Credit Spread Indices," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2000028, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  4. Inui, Koji & Kijima, Masaaki, 1998. "A Markovian Framework in Multi-Factor Heath-Jarrow-Morton Models," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 33(03), pages 423-440, September.
  5. Ram Bhar & Carl Chiarella, 1995. "Transformation of Heath-Jarrow-Morton Models to Markovian Systems," Working Paper Series 53, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
  6. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
  7. Hiroshi Shirakawa, 1991. "Interest Rate Option Pricing With Poisson-Gaussian Forward Rate Curve Processes," Mathematical Finance, Wiley Blackwell, vol. 1(4), pages 77-94.
  8. Björk, Tomas & Gombani, Andrea, 1997. "Minimal Realizations of Forward Rates," Working Paper Series in Economics and Finance 182, Stockholm School of Economics.
  9. Jean -Luc Prigent & Olivier Renault & Olivier Scaillet, 2000. "An Empirical Investigation in Credit Spread Indices," Working Papers 2000-59, Centre de Recherche en Economie et Statistique.
  10. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
  11. Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, vol. 106(1), pages 27-65, January.
  12. Carl Chiarella & Oh Kwon, 2003. "Finite Dimensional Affine Realisations of HJM Models in Terms of Forward Rates and Yields," Review of Derivatives Research, Springer, vol. 6(2), pages 129-155, May.
  13. Tomas Björk & Yuri Kabanov & Wolfgang Runggaldier, 1997. "Bond Market Structure in the Presence of Marked Point Processes," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 211-239.
  14. Sarig, Oded & Warga, Arthur, 1989. " Some Empirical Estimates of the Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 44(5), pages 1351-60, December.
  15. To, Thuy Duong & Carl Chiarella, 2003. "The Jump Component of the Volatility Structure of Interest Rate Futures Markets: An International Comparison," Royal Economic Society Annual Conference 2003 205, Royal Economic Society.
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Citations

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Cited by:
  1. Carl Chiarella & Samuel Chege Maina & Christina Nikitopoulos-Sklibosios, 2010. "Markovian Defaultable HJM Term Structure Models with Unspanned Stochastic Volatility," Research Paper Series 283, Quantitative Finance Research Centre, University of Technology, Sydney.
  2. Nicola Bruti-Liberati & Christina Nikitopoulos-Sklibosios & Eckhard Platen & Erik Schlogl, 2009. "Alternative Defaultable Term Structure Models," Research Paper Series 242, Quantitative Finance Research Centre, University of Technology, Sydney.
  3. Laura Morino & Wolfgang J. Ruggaldier, 2014. "On multicurve models for the term structure," Science & Finance (CFM) working paper archive 1401.5431, Science & Finance, Capital Fund Management.
  4. Carl Chiarella & Samuel Chege Maina & Christina Nikitopoulos-Sklibosios, 2011. "Credit Derivative Pricing with Stochastic Volatility Models," Research Paper Series 293, Quantitative Finance Research Centre, University of Technology, Sydney.

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