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Credit Derivatives Pricing With Stochastic Volatility Models

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Author Info

  • CARL CHIARELLA

    ()
    (Finance Discipline Group, UTS Business School, University of Technology, Sydney, P.O. Box 123, Broadway, NSW 2007, Australia)

  • SAMUEL CHEGE MAINA

    ()
    (E.ON Energy Trading SE, Holzstrasse 6, 40221 Dusseldorf, Germany)

  • CHRISTINA NIKITOPOULOS SKLIBOSIOS

    ()
    (Finance Discipline Group, UTS Business School, University of Technology, Sydney, P.O. Box 123, Broadway, NSW 2007, Australia)

Abstract

This paper proposes a model for pricing credit derivatives in a defaultable HJM framework. The model features hump-shaped, level dependent, and unspanned stochastic volatility, and accommodates a correlation structure between the stochastic volatility, the default-free interest rates, and the credit spreads. The model is finite-dimensional, and leads (a) to exponentially affine default-free and defaultable bond prices, and (b) to an approximation for pricing credit default swaps and swaptions in terms of defaultable bond prices with varying maturities. A numerical study demonstrates that the model captures stylized various features of credit default swaps and swaptions.

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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): 16 (2013)
Issue (Month): 04 ()
Pages: 1350019-1-1350019-28

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Handle: RePEc:wsi:ijtafx:v:16:y:2013:i:04:p:1350019-1-1350019-28

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Related research

Keywords: Stochastic volatility; Heath–Jarrow–Morton framework; defaultable bond prices; credit spreads; CDS rates;

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References

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  1. 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.
  2. 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.
  3. Carl Chiarella & Erik Schlögl & Christina Nikitopoulos-Sklibosios, 2004. "A Markovian Defaultable Term Structure Model with State Dependent Volatilities," Research Paper Series 135, Quantitative Finance Research Centre, University of Technology, Sydney.
  4. Philipp J. Schonbucher, 1997. "Team Structure Modelling of Defaultable Bonds," FMG Discussion Papers dp272, Financial Markets Group.
  5. Casassus, Jaime & Collin-Dufresne, Pierre & Goldstein, Bob, 2005. "Unspanned stochastic volatility and fixed income derivatives pricing," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2723-2749, November.
  6. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
  7. Chiarella, Carl & Fanelli, Viviana & Musti, Silvana, 2011. "Modelling the evolution of credit spreads using the Cox process within the HJM framework: A CDS option pricing model," European Journal of Operational Research, Elsevier, vol. 208(2), pages 95-108, January.
  8. Carl Chiarella & Oh-Kang Kwon, 2000. "A Class of Heath-Jarrow-Morton Term Structure Models with Stochastic Volatility," Research Paper Series 34, Quantitative Finance Research Centre, University of Technology, Sydney.
  9. Mascia Bedendo & Lara Cathcart & Lina El-Jahel, 2007. "The Slope Of The Term Structure Of Credit Spreads: An Empirical Investigation," Journal of Financial Research, Southern Finance Association & Southwestern Finance Association, vol. 30(2), pages 237-257.
  10. Robert A. Jarrow, 2001. "Counterparty Risk and the Pricing of Defaultable Securities," Journal of Finance, American Finance Association, vol. 56(5), pages 1765-1799, October.
  11. 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.
  12. Chan, K C, et al, 1992. " An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-27, July.
  13. Li Chen & Damir Filipovic, 2003. "Credit Derivatives in an Affine Framework," Finance 0307002, EconWPA.
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