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Credit Derivatives Pricing With Stochastic Volatility Models

Author

Listed:
  • 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.

Suggested Citation

  • Carl Chiarella & Samuel Chege Maina & Christina Nikitopoulos Sklibosios, 2013. "Credit Derivatives Pricing With Stochastic Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(04), pages 1-28.
  • Handle: RePEc:wsi:ijtafx:v:16:y:2013:i:04:n:s0219024913500192
    DOI: 10.1142/S0219024913500192
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    References listed on IDEAS

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    1. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
    2. 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 1209-1227, July.
    3. repec:wsi:ijtafx:v:16:y:2013:i:04:n:s0219024913500192 is not listed on IDEAS
    4. Carl Chiarella & Christina Nikitopoulos Sklibosios & Erik Schlögl, 2007. "A Markovian Defaultable Term Structure Model With State Dependent Volatilities," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(01), pages 155-202.
    5. 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.
    6. 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.
    7. 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.
    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. 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.
    10. Carl Chiarella & Samuel Chege Maina & Christina Nikitopoulos Sklibosios, 2013. "Credit Derivatives Pricing With Stochastic Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(04), pages 1-28.
    11. Philipp J. Schonbucher, 1997. "Team Structure Modelling of Defaultable Bonds," FMG Discussion Papers dp272, Financial Markets Group.
    12. 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.
    13. 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..
    14. 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.
    15. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 5.
    16. Li Chen & Damir Filipovic, 2003. "Credit Derivatives in an Affine Framework," Finance 0307002, University Library of Munich, Germany.
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    Cited by:

    1. Carl Chiarella & Samuel Chege Maina & Christina Nikitopoulos Sklibosios, 2013. "Credit Derivatives Pricing With Stochastic Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(04), pages 1-28.
    2. Fanelli, Viviana, 2016. "A defaultable HJM modelling of the Libor rate for pricing Basis Swaps after the credit crunch," European Journal of Operational Research, Elsevier, vol. 249(1), pages 238-244.

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