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Calibrating probability distributions with convex-concave-convex functions: application to CDO pricing

Author

Listed:
  • Alexander Veremyev

    ()

  • Peter Tsyurmasto

    ()

  • Stan Uryasev

    ()

  • R. Rockafellar

    ()

Abstract

This paper considers a class of functions referred to as convex-concave-convex (CCC) functions to calibrate unimodal or multimodal probability distributions. In discrete case, this class of functions can be expressed by a system of linear constraints and incorporated into an optimization problem. We use CCC functions for calibrating a risk-neutral probability distribution of obligors default intensities (hazard rates) in collateral debt obligations (CDO). The optimal distribution is calculated by maximizing the entropy function with no-arbitrage constraints given by bid and ask prices of CDO tranches. Such distribution reflects the views of market participants on the future market environments. We provide an explanation of why CCC functions may be applicable for capturing a non-data information about the considered distribution. The numerical experiments conducted on market quotes for the iTraxx index with different maturities and starting dates support our ideas and demonstrate that the proposed approach has stable performance. Distribution generalizations with multiple humps and their applications in credit risk are also discussed. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Alexander Veremyev & Peter Tsyurmasto & Stan Uryasev & R. Rockafellar, 2014. "Calibrating probability distributions with convex-concave-convex functions: application to CDO pricing," Computational Management Science, Springer, vol. 11(4), pages 341-364, October.
  • Handle: RePEc:spr:comgts:v:11:y:2014:i:4:p:341-364
    DOI: 10.1007/s10287-013-0176-4
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    References listed on IDEAS

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    1. Monteiro, Ana Margarida & Tutuncu, Reha H. & Vicente, Luis N., 2008. "Recovering risk-neutral probability density functions from options prices using cubic splines and ensuring nonnegativity," European Journal of Operational Research, Elsevier, vol. 187(2), pages 525-542, June.
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    6. Bhupinder Bahra, 1997. "Implied risk-neutral probability density functions from option prices: theory and application," Bank of England working papers 66, Bank of England.
    7. Miller, Douglas J. & Liu, Wei-han, 2002. "On the recovery of joint distributions from limited information," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 259-274, March.
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