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

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  • 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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    Cited by:

    1. Ba Chu & Stephen Satchell, 2016. "Recovering the Most Entropic Copulas from Preliminary Knowledge of Dependence," Econometrics, MDPI, vol. 4(2), pages 1-21, March.

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