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On the Range of Admissible Term-Structures

Author

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  • Areski Cousin

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

  • Ibrahima Niang

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

Abstract

In this paper, we analyze the diversity of term structure functions (e.g., yield curves, swap curves, credit curves) constructed in a process which complies with some admissible properties: arbitrage-freeness, ability to fit market quotes and a certain degree of smoothness. When present values of building instruments are expressed as linear combinations of some primary quantities such as zero-coupon bonds, discount factor, or survival probabilities, arbitrage-free bounds can be derived for those quantities at the most liquid maturities. As a matter of example, we present an iterative procedure that allows to compute model-free bounds for OIS-implied discount rates and CDS-implied default probabilities. We then show how mean-reverting term structure models can be used as generators of admissible curves. This framework is based on a particular specification of the mean-reverting level which allows to perfectly reproduce market quotes of standard vanilla interest-rate and default-risky securities while preserving a certain degree of smoothness. The numerical results suggest that, for both OIS discounting curves and CDS credit curves, the operational task of term-structure construction may be associated with a significant degree of uncertainty.

Suggested Citation

  • Areski Cousin & Ibrahima Niang, 2014. "On the Range of Admissible Term-Structures," Working Papers hal-00968943, HAL.
    • Handle: RePEc:hal:wpaper:hal-00968943
    Note: View the original document on HAL open archive server: https://hal.science/hal-00968943
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    References listed on IDEAS

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    Cited by:

    1. François Bachoc & Emile Contal & Hassan Maatouk & Didier Rullière, 2017. "Gaussian processes for computer experiments," Post-Print hal-01665936, HAL.

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