On the Range of Admissible Term-Structures

Areski Cousin () and Ibrahima Niang
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Areski Cousin: LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon
Ibrahima Niang: LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon

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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.

Keywords: Term-structure construction methods; OIS discounting curves; credit curves; model risk; arbitrage-free bounds; affine term-structure models (search for similar items in EconPapers)
Date: 2014-04-01
New Economics Papers: this item is included in nep-ger
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