On the Range of Admissible Term-Structures

Areski Cousin (1) , Ibrahima Niang (1)

1 SAF - Laboratoire de Sciences Actuarielle et Financière

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.

Mots clés: Term-structure construction methods; OIS discounting curves; credit curves; model risk; arbitrage-free bounds; affine term-structure models

Domaines: Finance quantitative [q-fin.CP]; Gestion des risques [q-fin.RM]

Areski Cousin, Ibrahima Niang. On the Range of Admissible Term-Structures. 2014. ⟨hal-00968943⟩