  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 smooth- ness. When present values of
building instruments are expressed as linear combinations of some primary
quantities such as zero-coupon bonds, discount factor, or survival probabilit-
ies, 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 al-
lows 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.
