  Due to the lack of reliable market information, building financial
term-structures may be associated with a significant degree of uncertainty. In
this paper, we propose a new term-structure interpolation method that extends
classical spline techniques by additionally allowing for quantification of
uncertainty. The proposed method is based on a generalization of kriging models
with linear equality constraints (market-fit conditions) and shape-preserving
conditions such as monotonicity or positivity (no-arbitrage conditions). We
define the most likely curve and show how to build confidence bands. The
Gaussian process covariance hyper-parameters under the construction constraints
are estimated using cross-validation techniques. Based on observed market
quotes at different dates, we demonstrate the efficiency of the method by
building curves together with confidence intervals for term-structures of OIS
discount rates, of zero-coupon swaps rates and of CDS implied default
probabilities. We also show how to construct interest-rate surfaces or default
probability surfaces by considering time (quotation dates) as an additional
dimension.
