Abstracts

In this paper, we analyze the set of term-structure curves (interest-rate or credit term-structures) which are perfectly compatible with market quotes (interest-rate products or CDS spreads) and which do not generate any arbitrage opportunity. We first provide AOA bounds for spot interest rates and risk-neutral default probabilities at the most liquid maturities. We then show how mean-reverting affine term-structure models can be used to assess model risk embedded in yield curve construction methods. This framework is based on a piecewise-constant specification of the long-term mean parameter which allows to perfectly reproduce market price of standard vanilla IR and CDS products. Two particular families of affine term-structure models are investigated: OU driven by Lévy processes and CIR processes. We give conditions on the implied parameters for the model to be free of arbitrage opportunity. Finally, we propose a mathematical tool based on Sobol indices to study the contribution of each parameter on the term-structure uncertainty. As for IR curves, illustrations are provided in a single-curve and in a multi-curve environment. We also show how this methodology can be used to study model risk in the assessment of counterparty risk, where risk-neutral default distribution has been stripped from CDS spreads at several standard maturities.