Affine arbitrage-free yield net models with application to the euro debt crisis

We develop a parsimonious class of affine arbitrage-free yield net models for consistent bond pricing across maturities and issuers of different risk levels. Containing a core curve and multiple peripheral curves, the yield net is spanned by three layers of factors: base factors spanning all curves, and common and individual spread factors. Under the arbitrage-free assumption, we prove a parsimonious solution to the risk-neutral process that guarantees joint identification of parameters and latent states. By using a Bayesian estimation method with a marginal Metropolis-Hastings algorithm and specification tests based on MCMC output, we apply the model to weekly treasury yields of Germany, Italy, Spain, and Greece from 2009 to 2016. The results show that the extracted common credit risk is a level factor in spread, and market liquidity risk is a slope factor. Further, the net structure helps reconstruct the Greek yield curve even with only its 10-year yield available throughout the sample.