An Arbitrage-Free Yield Net Model with Application to the Euro Debt Crisis

Abstract

We develop a parsimonious arbitrage-free yield net model for consistent bond pricing across maturities and issuers. Containing a core curve and multiple periphery curves, the yield net is spanned by three layers of factors: base factors spanning all curves, common spread factors spanning all periphery yield spreads, and specific factors each spanning yield spreads of a periphery issuer. Under the arbitrage-free assumption, we prove a parsimonious solution to the risk-neutral process that guarantees strong identification on the latent risk factors and parameters. We apply the model to Treasury yields of Germany and GIIPS countries from 2009 to 2016. The model fits data remarkably well and disentangles the common credit risk, market liquidity risk, and country-specific risks. The results demonstrate that relative risk pricing determines signs and magnitudes of the "flight to liquidity" effect and spillover effects among bonds of different issuers.