Sequential arbitrage measurement in bond markets : theory and empirical applications in the Euro-zone

We develop a mathematical programing approach in order to measure the arbitrage size in bond markets. Transaction costs may be incorporated. The obtained arbitrage measures have two interesting interpretations: On the one hand they provide the highest available arbitrage profit with respect to the price of the sold (bought) securities. On the other hand they give the minimum relative (per dollar) bid (ask) price modification leading to an arbitrage free market. Moreover, some primal problems lead to optimal arbitrage strategies (if available), while their dual problems generate proxies for the Term Structure of Interest Rates. The developed methodology permits us to implement an empirical test in the Euro-zone during the Euro crisis. Classical literature justifies the relevance of empirical analyses verifying the degree of efficiency during market turmoils. Our empirical study of the German, French and Spanish sovereign bonds markets finds that the main arbitrage opportunities come from the price differences between maturity-matched strips or "On-The-Run Premium" for zero-coupon bonds. When we remove the strips and the zero-coupon bonds the arbitrage still exists in the Spanish market.