Treasury Market as a Utility-Maximizer: A Novel Specialness Premia Specification and Regime Indicator

Though many research efforts examining the "specialness" phenomenon in the Treasury market have economically justified on-the-run premia with arguments of higher liquidity and lower search frictions, little work has been done to derive and illustrate no-arbitrage specifications for on-the-run premia, taking into account both existing Heath-Jarrow-Morton yield constraints and the dynamics of specialness. Using stochastic control and framing the special Treasury market itself as an agent that endogenously minimizes penalties and maximizes rewards associated with on-the-run premia, we derive a no-arbitrage SDE specification for on-the-run premia of zero-coupon-bonds (ZCBs) and a regime function that indicates the market's utility gain from a special issue's high liquidity. We empirically illustrate the derived specification through maximum likelihood estimation and statistical comparison with realized on-the-run premia.