A search-based theory of the on-the-run phenomenon

We propose a model in which assets with identical cash flows can trade at different prices. Agents enter into an infinite-horizon, steady-state market to establish long or short positions. Both the spot and the asset-lending market operate through search. Short-sellers can endogenously concentrate in one asset because of search externalities and the constraint that they must deliver the asset they borrowed. As a result, that asset enjoys both greater liquidity, measured by search times, and a higher lending fee ("specialness"). Liquidity and specialness translate into price premia that are consistent with no-arbitrage. We derive closed-form solutions for small frictions, and can generate price differentials in line with observed on-the-run premia.