We study liquidity and systemic risk in high-value payment systems. Flows in high-value systems are characterized by high velocity, meaning that the total amount paid and received is high relative to the stock of reserves. In such systems, banks rely heavily on incoming funds to finance outgoing payments, necessitating a high degree of coordination and synchronization. We use lattice-theoretic methods to solve for the unique fixed point of an equilibrium mapping and conduct comparative statics analyses on changes to the environment. We find that banks attempting to conserve liquidity cause an increase in the demand for intraday credit and, ultimately, a disruption of payments. Additionally, we find that when a bank is identified as vulnerable to failure and other banks choose to cancel payments to that bank, there are systemic repercussions for the whole financial system.