The recent financial crisis has shown that liquidity risk is far more important and intricate than regulators had previously acknowledged. The shift from bank-based to market-based financial systems and from deferred net settlement systems to liquidity-demanding real-time gross settlement of payments explains some of the shortcomings of traditional liquidity risk management. Although liquidity regulations do exist, they are still in an early stage of development and discussion. Moreover, not all connotations of liquidity are being equally addressed. Unlike market and funding liquidity, intraday liquidity has been absent from financial regulation, and has appeared only recently, after the crisis. This paper addresses the measurement of large-value payment system intraday liquidity risk. Based on the generation of bivariate Poisson random numbers for simulating the minute-by-minute arrival of received and executed payments, each financial institution's intraday payments' time-varying volume and degree of synchrony (ie, timing) is modeled. Modeling the uncertainty of intraday payments allows us to oversee participants' intraday behavior, to assess their ability to fulfill intraday payments at a certain confidence level, to identify participants that are nonresilient to changes in payment timing mismatches, and to estimate intraday liquidity buffers. These results are useful for financial authorities and institutions given the increased importance of liquidity risk as a source of systemic risk, and the recent regulatory amendments.