Term structure modeling with overnight rates beyond stochastic continuity
针对隔夜利率在预定日期出现跳跃和尖峰的特征，提出了一个广义HJM框架下的期限结构模型，引入仿射半鞅处理随机不连续性，并给出了债券和上限期权的定价公式及局部风险最小化对冲方法。
Abstract Overnight rates, such as the Secured Overnight Financing Rate (SOFR) in the United States, are central to the current reform of interest rate benchmarks. A striking feature of overnight rates is the presence of jumps and spikes occurring at predetermined dates due to monetary policy interventions and liquidity constraints. This corresponds to stochastic discontinuities (i.e., discontinuities occurring at ex ante known points in time) in their dynamics. In this work, we propose a term structure modeling framework based on overnight rates and characterize absence of arbitrage in a generalized Heath–Jarrow–Morton (HJM) setting. We extend the classical short‐rate approach to accommodate stochastic discontinuities, developing a tractable setup driven by affine semimartingales. In this context, we show that simple specifications allow to capture stylized facts of the jump behavior of overnight rates. In a Gaussian setting, we provide explicit valuation formulas for bonds and caplets. Furthermore, we investigate hedging in the sense of local risk‐minimization when the underlying term structures feature stochastic discontinuities.