论文标题
术语结构建模，其隔夜速率超出随机连续性
Term structure modelling with overnight rates beyond stochastic continuity
论文作者
论文摘要
在美国的隔夜利率（例如SOFR（获得过夜融资率））对于当前利率基准改革至关重要。通宵费率的一个惊人特征是由于货币政策干预措施和流动性限制，在预定日期存在跳跃和峰值的存在。这对应于动力学中的随机不连续性（即发生在已知的时间点上的不连续性）。在这项工作中，我们提出了一个基于隔夜费率的术语结构建模框架，并表征了广义的希思·贾罗 - 摩尔顿（HJM）设置中的套利。我们扩展了经典的短期方法，以适应随机不连续性，从而开发出由仿射半明星驱动的可拖动设置。在这种情况下，我们表明，简单的规格允许捕获过夜费率跳跃行为的风格化事实。在高斯环境中，我们为债券和胶囊提供明确的估值公式。此外，当潜在的术语结构具有随机不连续性时，我们会根据局部风险最小化的意义研究对冲。
Overnight rates, such as the SOFR (Secured Overnight Financing Rate) in the US, 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 modelling framework based on overnight rates and characterize absence of arbitrage in a generalised 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.
