隔夜利率超过随机连续性的期限结构建模

IF 1.6 3区 经济学 Q3 BUSINESS, FINANCE Mathematical Finance Pub Date : 2023-08-18 DOI:10.1111/mafi.12415
Claudio Fontana, Zorana Grbac, Thorsten Schmidt
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引用次数: 0

摘要

隔夜利率,如美国的隔夜担保融资利率(SOFR),是当前利率基准改革的核心。隔夜利率的一个显著特征是,由于货币政策干预和流动性限制,在预定日期出现跳跃和飙升。这对应于其动力学中的随机不连续性(即,在预先已知的时间点发生的不连续性)。在这项工作中,我们提出了一个基于隔夜利率的期限结构建模框架,并描述了广义Heath–Jarrow–Morton(HJM)环境中不存在套利的特征。我们扩展了经典的短速率方法以适应随机不连续性,开发了一个由仿射半鞅驱动的可处理设置。在这种情况下,我们展示了简单的规范允许捕捉隔夜利率跳跃行为的程式化事实。在高斯设置中,我们提供了债券和caplets的显式估值公式。此外,当潜在的期限结构具有随机不连续性时,我们研究了局部风险最小化意义上的套期保值。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

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Term structure modeling with overnight rates beyond stochastic continuity

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.

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来源期刊
Mathematical Finance
Mathematical Finance 数学-数学跨学科应用
CiteScore
4.10
自引率
6.20%
发文量
27
审稿时长
>12 weeks
期刊介绍: Mathematical Finance seeks to publish original research articles focused on the development and application of novel mathematical and statistical methods for the analysis of financial problems. The journal welcomes contributions on new statistical methods for the analysis of financial problems. Empirical results will be appropriate to the extent that they illustrate a statistical technique, validate a model or provide insight into a financial problem. Papers whose main contribution rests on empirical results derived with standard approaches will not be considered.
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