Affiliation:
1. Department of Mathematics “Tullio Levi‐Civita” University of Padova Padova Italy
2. Laboratoire de Probabilités, Statistique et Modélisation Paris Cité University Paris France
3. Albert‐Ludwigs University of Freiburg Freiburg Germany
Abstract
AbstractOvernight 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.
Funder
Università degli Studi di Padova
Subject
Applied Mathematics,Economics and Econometrics,Social Sciences (miscellaneous),Finance,Accounting
Cited by
1 articles.
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