Titre : Overnight rates and term structure modeling beyond stochastic continuity
Abstract : Overnight rates, such as the Secured Overnight Financing Rate (SOFR), are central in the current reform of interest rate benchmarks. A specific feature of overnight rates is the presence of jumps and spikes occurring at predetermined dates, mainly due to monetary policy interventions. This corresponds to stochastic discontinuities in their dynamics. We propose a generalized Heath-Jarrow-Morton (HJM) setup allowing for stochastic discontinuities and characterize absence of arbitrage. We extend the classical short-rate approach to accommodate stochastic discontinuities, developing a tractable setup driven by affine semimartingales. 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. Based on joint work with Z. Grbac and T. Schmidt.
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