Stochastics and Finance: Fontana -- Term structure modeling with overnight rates beyond stochastic continuity

Dear All, 

Welcome to the Stochastics and Finance seminar this semester! We will resume next week;
talks’ details will be updated on the website.  On Wednesday March 30 at 8pm Claudio
Fontana will give a talk via Zoom.  

Zoom link: https://uni-sydney.zoom.us/j/89793072039 

Speaker: Claudio Fontana (University of Padova) 

Title: Term structure modeling with overnight rates beyond stochastic continuity 

Abstract: In the current reform of interest rate benchmarks, a central role is played by
risk-free rates (RFRs), such as SOFR (secured overnight financing rate) in the US.  A
key feature of RFRs is the presence of jumps and spikes at periodic time intervals as a
result of regulatory and liquidity constraints.  This corresponds to stochastic
discontinuities (i.e., jumps occurring at predetermined dates) in the dynamics of RFRs.
In this work, we propose a general modelling framework where RFRs and term rates can
have stochastic discontinuities and characterize absence of arbitrage in an extended HJM
setup.  When the term rate is generated by the RFR itself, we show that it solves a
BSDE, whose driver is determined by the HJM drift restrictions.  We develop a tractable
specification driven by affine semimartingales, also extending the classical short rate
approach to the case of stochastic discontinuities.  In this context, we show that a
simple specification allows to capture stylized facts of the jump behavior of overnight
rates.  In a Gaussian setting, we provide explicit valuation formulas for bonds and
caplets.  Finally, we study hedging in the sense of local risk-minimization when the
underlying term structures have stochastic discontinuities.  Based on joint work with
Zorana Grbac and Thorsten Schmidt.
https://www.maths.usyd.edu.au/u/SemConf/Stochastics_Finance/seminar.html 

Please feel free to forward this message to anyone who might be interested in this
talk.  

Kind regards, Anna