Caplet Pricing with Backward-Looking Rates

Turfus, Colin

doi:10.2139/ssrn.3527091

Cited by 5 publications

(3 citation statements)

References 10 publications

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“…Classical short-rate models have been revisited in the post-Libor universe by several authors, starting from Mercurio (2018). Several recent works employ the classical Hull-White model (see, e.g., Hofman (2020), Turfus (2020), Hasegawa (2021)). Always in a short-rate setup, Skov and Skovmand (2021) propose a multifactor Gaussian model in order to analyze SOFR futures, while Fontana (2023) develops a model driven by general affine processes in view of pricing applications.…”

Section: Related Literaturementioning

confidence: 99%

Term structure modeling with overnight rates beyond stochastic continuity

Fontana,

Grbac,

Schmidt

2023

Mathematical Finance

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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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Section: Related Literaturementioning

confidence: 99%

Term structure modeling with overnight rates beyond stochastic continuity

Fontana,

Grbac,

Schmidt

2023

Mathematical Finance

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“…In this direction, one of the first contributions is Mercurio (2018), who develops a short rate model for SOFR by adding a deterministic spread to the OIS rate. The Hull-White model has been applied to RFRs in Hofman (2020) and Turfus (2020). More recently, Skov and Skovmand (2021) have proposed a multi-factor Gaussian short-rate model in order to describe the SOFR futures market, while Fontana (2022) formulates a short-rate model for RFRs based on a general affine process in view of pricing applications.…”

Section: Introductionmentioning

confidence: 99%

Term structure modelling with overnight rates beyond stochastic continuity

Fontana,

Grbac,

Schmidt

2022

Preprint

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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. In general, this BSDE may admit multiple solutions and we provide sufficient conditions ensuring uniqueness. 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.

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“…In recent short-rate approaches to RFR modeling, the Hull-White model has remained dominant. This is for instance the case of [Has21,Hof20,Tur21,Xu22], where pricing formulae for backwardlooking caplets are derived 3 , and also of [RB21], where in addition collateralization and funding costs are taken into account. However, the Hull-White model does not support volatility smiles (see, e.g., [Pit20]).…”

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confidence: 99%