Dynamic term structure models for SOFR futures

Skov, Jacob Bjerre; Skovmand, David

doi:10.1002/fut.22246

Cited by 24 publications

(16 citation statements)

References 31 publications

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“…Due to its affine structure, our model setup allows for an exact computation of the error induced by the continuous-time approximation. However, it is empirically shown in [SS21] that this approximation error is practically negligible.…”

Section: Model Setupmentioning

confidence: 99%

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Caplet pricing in affine models for alternative risk-free rates

Fontana¹

2022

Preprint

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Section: Model Setupmentioning

confidence: 99%

“…In the specific case of Gaussian affine diffusive models, the futures pricing formula stated in Proposition 5.2 reduces to the explicit formula utilized in the recent work [SS21].…”

Section: D\{0}mentioning

confidence: 99%

Caplet pricing in affine models for alternative risk-free rates

Fontana¹

2022

Preprint

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“…Lyashenko and Mercurio (2019) propose an extension to the LIBOR Market Model to accommodate the in-arrears setting nature of term rates related to SOFR and overnight benchmark rates in general. Skov and Skovmand (2020) show that a three-factor Gaussian arbitrage-free Nelson/Siegel model is well suited for the SOFR futures market, but they do not include the time series of SOFR itself in their estimation.…”

Section: Introductionmentioning

confidence: 98%

“…However, one could argue that this is because target rates are only updated in discrete increments. Our model could be extended to reflect this, but as a first approximation, we'll accept the implication of a continuous distribution of jump sizes for now, with jumps occurring at every FOMC meeting date.18 Note that the term (t − xi) appearing in the triple sum reflects a feature of a classical Gaussian term structure model without mean reversion (as noted, for example, inSchlögl and Sommer (1998)), that the term structure of forward rates endogenously steepens ever more (see also (28) above) as time passesthis can be avoided by introducing mean reversion.19Skov and Skovmand (2020) show that a three-factor Gaussian arbitrage-free Nelson/Siegel model is well suited for the SOFR futures market, but they do not include the time series of SOFR itself in their estimation, i.e., their objective is not to match the SOFR dynamics, which have a substantial piecewise flat component.…”

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confidence: 99%

Short Rate Dynamics: A Fed Funds and SOFR perspective

Gellert¹,

Schlögl²

2021

Preprint

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The Secured Overnight Funding Rate (SOFR) is becoming the main Risk-Free Rate benchmark in US dollars, thus interest rate term structure models need to be updated to reflect the key features exhibited by the dynamics of SOFR and the forward rates implied by SOFR futures. Historically, interest rate term structure modelling has been based on rates of substantially longer time to maturity than overnight, but with SOFR the overnight rate now is the primary market observable. This means that the empirical idiosyncrasies of the overnight rate cannot be ignored when constructing interest rate models in a SOFR-based world.As a rate reflecting transactions in the Treasury overnight repurchase market, the dynamics of SOFR are closely linked to the dynamics Effective Federal Funds Rate (EFFR), which is the interest rate most directly impacted by US monetary policy target rate decisions. Therefore, these rates feature jumps at known times (Federal Open Market Committee meeting dates), and market expectations of these jumps are reflected in prices for futures written on these rates. On the other hand, forward rates implied by Fed Funds and SOFR futures continue to evolve diffusively. The model presented in this paper reflects the key empirical features of SOFR dynamics and is calibrated to futures prices. In particular, the model reconciles diffusive forward rate dynamics with piecewise constant paths of the target short rate. † The authors thank Leif Andersen for helpful comments on a previous draft of this paper. The usual disclaimers apply.

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“…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. Always in a short-rate perspective, Rutkowski and Bickersteth (2021) propose a Vasiček joint model for SOFR and other reference rates and study the hedging of SOFR-based derivatives, also in the presence of funding costs and collateralization.…”

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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Dynamic term structure models for SOFR futures

Cited by 24 publications

References 31 publications

Caplet pricing in affine models for alternative risk-free rates

Caplet pricing in affine models for alternative risk-free rates

Short Rate Dynamics: A Fed Funds and SOFR perspective

Term structure modelling with overnight rates beyond stochastic continuity

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