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SOFR derivatives market remains illiquid and incomplete so it is not amenable to classical risk-neutral term structure models which are based on the assumption of perfect liquidity and completeness. This paper develops a statistical SOFR term structure model that is well-suited for risk management and derivatives pricing within the incomplete markets paradigm. The model incorporates relevant macroeconomic factors tha…
The LIBOR rate is currently scheduled for discontinuation, and the replacement advocated by regulators in the US is the Secured Overnight Financing Rate (SOFR). The change has the potential to disrupt the $200 trillion market of derivatives and debt tied to the LIBOR. The only SOFR linked derivative with any significant liquidity and trading history is the SOFR futures contract, traded at the CME since 2018. We use t…
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 …
In this paper, we propose a semi-analytical approach to pricing options on SOFR futures where the underlying SOFR follows a time-dependent CEV model. By definition, these options change their type at the beginning of the reference period: before this time, this is an American option written on a SOFR forward price as an underlying, and after this point, this is an arithmetic Asian option with an American style exerci…
We introduce a perturbative formalism to solve the backward-looking futures pricing problem. The formalism is based on a time-ordered exponential series which allows to derive the functional form of the integral kernel associated to the backward-Kolmogorov diffusion PDE. We present an analytic pricing formula for SOFR futures contracts under an extension of the Hull-White model which incorporates not only the intrins…
The LIBOR has served since the 1970s as a fundamental measure for floating term rates across multiple currencies and maturities. However, in 2017 the Financial Conduct Authority announced the discontinuation of LIBOR from the end of 2021 and the New York Fed declared the Treasury repo financing rate, called the Secured Overnight Financing Rate (SOFR), as a candidate for a new reference rate for interest rate swaps de…
The financial industry has undergone a significant transition from the London Interbank Offered Rates (LIBORs) to Risk Free Rates (RFRs) such as, e.g., the Secured Overnight Financing Rate (SOFR) in the U.S. and the Cash Rate (AONIA) in Australia, as primary benchmark rates for borrowing costs. The paper examines the pricing and hedging method for financial products in a cross-currency framework with the special emph…
Overnight rates, such as the SOFR (Secured Overnight Financing Rate) in the US, 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…
With the reform of interest rate benchmarks, interbank offered rates (IBORs) like LIBOR have been replaced by risk-free rates (RFRs), such as the Secured Overnight Financing Rate (SOFR) in the U.S. and the Euro Short-Term Rate (\euro STR) in Europe. These rates exhibit characteristics like jumps and spikes that correspond to specific market events, driven by regulatory and liquidity constraints. To capture these char…
In the LIBOR era, banks routinely tied revolving credit facilities to credit-sensitive benchmarks. This study assesses the Across-the-Curve Credit Spread Index (AXI) -- a transparent, transaction-based measure of wholesale bank funding costs -- as a complement to SOFR, summarizing its behavior, construction, and loan-pricing implications. AXI aggregates observable unsecured funding transactions across short- and long…
We provide a general HJM framework for forward contracts written on abstract market indices with arbitrary fixing and payment adjustments, and featuring collateralization in any currency denominations. In view of this, we first provide a thorough study of cross-currency markets in the presence of collateral and incompleteness. Then we give a general treatment of collateral dislocations by describing the instantaneous…
Applying historical data from the USD LIBOR transition period, we estimate a joint model for SOFR, Fed Funds, and Eurodollar futures rates as well as spot USD LIBOR and term repo rates. The framework endogenously models basis spreads between each of the benchmark rates and allows for the decomposition of spreads. Modelling the LIBOR-OIS spread as credit and funding-liquidity roll-over risk, we find that the spike in …
The role of collateral in derivative pricing has evolved beyond credit risk mitigation, particularly following the global financial crisis, when funding costs and basis spreads became central to valuation practices. This development coincided with the transition from the London Interbank Offered Rate (LIBOR) to risk-free rates (RFRs) and the increasing standardization of collateralised trading. We study the valuation…
In this paper, we present an alternative perspective on the mean-field LIBOR market model introduced by Desmettre et al. in arXiv:2109.10779. Our novel approach embeds the mean-field model in a classical setup, but retains the crucial feature of controlling the term rate's variances over large time horizons. This maintains the market model's practicability, since calibrations and simulations can be carried out effici…
SOFR is the Secured Overnight Financing Rate, a key benchmark for U.S. dollar funding based on overnight Treasury repo transactions.
SOFR Rate (Rates).
SOFR Futures (Rates).
SOFR Transition Basis — Spread and convexity differences from LIBOR to SOFR products.
Eurodollar Legacy Futures — Legacy LIBOR STIR futures superseded by SOFR contracts.
SOFR Futures Strip (Rates).
SOFR Path 1M (Rates).
SOFR Path 3M (Rates).
SOFR Path 6M (Rates).
SOFR Path 1Y (Rates).
SOFR Path 2Y (Rates).
SOFR Path 5Y (Rates).
SOFR Path 7Y (Rates).
SOFR Path 10Y (Rates).
SOFR Path 20Y (Rates).
SOFR Path 30Y (Rates).
SOFR Path front (Rates).
SOFR Path belly (Rates).
SOFR Path long-end (Rates).
SOFR Path ultra-long (Rates).
SOFR Path Fed (Rates).
SOFR Path ECB (Rates).
SOFR Path BoE (Rates).
SOFR Path BoJ (Rates).
SOFR Path PBoC (Rates).
SOFR Path RBA (Rates).
SOFR Path BoC (Rates).
Eurodollar Legacy Futures — Legacy LIBOR STIR futures superseded by SOFR contracts.
SOFR is the Secured Overnight Financing Rate, a key benchmark for U.S. dollar funding based on overnight Treasury repo transactions.
SOFR Futures (Rates).
SOFR Futures Strip (Rates).
SOFR Path 10Y (Rates).
SOFR Path 1M (Rates).
SOFR Path 1Y (Rates).
SOFR Path 20Y (Rates).
SOFR Path 2Y (Rates).
SOFR Path 30Y (Rates).
SOFR Path 3M (Rates).
SOFR Path 5Y (Rates).
SOFR Path 6M (Rates).
SOFR Path 7Y (Rates).
SOFR Path belly (Rates).
SOFR Path BoC (Rates).
SOFR Path BoE (Rates).
SOFR Path BoJ (Rates).
SOFR Path ECB (Rates).
SOFR Path Fed (Rates).
SOFR Path front (Rates).
SOFR Path long-end (Rates).
SOFR Path PBoC (Rates).
SOFR Path RBA (Rates).