Paper: arXiv 2409.04903

Abstract

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 exercise written on the daily SOFR rates. We develop a new version of the GIT method and solve both problems semi-analytically, obtaining the option price, the exercise boundary, and the option Greeks. This work is intended to address the concern that the transfer from LIBOR to SOFR has resulted in a situation in which the options of the key money market (i.e., futures on the reference rate) are options without any pricing model available. Therefore, the trading in options on 3M SOFR futures currently ends before their reference quarter starts, to eliminate the final metamorphosis into exotic options.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a semi-analytical solution using advanced stochastic calculus and PDE transformations, but lacks empirical validation such as backtests, datasets, or statistical metrics.

Research Flowchart

  flowchart TD
  A["Research Goal:<br/>Model options on SOFR futures<br/>handling type change at reference period"] --> B["Key Methodology:<br/>Semi-analytical approach using<br/>Generalized Integral Transform (GIT) method"]
  B --> C["Inputs:<br/>Time-dependent CEV model<br/>for SOFR rates"]
  C --> D["Computational Process:<br/>Solve American option on forward price<br/>pre-reference period"]
  D --> E["Computational Process:<br/>Solve American-style Asian option<br/>on daily rates post-reference"]
  E --> F["Key Findings:<br/>Option price, Exercise boundary,<br/>Greeks; Enables trading<br/>through reference period"]

Cited References (35)

  1. Semi-closed form solutions for barrier and American options written on a time-dependent Ornstein-Uhlenbeck process (2021)
  2. Closed form optimal exercise boundary of the American put option (2021)
  3. American options in time-dependent one-factor models: Semi-analytic pricing, numerical methods and ML support (2024)
  4. Semi-analytic pricing of American options in time-dependent jump-diffusion models with exponential jumps — → 2308.08760
  5. High-performance American option pricing (2016)
  6. Simple/Robust/Fast/Smooth Finite Difference Methods forAmerican Options
  7. Fast American Option Pricing: The Double-Boundary Case
  8. Generalized Integral Transforms in Mathematical Finance (2021)
and 27 more
  1. Three-Month SOFR (2024) — link
  2. SOFR Derivative Pricing Using a Short Rate Model (2021) — link
  3. Trading SOFR Options (2019)
  4. SOFR Futures and Options (2022)
  5. Semi-closed form prices of barrier options in the Hull-White model (2020)
  6. Pricing Interest-Rate-Derivative Securities (1990)
  7. Interest Rate Modeling (2010)
  8. Analytic risk-free-rates option pricing with smile and skew (2023)
  9. Robust numerical methods for PDE models of Asian options (1997)
  10. A Simple Multi-Curve Model for Pricing SOFR Futures and Other Derivatives (2018) — link
  11. Finite difference scheme versus piecewise binomial lattice for interest rates under the skew CEV model (2023)
  12. The Value of an Asian Option. (1995)
  13. A P.D.E. approach to Asian options: analytical and numerical evidence (1997)
  14. Pricing arithmetic Asian and Amerasian options:A diffusion operator integral expansion approach (2023)
  15. Discounted optimal stopping for maxima in diffusion models with finite horizon (2006)
  16. Pricing of Arithmetic Average Asian Option by Combining Variance Reduction and Quasi-Monte Carlo Method (2023)
  17. Negative Interest Rates for Dummies (2020) — [link](https://derivativelogic.com/dl-report-category/negative-interest-rates-for-dummies#:~:text=Could SOFR go negative?,read that right, 0.01%.)
  18. A penalty method for American options with jump diffusion processes (2004)
  19. Computational Methods for Solving System of Volterra Integral Equation (2011)
  20. Associated Weber–Orr Transform, Biot–Savart Law and Explicit Form of the Solution of 2D Stokes System in Exterior of the Disc (2019) — link
  21. Weber’s integral Theorem (1921)
  22. Diffusion Processes with Reflection (2009)
  23. Encyclopedia of Quantitative Finance (2010)
  24. Semi-closed form prices of barrier options in the time-dependent CEV and CIR models (2020)
  25. Tata Lectures on Theta (1983)
  26. American option (2022) — link
  27. American Call Options Under Jump-Diffusion Processes, A Fourier Transform Approach

1 of 35 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.