Semi-analytical pricing of options written on SOFR futures

ArXiv ID: 2409.04903 “View on arXiv”

Authors: Unknown

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.

Keywords: SOFR Futures, Options Pricing, CEV Model, American Options, Asian Options

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats
  • Why: 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.
  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"]