Semi-analytical pricing of options written on SOFR futures

TL;DR

This paper introduces a semi-analytical method for pricing complex SOFR futures options that change type mid-period, addressing a gap caused by the LIBOR to SOFR transition.

Contribution

It develops a novel semi-analytical approach using an enhanced GIT method for pricing hybrid American and Asian options on SOFR futures with a time-dependent CEV model.

Findings

Successfully derives option prices, exercise boundaries, and Greeks.

Addresses a key market gap caused by the LIBOR-SOFR transition.

Provides a practical framework for trading SOFR futures options.

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.