How SOFR Futures Prices Reflect Average and Compounded Rates

Summary

The document explains how SOFR futures prices are tied to realized overnight rates during their reference period. For one-month contracts, the settlement rate is the arithmetic average of observed SOFR rates; for three-month contracts, it is based on daily compounding over the reference quarter. In both cases, the futures price at expiration is expressed as one minus the relevant rate.

The formulas distinguish averaging from compounding and account for the number of days in the period in the three-month calculation. The explanation concerns the rate used to determine the contract’s price at expiration. It does not show how to derive a current quote for a future contract month from market data, funding assumptions, or expectations. No empirical example or broader pricing model is provided, so the formulas alone do not explain a live quote observed before the reference period has occurred.

Key ideas

• At expiration, a one-month SOFR futures price equals one minus the arithmetic average of observed SOFR rates for the contract month.
• A three-month SOFR futures settlement rate is calculated by compounding daily SOFR rates over its reference quarter.
• The three-month calculation annualizes the compounded return using the day count in the reference period.
• The settlement formulas do not by themselves explain how the market determines a quote before the reference period.

Tags

# How are SOFR futures contract quotes determined?


# How are SOFR futures contract quotes determined?












I am currently conducting a research on SOFR and have a small question. Suppose I am in June right now and on the CME website I see SOFR Futures quote for the month of September to be 98.6786.

I wish to know how these futures quotes are determined for September, given that we are in June right now.

Is there a specific formula for computing, if yes, please mention here.

## Answer by David Duarte (score 1, accepted)

https://quant.stackexchange.com/a/55045

A CME SOFR futures price in expiration is equal to 1 − R where R is an arithmetic average of observed SOFR rates during the contract month for the one month futures:

$$P_{1m} = 1 - R$$ $$R = \frac{1}{N}\sum_{t}r_t$$

and the compounded daily rate during the reference quarter for three-month futures:

$$P_{3m} = 1 - R$$ $$R = \frac{360}{N} \left( \prod_{t}( 1 + \frac{r_t d_ t}{360} ) - 1 \right)$$

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.