# 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.

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:

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

• At expiration the futures price is determined by this formula. Before expiration can I say that the price is determined by the market's expectation of what this formula will produce later? (or is that too naive? do I have to apply any "adjustments" to go from the risk neutral expectation to the SOFR futures price, such as convexity adjustment, risk premium, etc. ?). Jun 19 '20 at 10:01
• There are 2 convexity adjustments (1) as for Eurodollar futures, the nature of futures versus FRAs creates an adjustment (2) for the monthly futures, the fact we have an arithmetic mean rather than geometric creates a second adjustment. However for short dated contracts <2yrs both are tiny.
– dm63
Jun 19 '20 at 10:08
• Even for determining Eurodollar quotes, is it just an expectation of market participants just like in case of SOFR? Please confirm Jun 20 '20 at 11:33
• Yes the new SOFR futures are very similar to the (older and very successful) ED futures in this respect. Jun 20 '20 at 12:49