Why SOFR One-Month Futures Rates Do Not Directly Give Discount Factors

Summary

The document distinguishes the rate implied by one-month SOFR futures from the discount factor needed to construct a curve. It expresses the futures rate as an expected average of short rates over the reference month, while a discount factor depends on the expected exponential of the accumulated short rate. Knowing the expected integral alone does not generally determine that exponential expectation.

The question asks whether one-month SOFR futures should be used in curve bootstrapping and how QuantLib uses them to infer discount factors. However, the supplied text contains no answer, implementation details, or conclusion about QuantLib. Its useful contribution is therefore the mathematical distinction that motivates the question, along with an explicit reminder that a futures quote is not itself a discount factor. Further assumptions or a pricing model would be needed to bridge the quantities.

Key ideas

• A one-month SOFR futures rate represents an expected average short rate over its reference period.
• A discount factor depends on the expected exponential of the integrated short rate.
• The expected integrated rate alone generally does not determine the discount factor.
• The document poses, but does not resolve, how SOFR futures enter curve bootstrapping or QuantLib.

Tags

# Using SOFR 1M futures for curve construction/bootstrapping


# Using SOFR 1M futures for curve construction/bootstrapping












Using continuous time notation, the 1M SOFR futures rate R (price is 1-R) is $$ R = \frac1T E^Q_t \left[\int_0^T r_u du \right] $$ where $[0,T]$ is the reference month.

So I initially thought that the SOFR 1M futures price is used in SOFR curve bootstrapping. But now I am wondering how is it used, by eg quantlib, and if it should be used at all.

Suppose you'd like to have the discount factor for date $T$ then what you need is $$ E^Q_t \left[e^{- \int_t^T r_u du }\right] $$ which clearly does not follow from knowledge of $$ E^Q_t \left[\int_t^T r_u du \right] $$ alone.

So my question is two-fold actually:

- Should 1M sofr futures be used to bootstrap a curve

- Does ql use 1m sofr futures for backing out discount factors, and if so how exactly?

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