Re: [Quantlib-users] How's the FedFund rate calculated?

[Mike D. <mik...@gm...>]

FWIW, this is the underlying market convention for the FF contracts.  It's
the same exact math as 1m SOFR futures.

https://www.cmegroup.com/education/files/sofr-futures-settlement-calculation-methodologies.pdf

On Tue, Mar 12, 2024 at 8:12 PM jian Xu <jia...@gm...> wrote:

> Hi,
>
> I'm trying to understand how the zero rate from FedFund rates are
> calculated.  For example, if I have May FedFunds futures quoting at 5% on
> May 1, 2, 3, and now I'm standing on May 4, so if I calculate the one day
> forward rate R (continuous compounding, actual/360), then I think it should
> be
>
> exp(- R * yearFrac) = (1+ 5%/360) ^ (-360*yearFrac)
>
> where yearFrac = 1/360.
>
> This gives R = 0.0499652
>
> However, if I use the following QuantLib code, I got 0.0499267.  Can
> anyone tell me where the small difference is from?  Thank you very much.
>
> ----------------------------------------
> import QuantLib as ql
> today = ql.Date(4, 5, 2023)
> ql.Settings.instance().evaluationDate = today
> ff_index = ql.FedFunds()
> hist_quote = 95.
> hist_rate = (100 - hist_quote)/100.
>
> ff_index.addFixing(ql.Date(1, 5, 2023), hist_rate)
> ff_index.addFixing(ql.Date(2, 5, 2023), hist_rate)
> ff_index.addFixing(ql.Date(3, 5, 2023), hist_rate)
>
> calendar = ql.UnitedStates(ql.UnitedStates.GovernmentBond)
> ff_day_counter = ql.Actual360()
>
> quoted_rates = [
>     (ql.QuoteHandle(ql.SimpleQuote(hist_quote)), ql.Date(31, 5, 2023)),
>     (ql.QuoteHandle(ql.SimpleQuote(hist_quote)), ql.Date(30, 6, 2023)),
> ]
> convexityAdjustment = ql.QuoteHandle()
> ff_helpers = []
> for rate, maturity in quoted_rates:
>     ff_helpers.append(ql.OvernightIndexFutureRateHelper(rate,
>                                                         today,
>                                                         maturity,
>                                                         ff_index,
>
> convexityAdjustment,
>
> ql.RateAveraging.Simple))
>
> ff_yield_curve_simple = ql.PiecewiseFlatForward(today, ff_helpers,
> ff_day_counter)
> zr = ff_yield_curve_simple.zeroRate(ql.Date(5, 5, 2023), ql.Actual360(),
> ql.Continuous, ql.Daily)
> print(zr.rate())    # 0.04999267
>
>
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