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

[jian Xu <jia...@gm...>]

Hi Mike,
Thank you very much for the documentation.  I followed the exact formula
Daily Interest Accumulation Factor (DIAF) = 1 + di/360 * ri / 100

And the DIAF for May 1,2,3,4, 2023 are all
1 + 1/360 * 5/100 = 1.00013889

So I think the corresponding one day zero rate should be
ln(DIAF) * 360 = 0.049996528

Which is the same as what I got before.  But I still don't know how to get
this number from QuantLib.  Or was my calculation wrong?

Jian




On Tue, Mar 12, 2024 at 8:17 PM Mike DelMedico <mik...@gm...>
wrote:

> 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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>