Errors / FuturesRateHelper Convexity Adjustment Yield Curve bootstrapping issue

[is-source]

Hi all,

I am facing an issue with bootstrapping my Bbsw3M curve. I have sourced market quotes from LSEG Refinitiv for 3M deposit, futures, and swap rates.

In using the FuturesRateHelper, specifically the convexity adjustment I receive the error:

RuntimeError: 1st iteration: failed at 5th alive instrument, pillar March 17th, 2026, maturity March 17th, 2026, reference date September 13th, 2024: root not bracketed: f[-1,1] -> [1.670495e+01,2.187378e+02]

Note that I have no issues with getting my aonia curve.

Thanks in advance for your help with these issues.

My complete code is as follows:
import QuantLib as ql
import refinitiv.data as rd
import os
import matplotlib.pyplot as plt
from matplotlib.ticker import PercentFormatter

today = ql.Date(11, ql.September, 2024)
ql.Settings.instance().evaluationDate = today

os.environ["RD_LIB_CONFIG_PATH"] = "./Configuration"
rd.open_session()

depo_data = rd.get_data(universe = ["AUDOND=", "AUDSND=", "AUDTND=",
"AUDSWD=", "AUD2WD=","AUD3WD=", "AUD3MD="],
fields = "MID_PRICE")

fut_data = rd.get_data(universe= ["YBAH5", "YBAM5", "YBAU5",
"YBAZ5", "YBAH6", "YBAM6",
"YBAU6", "YBAZ6"],
fields = ["BID", "CONVX_BIAS", "EXPIR_DATE"])

irs_data = rd.get_data(universe=["AUDQM3AB1Y=", "AUDQM3AB2Y=", "AUDQM3AB3Y=",
"AUDQM3AB4Y=", "AUDQM3AB5Y=", "AUDQM3AB7Y=",
"AUDQM3AB10Y="], fields = "MID_PRICE")

rd.close_session()

bbsw_helpers = []

bbsw_helpers = [
ql.DepositRateHelper(
ql.QuoteHandle(ql.SimpleQuote(depo_data.loc[depo_data['Instrument']=='AUD3MD=', 'MID_PRICE'].values[0] / 100)),
ql.Period(3, ql.Months),
3,
ql.Australia(),
ql.Following,
False,
ql.Actual360(),
)
]

bbsw3m = ql.Bbsw3M()

bbsw_helpers += [
ql.FuturesRateHelper(
ql.QuoteHandle(
ql.SimpleQuote(
fut_data.loc[fut_data['Instrument'] == inst, 'BID'].values[0]
)
),
start_date,
bbsw3m,
ql.QuoteHandle(fut_data.loc[fut_data['Instrument'] == inst, 'CONVX_BIAS'].values[0]),
ql.Futures.IMM
)
for inst, start_date in [
("YBAH5", ql.Date(19, ql.March, 2025)),
("YBAM5", ql.Date(18, ql.June, 2025)),
("YBAU5", ql.Date(17, ql.September, 2025)),
("YBAZ5", ql.Date(17, ql.December, 2025)),
("YBAH6", ql.Date(18, ql.March, 2026)),
("YBAM6", ql.Date(17, ql.June, 2026)),
("YBAU6", ql.Date(16, ql.September, 2026)),
("YBAZ6", ql.Date(16, ql.December,2026))
]
]

discount_curve = ql.RelinkableYieldTermStructureHandle()
discount_curve.linkTo(aonia_curve)

bbsw_helpers += [
ql.SwapRateHelper(
ql.QuoteHandle(ql.SimpleQuote(3.516/100)),
ql.Period(5, ql.Years),
ql.Australia(),
ql.Annual,
ql.Following,
ql.Actual365(),
bbsw3m,
ql.QuoteHandle()
ql.Period(0, Days),
discount_curve)
]

bbsw3m_curve = ql.PiecewiseConvexMonotoneForward(
2, ql.Australia(), bbsw_helpers, ql.Actual365Fixed()
)
bbsw3m_curve.enableExtrapolation()

today = bbsw3m_curve.referenceDate()
end = today + ql.Period(60, ql.Years)
bbsw_dates = [
ql.Date(serial)
for serial in range(today.serialNumber(), end.serialNumber() + 1)]
bbsw_rates = [
bbsw3m_curve.forwardRate(
d, bbsw3m.maturityDate(d), ql.Actual360(), ql.Simple
).rate()
for d in bbsw_dates
]

ax = plt.figure(figsize=(9, 6)).add_subplot(1, 1, 1)
ax.axhline(0.0, linewidth=1, color="black")
ax.set_xlim(min(bbsw_dates).to_date(), max(bbsw_dates).to_date())
ax.yaxis.set_major_formatter(PercentFormatter(1.0))
ax.plot_date([d.to_date() for d in bbsw_dates], bbsw_rates, "-")

plt.xlabel('Date')
plt.ylabel('Rate')
plt.title("BBSW Curve")
plt.grid(True)
plt.show()

For reference, the data I have obtained for deposits, futures and swaps are as follows:

Deposits
Instrument MID_PRICE
0 AUDOND= 4.3
1 AUDSND= 4.25
2 AUDTND= 4.3
3 AUDSWD= 4.35
4 AUD2WD= 4.58
5 AUD3WD= 4.42
6 AUD3MD= 4.49

Futures
Instrument BID CONVX_BIAS EXPIR_DATE
0 YBAH5 96.19 0.262 2025-03-13
1 YBAM5 96.48 0.482 2025-06-12
2 YBAU5 96.63 0.758 2025-09-11
3 YBAZ5 96.73 1.086 2025-12-11
4 YBAH6 96.8 1.464 2026-03-12
5 YBAM6 96.83 1.889 2026-06-11
6 YBAU6 96.84 2.359 2026-09-10
7 YBAZ6 96.81 2.871 2026-12-10

SWAPS
Instrument MID_PRICE
0 AUDQM3AB1Y= 3.987
1 AUDQM3AB2Y= 3.621
2 AUDQM3AB3Y= 3.492
3 AUDQM3AB4Y= 3.475
4 AUDQM3AB5Y= 3.516
5 AUDQM3AB7Y= 3.651
6 AUDQM3AB10Y= 3.833

[boring-cyborg]

Thanks for posting! It might take a while before we look at your issue, so don't worry if there seems to be no feedback. We'll get to it.

[lballabio]

Looking at the code, I'd say that the convexity adjustment is a rate and should be divided by 100 to be in the correct units (like you already do with deposit rates, for instance).