Zero Rates for Deposits using Quantlib Python

Question

I have used QuantLib Python to construct a zero curve from deposits and bonds.

Below are my codes:

import QuantLib as ql

valuationDate = ql.Date(30, 6, 2021)
ql.Settings.instance().evaluationDate = valuationDate
calendar = ql.NullCalendar()
dayConvention = ql.Actual360()
businessConvention = ql.Following
couponFrequency = ql.Semiannual

depositRates = [1.03, 1.13, 1.43]
depositMaturities = ['91D', '182D', '364D']
depositHelpers = [ql.DepositRateHelper(ql.QuoteHandle(ql.SimpleQuote(r/100.0)), 
                    ql.Period(m), 
                    2,
                    calendar, 
                    businessConvention,
                    True,
                    dayConvention) for r, m in zip(depositRates, depositMaturities)]

bondPrices = [98.452, 99.955, 100.68, 94.251, 89.1395]
bondMaturities = ['3Y', '5Y', '10Y', '15Y', '20Y']
bondCoupons = [1.85, 3.10, 4.45, 4.17, 4.17]
bondHelpers = []
for r, m, z in zip(bondPrices, bondMaturities, bondCoupons):
                    terminationDate = valuationDate + ql.Period(m)
                    schedule = ql.Schedule(valuationDate, terminationDate, ql.Period(couponFrequency), calendar, businessConvention, businessConvention, ql.DateGeneration.Forward, True)
                    bondHelper = ql.FixedRateBondHelper(ql.QuoteHandle(ql.SimpleQuote(r)), 2, 100, schedule, [z/100], dayConvention, businessConvention)
                    bondHelpers.append(bondHelper)
                
rateHelpers = depositHelpers + bondHelpers

yieldCurve = ql.PiecewiseLogCubicDiscount(valuationDate, rateHelpers, dayConvention)
yieldCurve.enableExtrapolation()

dates = [date for date in yieldCurve.dates()]
zeroRates = []

for d in dates[1:]:
    years = dayConvention.yearFraction(valuationDate, d)
    zeroRate = yieldCurve.zeroRate(d, dayConvention, ql.Compounded, couponFrequency).rate()
    zeroRates.append(zeroRate * 100)

However, for the deposits, since these are already zero-coupon, I would expect the zero rates to be exactly equal to the par rates inserted in the depositHelpers list.

Unfortunately, this is not the case, as can be seen below:

for i in range(0, 3, 1):
    print('Par rate:', depositRates[i], '; Zero rate:', zeroRates[i])

The results are as follows:

Par rate: 1.03 ; Zero rate: 1.0305594755884773
Par rate: 1.13 ; Zero rate: 1.1285118046763465
Par rate: 1.43 ; Zero rate: 1.4224679299821297

Can someone please explain what I'm doing wrong? Thanks a lot.

Answer 1

I just changed the last part of your code and removed the bonds as they don't affect the first rates.

The problem is that your zero rates have 2 extra days in relation to your deposits. You can change the curve reference date to match your instruments by changing the inputs from a fixed date to a relative date based on a calendar (it will be based on the evaluationDate).

rateHelpers = depositHelpers #+ bondHelpers

yieldCurve = ql.PiecewiseLinearZero(2, calendar, rateHelpers, dayConvention)
yieldCurve.enableExtrapolation()

for helper in depositHelpers:
    dt = helper.maturityDate()
    zeroRate = yieldCurve.zeroRate(dt, dayConvention, ql.Simple).rate()
    print(f"{dt.ISO()}, {zeroRate:.6%}, {helper.quote().value():.6%}")

2021-10-01, 1.030000%, 1.030000%
2021-12-31, 1.130000%, 1.130000%
2022-07-01, 1.430000%, 1.430000%