I'm creating a PiecewiseCubicZerocurve and a PiecewiseLogCubicDiscount and obtaining the 1-year Zero rate from both curves. I expect my 1-year zero rate to be equal to my 1-year par rate.
I got two questions:
I tried playing around with the number of business days and the convention. But that has not solved the problem so far.
from QuantLib import *
today = Date(29, 1, 2019)
Settings.instance().evaluationDate = today
convention = Actual365Fixed()
helpers = [OISRateHelper(2, Period(*tenor),
QuoteHandle(SimpleQuote(rate)), Eonia())
for rate, tenor in [(0.001, (1, Years)), (0.002, (2,Years))]]
curve1 = PiecewiseCubicZero(0, TARGET(), helpers, convention)
curve2 = PiecewiseLogCubicDiscount(0, TARGET(), helpers, convention)
print('discount factor (zero)', curve1.discount(today + Period(1, Years)))
print('discount factor (discount)', curve2.discount(today + Period(1, Years)))
print('expected discount factor', 1/(1+0.001))
print('zero (zero)', curve1.zeroRate(today + Period(1, Years), convention, Annual))
print('zero (discount)', curve2.zeroRate(today + Period(1, Years), convention, Annual))
print('expected zero 0.1%')
Print statements output:
discount factor (zero) 0.9989871380405977
discount factor (discount) 0.9989954702856564
expected discount factor 0.9990009990009991
zero (zero) 0.101389 % Actual/365 (Fixed) Annual compounding
zero (discount) 0.100554 % Actual/365 (Fixed) Annual compounding
expected zero 0.1%
I think it is a matter of Business Day Convention and Settlement Days.
When using convention = Actual360(), which is standard for EONIA, and 0 settlementDays in the OISRateHelper (instead of 2), I get the following ouput:
zero (zero) 0.099999 % Actual/360 Annual compounding
zero (discount) 0.099999 % Actual/360 Annual compounding
expected zero 0.1%
When using settlementDays > 0, you have to adjust your curves and your maturity date accordingly.