Re: [Quantlib-users] not getting linear interpolation in zero curve

[Luigi B. <lui...@gm...>]

Compounded vs continuous can be managed — but it's the conversion of dates
into times that Actual/Actual gets wrong.  For more details, see <
https://www.youtube.com/watch?v=dQjd3hAshj4>.

Hope this helps,
    Luigi


On Fri, Jul 7, 2023 at 5:37 PM Alex Leonard <aml...@gm...> wrote:

> Hi Philippe,
>
> So correct me if I'm wrong but net the issue is that the curve is
> interpolating continuously compounded rates and I am charting compounded
> rates which is producing this zigzag pattern. I see that when I change my
> zeroRate function to price using continuously compounded rates the
> interpolation looks smooth. The issue I was encountering was that when I
> would calculate Z spreads on USTs ~ 2 weeks apart they were producing very
> different levels when using an OIS curve they were more or less the same.
> It looks like this is due to the 'stepped' pattern of the discrete
> interpolation producing the same discount rates for cash flows even though
> they were close but different times. I am guessing using
> continuous compounding on the z spread calculation should fix that.
>
> Much appreciated for pointing me in the right direction,
>
> Alex
>
> On Thu, Jul 6, 2023 at 11:45 PM philippe hatstadt <pha...@ma...>
> wrote:
>
>> Actual/Actual or 30/360 should never ever be used as the internal day
>> count representation of a zero curve. Actual/360 or Actual/365 is safe. Be
>> careful to not confuse the day count basis of instruments versus that of
>> the curve itself.
>> Zero rates are jagged if you use linear instantaneous zeros. If you plan
>> to bump rates to compute hedges, a stepwise zero if better, which is the
>> same as log linear discount factors. Linear zeroes have bad perturbation
>> propagation behavior and any spline obviously. Stepwise zeros do not.
>> If you want a smooth curve for relative value, Nelson-Siegel works well.
>>
>> Regards
>>
>> Philippe Hatstadt
>> +1-203-252-0408
>>
>>
>> > On Jul 6, 2023, at 5:18 PM, Alex Leonard <aml...@gm...> wrote:
>> >
>> > 
>> > Hello,
>> >
>> > I have recently started using quantlib in python so hope this hasn't
>> been answered many times before
>> >
>> > I was trying to bootstrap a zero curve with benchmark USTs and I
>> noticed that the zero rates were jagged in between the nodes. I
>> subsequently tried building a zeroCurve with the bootstrapped node points
>> and the interpolated zero rates are still jagged even with a simple linear
>> interp.  Just as a toy example I put together the following.  I have
>> attached the graph of the zero rates with the zig zag forwards. Is there
>> some interpolation method I need to instantiate somewhere?
>> >
>> > I have additionally noticed that when I change the dayCounter to
>> ActualActual(1) the forwards are stepped instead of zig zagged. Any help is
>> much appreciated.
>> >
>> > thanks in advance,
>> >
>> > Alex
>> >
>> > #########################
>> >
>> > import datetime
>> > import pandas as pd
>> > import matplotlib.pyplot as plt
>> > import QuantLib as ql
>> > from dateutil.relativedelta import relativedelta
>> >
>> > #setting up the day
>> > date = pd.Timestamp(2015, 1, 20)
>> > day = datetime.datetime(date.year, date.month, date.day)
>> > today = ql.Date(day.day, day.month, day.year)
>> > ql.Settings.instance().evaluationDate = today
>> >
>> > #data points and the curve
>> > dates = [ql.Date(20,1,2015),ql.Date(15,2,2016), ql.Date(15,2,2017),
>> ql.Date(15,2,2018)]
>> > zeros = [0.001,0.01, 0.02, 0.03]
>> > curve = ql.ZeroCurve(dates, zeros, ql.ActualActual(3))
>> >
>> > #dates and zero rates to check smoothness of interpolation
>> > start = day
>> > end = day + relativedelta(years = 2)
>> > dates = pd.date_range(start, end, freq='B')
>> >
>> > rates = []
>> > for date in dates:
>> >     thisRate = curve.zeroRate(ql.Date(date.day,date.month,date.year),
>> ql.ActualActual(1), ql.Compounded, ql.Semiannual).rate()
>> >     rates.append(thisRate*100)
>> >
>> > plt.plot(dates,rates)
>> >
>> > #########################
>> > <Figure 2023-07-06 230502.png>
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