Quantlib Natural Cubic spline yield curve

Question

Is there an example to use Natural Cubic spline interpolation for yield curves in Quantlib python? I can see from the SWIG file that the interpolation is exposed but not sure how to use it.

I can see that some interpolation methods exposed in piecewiseyieldcurve file. Are the ones that I should be using?

Answer 1

QuantLib has several interpolation methods for yield curves. Here is an example of a few methods for Portuguese Government Bonds to get you started.

import QuantLib as ql
import pandas as pd

pgbs = pd.DataFrame(
    {'maturity': ['15-06-2020', '15-04-2021', '17-10-2022', '25-10-2023',
                  '15-02-2024', '15-10-2025', '21-07-2026', '14-04-2027',
                  '17-10-2028', '15-06-2029', '15-02-2030', '18-04-2034',
                  '15-04-2037', '15-02-2045'],
     'coupon': [4.8, 3.85, 2.2, 4.95,  5.65, 2.875, 2.875, 4.125,
                2.125, 1.95, 3.875, 2.25, 4.1, 4.1],
     'px': [102.532, 105.839, 107.247, 119.824, 124.005, 116.215, 117.708,
            128.027, 115.301, 114.261, 133.621, 119.879, 149.427, 159.177]})

calendar = ql.TARGET()
today = calendar.adjust(ql.Date(19, 12, 2019))
ql.Settings.instance().evaluationDate = today

bondSettlementDays = 2
bondSettlementDate = calendar.advance(
    today,
    ql.Period(bondSettlementDays, ql.Days))
frequency = ql.Annual
dc = ql.ActualActual(ql.ActualActual.ISMA)
accrualConvention = ql.ModifiedFollowing
convention = ql.ModifiedFollowing
redemption = 100.0

instruments = []
for idx, row in pgbs.iterrows():
    maturity = ql.Date(row.maturity, '%d-%m-%Y')
    schedule = ql.Schedule(
        bondSettlementDate,
        maturity,
        ql.Period(frequency),
        calendar,
        accrualConvention,
        accrualConvention,
        ql.DateGeneration.Backward,
        False)
    helper = ql.FixedRateBondHelper(
            ql.QuoteHandle(ql.SimpleQuote(row.px)),
            bondSettlementDays,
            100.0,
            schedule,
            [row.coupon / 100],
            dc,
            convention,
            redemption)

    instruments.append(helper)

params = [bondSettlementDate, instruments, dc]

methods = {
    'logLinearDiscount': ql.PiecewiseLogLinearDiscount(*params),
    'logCubicDiscount': ql.PiecewiseLogCubicDiscount(*params),
    'linearZero': ql.PiecewiseLinearZero(*params),
    'cubicZero': ql.PiecewiseCubicZero(*params),
    'linearForward': ql.PiecewiseLinearForward(*params),
    'splineCubicDiscount': ql.PiecewiseSplineCubicDiscount(*params),
}

pgbs.index = pd.to_datetime(pgbs.maturity)
for method in methods:
    pgbs[method] = pgbs.maturity.apply(
        lambda x: methods[method].zeroRate(
                                         ql.Date(x, '%d-%m-%Y'),
                                         dc,
                                         ql.Compounded,
                                         frequency
                                       ).rate()*100
    )

pgbs

Besides interpolation, you can also check out the FittedBondDiscountCurve class where you have several fitting methods (CubicBSplinesFitting, SimplePolynomialFitting, NelsonSiegelFitting, SvenssonFitting, ExponentialSplinesFitting)