QuantLib: How to bootstrap Yield Curve using 3M futures - Python

Question

I need to bootstrap a yieldcurve with 3M futures, using a cubic spline if possible.

Using, for example 3M Euribor, how do I bootstrap the yield curve using python?

I have a vector of dates and a vector of future prices.

I found about the QuantLib library, and more specifically, the ql.PiecewiseCubicZero. However there is a big lack of documentation on how to use it, and even more, with futures.

Any help would be much appreciated!

Answer 1

The theory and a worked-out example are in Ametrano and Bianchetti, Everything You Always Wanted to Know About Multiple Interest Rate Curve Bootstrapping but Were Afraid to Ask.

Recently I reproduced their example in Python; you can read my code at https://www.implementingquantlib.com/2023/09/ametrano-bianchetti.html.

Answer 2

If you want a really easy answer, you can do the following:

1. Convert your futures prices into rates e.g. $100 - price = rate$.

2. Construct a LineCurve in rateslib:

from rateslib import *
curve = LineCurve(
    nodes={
        dt(2023, 9, 21): 3.92,
        dt(2023, 12, 20): 4.01,
        dt(2024, 3, 20): 3.96,
        dt(2024, 6, 20): 3.83,
        dt(2024, 9, 20): 3.62,
        dt(2024, 12, 20): 3.42,
        dt(2025, 3, 20): 3.25,
    },
    t=[
        dt(2023, 9, 21), dt(2023, 9, 21), dt(2023, 9, 21), dt(2023, 9, 21),
        dt(2023, 12, 20),
        dt(2024, 3, 20),
        dt(2024, 6, 20),
        dt(2024, 9, 20),
        dt(2024, 12, 20),
        dt(2025, 3, 20), dt(2025, 3, 20), dt(2025, 3, 20), dt(2025, 3, 20),
    ]
)
curve.plot()

The t parameter is the knot sequence which is needed to instruct a cubic spline. You can read about this in the rateslib docs

The curve rate on 18th Jan 2024

>>> curve[dt(2024, 1, 18)]
4.008222134667067

The curve that is produced is a futures curves and it ignores convexity adjustments which are generally created by the presence of a swaps market.