Yield Curve Dynamics¶

A cursory look at the dynamics of ECB zero coupon bond yield curves¶

https://github.com/luphord/yield_curve_dynamics

Yield Curve Data by European Central Bank (ECB)¶

In [2]:

Image('../docs/_static/ecb_screenshot.png', width=600)

Out[2]:

Source: https://www.ecb.europa.eu/stats/financial_markets_and_interest_rates/euro_area_yield_curves/html/index.en.html

Data Format¶

ECB publishes the bond yield curve in a parametric form, the so-called Svensson Model. $$y(t) = \beta_0 + \beta_1 \Bigg(\frac{1-e^{\frac{-t}{\tau_1}}}{t / \tau_1}\Bigg) + \beta_2 \Bigg(\frac{1-e^{\frac{-t}{\tau_1}}}{t / \tau_1} - e^{\frac{-t}{\tau_1}}\Bigg) + \beta_3 \Bigg(\frac{1-e^{\frac{-t}{\tau_2}}}{t / \tau_2} - e^{\frac{-t}{\tau_2}}\Bigg)$$

In [3]:

import pandas as pd
pd.read_csv('../data/euryieldcurve.csv', parse_dates=['date'], index_col=0).head()

Out[3]:

	beta0	beta1	beta2	beta3	tau1	tau2
date
2009-01-02	0.108792	1.611718	10.426767	-0.958181	12.040810	0.750536
2009-01-05	0.169175	1.509803	10.714462	-1.009914	11.895374	1.047267
2009-01-06	0.010000	1.598177	11.598626	-0.739861	12.388537	1.047100
2009-01-07	0.352788	1.418221	11.118991	-1.540248	13.456747	0.616249
2009-01-08	0.383307	1.493448	10.785753	-2.052377	13.605817	0.617398

Yield Curve Animation¶

In [9]:

HTML(anim.to_html5_video())

Out[9]:

In [10]:

HTML(anim.to_jshtml())

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Keyrate Time Series¶

In [11]:

key_rates = keyrates(curves)
key_rates.plot(figsize=(12,8));

Stationary Log Differences¶

In [12]:

rate_changes = shifted_log_diff(key_rates)
rate_changes.plot(figsize=(12,8));

Principal Component Analysis¶

Explained Variance vs. Number of Factors¶

In [13]:

pca = perform_pca(rate_changes)
plot_pca2(pca);

Principal Component Analysis¶

The first three factors¶

In [15]:

plot_pca_components(pca);