.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/fixed_income/bonds/plot_02_strips_zero_coupon.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_fixed_income_bonds_plot_02_strips_zero_coupon.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_fixed_income_bonds_plot_02_strips_zero_coupon.py:


STRIPS: a bond as a portfolio of zeros
======================================

In February 1985 the US Treasury's STRIPS program (Separate Trading of
Registered Interest and Principal of Securities) let dealers split a note
into one zero-coupon security per payment date. A coupon bond is then
exactly a portfolio of zeros. If the strips are worth more than the bond,
dealers buy bonds and strip them. If they are worth less, dealers buy
strips and reconstitute the bond. Either trade pulls the two prices back
together.

.. GENERATED FROM PYTHON SOURCE LINES 15-25

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from financialkit.fixed_income import NelsonSiegelCurve, bond_cash_flows, strips_curve, strips_decomposition, strips_value, yield_to_maturity

    curve = NelsonSiegelCurve(0.05, -0.02, 0.01, 2.0)
    bond = bond_cash_flows(100.0, 0.055, 10.0)
    strips = strips_decomposition(bond)
    quotes = 100.0 * curve.discount(bond.times)








.. GENERATED FROM PYTHON SOURCE LINES 26-28

Strip prices and the bond they rebuild
--------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 28-36

.. code-block:: Python


    value = strips_value(bond, quotes)
    print(f"{len(strips)} strips; replication cost {value:.4f}")
    for market in (value - 0.25, value + 0.25):
        edge = value - market
        trade = "buy the bond, strip it, sell the strips" if edge > 0 else "buy the strips, reconstitute, sell the bond"
        print(f"bond at {market:.4f}: {trade} for {abs(edge):.2f}")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    20 strips; replication cost 105.5217
    bond at 105.2717: buy the bond, strip it, sell the strips for 0.25
    bond at 105.7717: buy the strips, reconstitute, sell the bond for 0.25




.. GENERATED FROM PYTHON SOURCE LINES 37-39

One yield versus a curve of strip yields
----------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 39-50

.. code-block:: Python


    implied = strips_curve(bond.times, quotes)
    ytm = yield_to_maturity(value, bond)
    fig, ax = plt.subplots()
    ax.plot(bond.times, 100 * implied.rates, "o-", label="strip (zero) yields")
    ax.axhline(100 * ytm, color="k", ls="--", label=f"bond yield to maturity {100 * ytm:.3f}%")
    ax.set_xlabel("strip maturity (years)")
    ax.set_ylabel("continuously compounded yield (%)")
    ax.legend()
    print("max strip-curve error vs the curve:", np.abs(implied.rates - curve.zero_rate(bond.times)).max())
    plt.show()



.. image-sg:: /api/gallery/fixed_income/bonds/images/sphx_glr_plot_02_strips_zero_coupon_001.png
   :alt: plot 02 strips zero coupon
   :srcset: /api/gallery/fixed_income/bonds/images/sphx_glr_plot_02_strips_zero_coupon_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    max strip-curve error vs the curve: 6.245004513516506e-17





.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.035 seconds)


.. _sphx_glr_download_api_gallery_fixed_income_bonds_plot_02_strips_zero_coupon.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../../lite/lab/index.html?path=api/gallery/fixed_income/bonds/plot_02_strips_zero_coupon.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_02_strips_zero_coupon.ipynb <plot_02_strips_zero_coupon.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_02_strips_zero_coupon.py <plot_02_strips_zero_coupon.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_02_strips_zero_coupon.zip <plot_02_strips_zero_coupon.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_