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DOC: add PTIRDs comparison #449

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DOC: add PTIRDs comparison #449

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9 changes: 8 additions & 1 deletion docs/source/g_cookbook.rst
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Expand Up @@ -6,16 +6,23 @@ Cookbook
This is a collection of more detailed examples and explanations that don't necessarily fall
into any one category.

**Curve Building**
**Interest Rate Curve Building**

.. toctree::
:titlesonly:

z_ptirds_curve.rst
z_swpm.rst
z_dependencychain.rst
z_turns.rst
z_quantlib.rst
z_curve_from_zero_rates.ipynb

**Credit Curve Building**

.. toctree::
:titlesonly:

z_cdsw.rst

**FX Volatility Surface Building**
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9 changes: 8 additions & 1 deletion docs/source/i_api.rst
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Expand Up @@ -280,16 +280,23 @@ Solver
Cookbook
=========

**Curve Building**
**Interest Rate Curve Building**

.. toctree::
:titlesonly:

z_ptirds_curve.rst
z_swpm.rst
z_dependencychain.rst
z_turns.rst
z_quantlib.rst
z_curve_from_zero_rates.ipynb

**Credit Curve Building**

.. toctree::
:titlesonly:

z_cdsw.rst

**FX Volatility Surface Building**
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87 changes: 87 additions & 0 deletions docs/source/plot_py/ptirds.py
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import matplotlib.pyplot as plt

from rateslib import Curve, Solver, IRS, dt, NoInput

def curve_factory(t):
return Curve(
nodes={
dt(2022, 1, 1): 1.0,
dt(2022, 3, 15): 1.0,
dt(2022, 6, 15): 1.0,
dt(2022, 9, 21): 1.0,
dt(2022, 12, 21): 1.0,
dt(2023, 3, 15): 1.0,
dt(2023, 6, 21): 1.0,
dt(2023, 9, 20): 1.0,
dt(2023, 12, 20): 1.0,
dt(2024, 3, 15): 1.0,
dt(2025, 1, 1): 1.0,
dt(2027, 1, 1): 1.0,
dt(2029, 1, 1): 1.0,
dt(2032, 1, 1): 1.0,
},
convention="act365f",
calendar="all",
t=t,
)


def solver_factory(curve):
args = dict(calendar="all", frequency="a", convention="act365f", payment_lag=0, curves=curve)
return Solver(
curves=[curve],
instruments=[
# Deposit
IRS(dt(2022, 1, 1), "1b", **args),
# IMMs
IRS(dt(2022, 3, 15), dt(2022, 6, 15), **args),
IRS(dt(2022, 6, 15), dt(2022, 9, 21), **args),
IRS(dt(2022, 9, 21), dt(2022, 12, 21), **args),
IRS(dt(2022, 12, 21), dt(2023, 3, 15), **args),
IRS(dt(2023, 3, 15), dt(2023, 6, 21), **args),
IRS(dt(2023, 6, 21), dt(2023, 9, 20), **args),
IRS(dt(2023, 9, 20), dt(2023, 12, 20), **args),
IRS(dt(2023, 12, 20), dt(2024, 3, 15), **args),
# Swaps
IRS(dt(2022, 1, 1), "3y", **args),
IRS(dt(2022, 1, 1), "5y", **args),
IRS(dt(2022, 1, 1), "7y", **args),
IRS(dt(2022, 1, 1), "10y", **args)
],
s=[
# Deposit
1.0,
# IMMS
1.05,
1.12,
1.16,
1.21,
1.27,
1.45,
1.68,
1.92,
# Swaps
1.68,
2.10,
2.20,
2.07
]
)


log_linear_curve = curve_factory(t=NoInput(0))
log_cubic_curve = curve_factory(
t=[dt(2022, 1, 1), dt(2022, 1, 1), dt(2022, 1, 1), dt(2022, 1, 1), dt(2022, 3, 15), dt(2022, 6, 15),
dt(2022, 9, 21), dt(2022, 12, 21), dt(2023, 3, 15), dt(2023, 6, 21), dt(2023, 9, 20), dt(2023, 12, 20),
dt(2024, 3, 15), dt(2025, 1, 1), dt(2027, 1, 1), dt(2029, 1, 1), dt(2032, 1, 1), dt(2032, 1, 1), dt(2032, 1, 1),
dt(2032, 1, 1)])
mixed_curve = curve_factory(
t=[dt(2024, 3, 15), dt(2024, 3, 15), dt(2024, 3, 15), dt(2024, 3, 15), dt(2025, 1, 1), dt(2027, 1, 1),
dt(2029, 1, 1), dt(2032, 1, 1), dt(2032, 1, 1), dt(2032, 1, 1), dt(2032, 1, 1)])
solver_factory(log_linear_curve)
solver_factory(log_cubic_curve)
solver_factory(mixed_curve)
fig, ax, line = log_linear_curve.plot("1b", comparators=[log_cubic_curve, mixed_curve],
labels=["log_linear", "log_cubic", "mixed"])
plt.show()
plt.close()
151 changes: 151 additions & 0 deletions docs/source/z_ptirds_curve.rst
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.. _cook-ptirds-curve-doc:

.. ipython:: python
:suppress:

from rateslib.curves import *
from rateslib.instruments import *
import matplotlib.pyplot as plt
from datetime import datetime as dt
import numpy as np
from pandas import DataFrame, option_context

Replicating the Single Currency Curve in Pricing and Trading Interest Rate Derivatives
*******************************************************************************************

The :ref:`Bloomberg SWPM Curve <cook-swpm-doc>` is obviously not the only way to build an interest
rate curve. In `Pricing and Trading Interest Rate Derivatives: A Practical Guide to Swaps <https://www.amazon.com/Pricing-Trading-Interest-Rate-Derivatives/dp/0995455538>`_
an example is given in *Chapter 6: Single Currency Curve Modelling* of a curve that uses IMM instruments.
Different modes of interpolation are exemplified in the *Table 6.2*, and this page will show how to replicate
those curves using *rateslib*.

First, here is a screenshot of the data from *Table 6.2*. Since no details of any of the conventions are stated
in the data we will assume that it is constructed with:

- Convention: *"Act365F"*,
- Calendar: *"all"* (which is all days and no holidays)
- Frequency: *"A"*

.. image:: _static/ptirdstable62.png
:alt: Pricing and Trading Interest Rate Derivatives Table 6.2
:width: 616
:align: center

The **nodes** needed for this curve are directly specified. We will build a *Curve* factory function
below so that it is easier later to build all the *Curves* with different interpolation.

.. ipython:: python

def curve_factory(t):
return Curve(
nodes={
dt(2022, 1, 1): 1.0,
dt(2022, 3, 15): 1.0,
dt(2022, 6, 15): 1.0,
dt(2022, 9, 21): 1.0,
dt(2022, 12, 21): 1.0,
dt(2023, 3, 15): 1.0,
dt(2023, 6, 21): 1.0,
dt(2023, 9, 20): 1.0,
dt(2023, 12, 20): 1.0,
dt(2024, 3, 15): 1.0,
dt(2025, 1, 1): 1.0,
dt(2027, 1, 1): 1.0,
dt(2029, 1, 1): 1.0,
dt(2032, 1, 1): 1.0,
},
convention="act365f",
calendar="all",
t=t,
)

To calibrate the *Curves* the *Instruments* are all swaps an their *effective* and *termination* dates only
need to be properly input. Their *rates* are also given.
Below we make a *Solver* factory function so that later we can solve different *Curves* without having to repeat all
the code and the setup.

.. ipython:: python

def solver_factory(curve):
args = dict(calendar="all", frequency="a", convention="act365f", payment_lag=0, curves=curve)
return Solver(
curves=[curve],
instruments=[
# Deposit
IRS(dt(2022, 1, 1), "1b", **args),
# IMMs
IRS(dt(2022, 3, 15), dt(2022, 6, 15), **args),
IRS(dt(2022, 6, 15), dt(2022, 9, 21), **args),
IRS(dt(2022, 9, 21), dt(2022, 12, 21), **args),
IRS(dt(2022, 12, 21), dt(2023, 3, 15), **args),
IRS(dt(2023, 3, 15), dt(2023, 6, 21), **args),
IRS(dt(2023, 6, 21), dt(2023, 9, 20), **args),
IRS(dt(2023, 9, 20), dt(2023, 12, 20), **args),
IRS(dt(2023, 12, 20), dt(2024, 3, 15), **args),
# Swaps
IRS(dt(2022, 1, 1), "3y", **args),
IRS(dt(2022, 1, 1), "5y", **args),
IRS(dt(2022, 1, 1), "7y", **args),
IRS(dt(2022, 1, 1), "10y", **args)
],
s=[
# Deposit
1.0,
# IMMS
1.05,
1.12,
1.16,
1.21,
1.27,
1.45,
1.68,
1.92,
# Swaps
1.68,
2.10,
2.20,
2.07
]
)

We will now build and solve the three *Curves* with the different types of interpolation to match
the book's values.
In order to add cubic spline interpolation we only need to add the *knot sequence* as the ``t`` parameter.

.. ipython:: python

log_linear_curve = curve_factory(t=NoInput(0))
log_cubic_curve = curve_factory(t=[dt(2022, 1, 1), dt(2022, 1, 1), dt(2022, 1, 1), dt(2022, 1, 1), dt(2022, 3, 15), dt(2022, 6, 15), dt(2022, 9, 21), dt(2022, 12, 21), dt(2023, 3, 15), dt(2023, 6, 21),dt(2023, 9, 20), dt(2023, 12, 20), dt(2024, 3, 15), dt(2025, 1, 1), dt(2027, 1, 1), dt(2029, 1, 1), dt(2032, 1, 1), dt(2032, 1, 1), dt(2032, 1, 1), dt(2032, 1, 1)])
mixed_curve = curve_factory(t=[dt(2024, 3, 15), dt(2024, 3, 15), dt(2024, 3, 15), dt(2024, 3, 15), dt(2025, 1, 1), dt(2027, 1, 1), dt(2029, 1, 1), dt(2032, 1, 1), dt(2032, 1, 1), dt(2032, 1, 1), dt(2032, 1, 1)])

.. ipython:: python

solver_factory(log_linear_curve)
solver_factory(log_cubic_curve)
solver_factory(mixed_curve)

The discount factors for each *Curve* are stated as below:

.. ipython:: python

df = DataFrame(
index=[_ for _ in log_linear_curve.nodes.keys()],
data={
"log-linear": [float(_) for _ in log_linear_curve.nodes.values()],
"log-cubic": [float(_) for _ in log_cubic_curve.nodes.values()],
"mixed": [float(_) for _ in mixed_curve.nodes.values()],
}
)
with option_context("display.float_format", lambda x: '%.6f' % x):
print(df)

The *Curves* are plotted.

.. ipython:: python

log_linear_curve.plot("1b", comparators=[log_cubic_curve, mixed_curve], labels=["log_linear", "log_cubic", "mixed"])

.. plot:: plot_py/ptirds.py

The same graph as shown in Pricing and Trading Interest Rate Derivatives (Table 6.2)

4 changes: 2 additions & 2 deletions python/rateslib/legs.py
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Expand Up @@ -1905,8 +1905,8 @@ class CreditProtectionLeg(BaseLeg):
recovery_rate=0.40,
notional=1000000,
)
premium_leg.cashflows(hazard_curve, disc_curve)
premium_leg.npv(hazard_curve, disc_curve)
protection_leg.cashflows(hazard_curve, disc_curve)
protection_leg.npv(hazard_curve, disc_curve)
""" # noqa: E501

def __init__(
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