.. _cook-cdsw-doc:

.. ipython:: python
   :suppress:

   from rateslib.curves import *
   from rateslib.instruments import *
   from rateslib.calendars import add_tenor
   from rateslib.solver import Solver
   from rateslib import defaults
   import matplotlib.pyplot as plt
   from datetime import datetime as dt
   import numpy as np
   from pandas import DataFrame, option_context
   defaults.reset_defaults()

Replicating a Pfizer Default Curve & CDS
*****************************************************************

The raw data necessary to build the curves and replicate the pricing of Pfizer CDS
is added to Python.

.. ipython:: python
   :suppress:

   print(defaults.print())

.. ipython:: python

   irs_tenor = ["1m", "2m", "3m", "6m", "12m", "2y", "3y", "4y", "5y", "6y", "7y", "8y", "9y", "10y", "12y"]
   irs_rates = [4.8457, 4.7002, 4.5924, 4.3019, 3.8992, 3.5032, 3.3763, 3.3295, 3.3165, 3.3195, 3.3305, 3.3450, 3.3635, 3.3830, 3.4245]
   cds_tenor = ["6m", "12m", "2y", "3y", "4y", "5y", "7y", "10y"]
   cds_rates = [0.11011, 0.14189, 0.20750, 0.26859, 0.32862, 0.37861, 0.51068, 0.66891]

Since the SOFR curve is a rates component, independent from the Pfizer credit component, we will build that,
separately, first. This is no different to any of the other tutorials or examples constructing a basic
SOFR curve - it places node dates at the maturity of each IRS and solves the curve with exact precision.

.. ipython:: python

   today = dt(2024, 10, 4)  # Friday 4th October 2024
   spot = dt(2024, 10, 8)  # Tuesday 8th October 2024

   disc_curve = Curve(
       nodes={
           today: 1.0,
           **{add_tenor(spot, _, "mf", "nyc"): 1.0 for _ in irs_tenor}
       },
       calendar="nyc",
       convention="act360",
       interpolation="log_linear",
       id="sofr"
   )

   us_rates_sv = Solver(
       curves=[disc_curve],
       instruments=[
           IRS(spot, _, spec="usd_irs", curves="sofr") for _ in irs_tenor
       ],
       s=irs_rates,
       instrument_labels=irs_tenor,
       id="us_rates"
   )

This framework for:

- **firstly,** structuring a *Curve* with chosen hyper-parameters such as *nodes*, *interpolation*, etc.,
- **secondly,** calibrating that *Curve* with a chosen set of market *Instruments*,

should now be familiar. Here we will create a hazard *Curve* for Pfizer using node dates at constant tenor points
(notice these are **not** the maturity of the so called *credit-imm dates* - but they could be if you wanted) and
then calibrate the curve with proper CDS market instruments and prices.

.. ipython:: python

   cds_eff = dt(2024, 9, 20)
   cds_mats = [add_tenor(dt(2024, 12, 20), _, "mf", "all") for _ in cds_tenor]

   hazard_curve = Curve(
       nodes={
           today: 1.0,
           **{add_tenor(spot, _, "mf", "nyc"): 1.0 for _ in cds_tenor}
       },
       calendar="all",
       convention="act365f",
       interpolation="log_linear",
       id="pfizer"
   )

   pfizer_sv = Solver(
       curves=[hazard_curve],
       pre_solvers=[us_rates_sv],
       instruments=[
           CDS(cds_eff, _, spec="us_ig_cds", curves=["pfizer", "sofr"]) for _ in cds_mats
       ],
       s=cds_rates,
       instrument_labels=cds_tenor,
       id="pfizer_cds"
   )

Lets look at the structure of the hazard rates generated. To do this we plot the *'1d'* overnight rates of the
*'pfizer'* hazard curve.

.. ipython:: python

   hazard_curve.plot("1d")

.. plot::

   from rateslib import *
   import matplotlib.pyplot as plt
   irs_tenor = ["1m", "2m", "3m", "6m", "12m", "2y", "3y", "4y", "5y", "6y", "7y", "8y", "9y", "10y", "12y"]
   irs_rates = [4.8457, 4.7002, 4.5924, 4.3019, 3.8992, 3.5032, 3.3763, 3.3295, 3.3165, 3.3195, 3.3305, 3.3450, 3.3635, 3.3830, 3.4245]
   cds_tenor = ["6m", "12m", "2y", "3y", "4y", "5y", "7y", "10y"]
   cds_rates = [0.11011, 0.14189, 0.20750, 0.26859, 0.32862, 0.37861, 0.51068, 0.66891]
   today = dt(2024, 10, 4)  # Friday 4th October 2024
   spot = dt(2024, 10, 8)  # Tuesday 8th October 2024
   disc_curve = Curve(
       nodes={
           today: 1.0,
           **{add_tenor(spot, _, "mf", "nyc"): 1.0 for _ in irs_tenor}
       },
       calendar="nyc",
       convention="act360",
       interpolation="log_linear",
       id="sofr"
   )
   us_rates_sv = Solver(
       curves=[disc_curve],
       instruments=[
           IRS(spot, _, spec="usd_irs", curves="sofr") for _ in irs_tenor
       ],
       s=irs_rates,
       instrument_labels=irs_tenor,
       id="us_rates"
   )
   cds_eff = dt(2024, 9, 20)
   cds_mats = [add_tenor(dt(2024, 12, 20), _, "mf", "all") for _ in cds_tenor]
   hazard_curve = Curve(
       nodes={
           today: 1.0,
           **{add_tenor(spot, _, "mf", "nyc"): 1.0 for _ in cds_tenor}
       },
       calendar="all",
       convention="act365f",
       interpolation="log_linear",
       id="pfizer"
   )
   pfizer_sv = Solver(
       curves=[hazard_curve],
       pre_solvers=[us_rates_sv],
       instruments=[
           CDS(cds_eff, _, spec="us_ig_cds", curves=["pfizer", "sofr"]) for _ in cds_mats
       ],
       s=cds_rates,
       instrument_labels=cds_tenor,
       id="pfizer_cds"
   )
   fig, ax, line = hazard_curve.plot("1d", labels=["Pfizer Hazard Rate"])
   plt.show()
   plt.close()

By definition, the probabilities of survival are calculable directly from the hazard *Curve*.

.. ipython:: python

   hazard_curve[dt(2025, 10, 4)]  # Probability Pfizer survives at least 1yr.
   hazard_curve[dt(2029, 10, 4)]  # Probability Pfizer survives at least 5yr.
   hazard_curve[dt(2034, 10, 4)]  # Probability Pfizer survives at least 10yr.

Pricing and risk metrics are calculable within *rateslib's* natural framework.
Let's build the traditional 5Y Pfizer CDS.

.. ipython:: python

   cds = CDS(
       effective=dt(2024, 9, 20),
       termination=dt(2029, 12, 20),
       spec="us_ig_cds",
       curves=["pfizer", "sofr"],
       notional=10e6,
   )
   cds.rate(solver=pfizer_sv)  # this compares to BBG: "Trd Sprd (bp)"
   cds.npv(solver=pfizer_sv)  # this compares to BBG: "Cash Amount"
   cds.analytic_delta(hazard_curve, disc_curve)
   cds.accrued(dt(2024, 10, 7))  # this is 17 days of accrued
   cds.delta(solver=pfizer_sv).groupby("solver").sum()  # this compares to: "Spread DV01" and "IR DV01"

Whe can also show the analytic risk if the recovery rate is increased by 1%. This is
the PnL purely for this contract.

.. ipython:: python

   cds.analytic_rec_risk(hazard_curve, disc_curve)

This does not compare with other systems `Rec Risk (1%)` of 78.75. To understand and return this
value consider the follow up cookbook
article :ref:`what are exogenous variables? <cook-exogenous-doc>`.