ZCIS#

class rateslib.instruments.ZCIS(*args, fixed_rate=NoInput.blank, leg2_index_base=NoInput.blank, leg2_index_fixings=NoInput.blank, leg2_index_method=NoInput.blank, leg2_index_lag=NoInput.blank, **kwargs)#

Bases: BaseDerivative

Create a zero coupon index swap (ZCIS) composing an ZeroFixedLeg and a ZeroIndexLeg.

Parameters:

  • args (dict) – Required positional args to BaseDerivative.

  • fixed_rate (float or None) – The fixed rate applied to the ZeroFixedLeg. If None will be set to mid-market when curves are provided.

  • index_base (float or None, optional) – The base index applied to all periods.

  • index_fixings (float, or Series, optional) – If a float scalar, will be applied as the index fixing for the first period. If a list of n fixings will be used as the index fixings for the first n periods. If a datetime indexed Series will use the fixings that are available in that object, and derive the rest from the curve.

  • index_method (str) – Whether the indexing uses a daily measure for settlement or the most recently monthly data taken from the first day of month.

  • index_lag (int, optional) – The number of months by which the index value is lagged. Used to ensure consistency between curves and forecast values. Defined by default.

  • kwargs (dict) – Required keyword arguments to BaseDerivative.

Examples

Construct a curve to price the example.

In [1]: usd = Curve(
   ...:     nodes={
   ...:         dt(2022, 1, 1): 1.0,
   ...:         dt(2027, 1, 1): 0.85,
   ...:         dt(2032, 1, 1): 0.65,
   ...:     },
   ...:     id="usd",
   ...: )
   ...: 

In [2]: us_cpi = IndexCurve(
   ...:     nodes={
   ...:         dt(2022, 1, 1): 1.0,
   ...:         dt(2027, 1, 1): 0.85,
   ...:         dt(2032, 1, 1): 0.70,
   ...:     },
   ...:     id="us_cpi",
   ...:     index_base=100,
   ...:     index_lag=3,
   ...: )
   ...:

Create the ZCIS, and demonstrate the rate(), npv(), analytic_delta(), and

In [3]: zcis = ZCIS(
   ...:     effective=dt(2022, 1, 1),
   ...:     termination="10Y",
   ...:     frequency="A",
   ...:     calendar="nyc",
   ...:     currency="usd",
   ...:     fixed_rate=2.05,
   ...:     convention="1+",
   ...:     notional=100e6,
   ...:     leg2_index_base=100.0,
   ...:     leg2_index_method="monthly",
   ...:     leg2_index_lag=3,
   ...:     curves=["usd", "usd", "us_cpi", "usd"],
   ...: )
   ...: 

In [4]: zcis.rate(curves=[usd, usd, us_cpi, usd])
Out[4]: 3.631120991031422

In [5]: zcis.npv(curves=[usd, usd, us_cpi, usd])
Out[5]: 13231298.577116087

In [6]: zcis.analytic_delta(usd, usd)
Out[6]: 78012.93808671228

A DataFrame of cashflows().

In [7]: zcis.cashflows(curves=[usd, usd, us_cpi, usd])
Out[7]: 
                Type Period  Ccy  Acc Start    Acc End    Payment Convention   DCF      Notional   DF   Rate Spread     Cashflow          NPV  FX Rate      NPV Ccy Collateral  Real Cashflow  Index Base  Index Val  Index Ratio
leg1 0  ZeroFixedLeg   None  USD 2022-01-01 2032-01-01 2032-01-02         1+ 10.00  100000000.00 0.65   2.05   None -22498308.13 -14621751.99     1.00 -14621751.99       None            NaN         NaN        NaN          NaN
leg2 0  ZeroIndexLeg   None  USD 2022-01-01 2032-01-01 2032-01-02          1  1.00 -100000000.00 0.65 100.00   None  42857142.86  27853050.57     1.00  27853050.57       None   100000000.00      100.00     142.86         1.43

For accurate sensitivity calculations; delta() and gamma(), construct a curve model.

In [8]: sofr_kws = dict(
   ...:     effective=dt(2022, 1, 1),
   ...:     frequency="A",
   ...:     convention="Act360",
   ...:     calendar="nyc",
   ...:     currency="usd",
   ...:     curves=["usd"]
   ...: )
   ...: 

In [9]: cpi_kws = dict(
   ...:     effective=dt(2022, 1, 1),
   ...:     frequency="A",
   ...:     convention="1+",
   ...:     calendar="nyc",
   ...:     leg2_index_method="monthly",
   ...:     currency="usd",
   ...:     curves=["usd", "usd", "us_cpi", "usd"]
   ...: )
   ...: 

In [10]: instruments = [
   ....:     IRS(termination="5Y", **sofr_kws),
   ....:     IRS(termination="10Y", **sofr_kws),
   ....:     ZCIS(termination="5Y", **cpi_kws),
   ....:     ZCIS(termination="10Y", **cpi_kws),
   ....: ]
   ....: 

In [11]: solver = Solver(
   ....:     curves=[usd, us_cpi],
   ....:     instruments=instruments,
   ....:     s=[3.40, 3.60, 2.2, 2.05],
   ....:     instrument_labels=["5Y", "10Y", "5Yi", "10Yi"],
   ....:     id="us",
   ....: )
   ....: 
SUCCESS: `func_tol` reached after 6 iterations (levenberg_marquardt), `f_val`: 3.5046314313449345e-17, `time`: 0.0169s

In [12]: zcis.delta(solver=solver)
Out[12]: 
local_ccy                     usd
display_ccy                   usd
type        solver label         
instruments us     5Y        0.00
                   10Y      -0.00
                   5Yi      -0.00
                   10Yi  83687.51

In [13]: zcis.gamma(solver=solver)
Out[13]: 
type                                           instruments                    
solver                                                  us                    
label                                                   5Y    10Y   5Yi   10Yi
local_ccy display_ccy type        solver label                                
usd       usd         instruments us     5Y          -0.00   0.00 -0.00   8.10
                                         10Y          0.00   0.00  0.00 -90.49
                                         5Yi         -0.00   0.00  0.00  -0.00
                                         10Yi         8.10 -90.49 -0.00  73.81

Attributes Summary

fixed_rate

If set will also set the fixed_rate of the contained leg1.

float_spread

If set will also set the float_spread of contained leg1.

index_base

If set will also set the index_base of the contained leg1.

leg2_fixed_rate

If set will also set the fixed_rate of the contained leg2.

leg2_float_spread

If set will also set the float_spread of contained leg2.

leg2_index_base

If set will also set the index_base of the contained leg1.

Methods Summary

analytic_delta(*args[, leg])

Return the analytic delta of a leg of the derivative object.

cashflows([curves, solver, fx, base])

Return the properties of all legs used in calculating cashflows.

cashflows_table([curves, solver, fx, base])

delta(*args, **kwargs)

Calculate the delta of the Instrument.

gamma(*args, **kwargs)

Calculate the gamma of the Instrument.

npv([curves, solver, fx, base, local])

Return the NPV of the derivative object by summing legs.

rate([curves, solver, fx, base])

Return the mid-market IRR rate of the ZCIS.

Attributes Documentation

fixed_rate#

If set will also set the fixed_rate of the contained leg1.

Note

fixed_rate, float_spread, leg2_fixed_rate and leg2_float_spread are attributes only applicable to certain Instruments. AttributeErrors are raised if calling or setting these is invalid.

Type:

float or None

float_spread#

If set will also set the float_spread of contained leg1.

Type:

float or None

index_base#

If set will also set the index_base of the contained leg1.

Note

index_base and leg2_index_base are attributes only applicable to certain Instruments. AttributeErrors are raised if calling or setting these is invalid.

Type:

float or None

leg2_fixed_rate#

If set will also set the fixed_rate of the contained leg2.

Type:

float or None

leg2_float_spread#

If set will also set the float_spread of contained leg2.

Type:

float or None

leg2_index_base#

If set will also set the index_base of the contained leg1.

Note

index_base and leg2_index_base are attributes only applicable to certain Instruments. AttributeErrors are raised if calling or setting these is invalid.

Type:

float or None

Methods Documentation

abstract analytic_delta(*args, leg=1, **kwargs)#

Return the analytic delta of a leg of the derivative object.

Parameters:

  • args – Required positional arguments supplied to BaseLeg.analytic_delta.

  • leg (int in [1, 2]) – The leg identifier of which to take the analytic delta.

  • kwargs – Required Keyword arguments supplied to BaseLeg.analytic_delta().

Return type:

float, Dual, Dual2

Examples

In [14]: curve = Curve({dt(2021,1,1): 1.00, dt(2025,1,1): 0.83}, id="SONIA")

In [15]: fxr = FXRates({"gbpusd": 1.25}, base="usd")

In [16]: irs = IRS(
   ....:     effective=dt(2022, 1, 1),
   ....:     termination="6M",
   ....:     frequency="Q",
   ....:     currency="gbp",
   ....:     notional=1e9,
   ....:     fixed_rate=5.0,
   ....: )
   ....: 

In [17]: irs.analytic_delta(curve, curve)
Out[17]: 47156.00216054951

In [18]: irs.analytic_delta(curve, curve, fxr)
Out[18]: <Dual: 58945.002701, (fx_gbpusd), [47156.0]>

In [19]: irs.analytic_delta(curve, curve, fxr, "gbp")
Out[19]: 47156.00216054951
cashflows(curves=NoInput.blank, solver=NoInput.blank, fx=NoInput.blank, base=NoInput.blank)#

Return the properties of all legs used in calculating cashflows.

Parameters:

  • curves (CurveType, str or list of such, optional) –

    A single Curve, LineCurve or id or a list of such. A list defines the following curves in the order:

  • solver (Solver, optional) – The numerical Solver that constructs Curves from calibrating instruments.

  • fx (float, FXRates, FXForwards, optional) – The immediate settlement FX rate that will be used to convert values into another currency. A given float is used directly. If giving a FXRates or FXForwards object, converts from local currency into base.

  • base (str, optional) – The base currency to convert cashflows into (3-digit code). Only used if fx is an FXRates or FXForwards object. If not given defaults to fx.base.

Return type:

DataFrame

Notes

If only one curve is given this is used as all four curves.

If two curves are given the forecasting curve is used as the forecasting curve on both legs and the discounting curve is used as the discounting curve for both legs.

If three curves are given the single discounting curve is used as the discounting curve for both legs.

Examples

In [1]: irs.cashflows([curve], fx=fxr)
Out[1]: 
               Type   Period  Ccy  Acc Start    Acc End    Payment Convention  DCF       Notional   DF Collateral  Rate  Spread     Cashflow          NPV  FX Rate      NPV Ccy
leg1 0  FixedPeriod  Regular  GBP 2022-01-01 2022-04-01 2022-04-03     ACT360 0.25  1000000000.00 0.94       None  5.00     NaN -12500000.00 -11792277.34     1.25 -14740346.67
     1  FixedPeriod  Regular  GBP 2022-04-01 2022-07-01 2022-07-03     ACT360 0.25  1000000000.00 0.93       None  5.00     NaN -12638888.89 -11785723.74     1.25 -14732154.68
leg2 0  FloatPeriod  Regular  GBP 2022-01-01 2022-04-01 2022-04-03     ACT360 0.25 -1000000000.00 0.94       None  4.62    0.00  11544335.50  10890720.47     1.25  13613400.59
     1  FloatPeriod  Regular  GBP 2022-04-01 2022-07-01 2022-07-03     ACT360 0.25 -1000000000.00 0.93       None  4.62    0.00  11673351.69  10885363.37     1.25  13606704.21
cashflows_table(curves=NoInput.blank, solver=NoInput.blank, fx=NoInput.blank, base=NoInput.blank)#
delta(*args, **kwargs)#

Calculate the delta of the Instrument.

For arguments see Sensitivities.delta().

gamma(*args, **kwargs)#

Calculate the gamma of the Instrument.

For arguments see Sensitivities.gamma().

npv(curves=NoInput.blank, solver=NoInput.blank, fx=NoInput.blank, base=NoInput.blank, local=False)#

Return the NPV of the derivative object by summing legs.

Parameters:

  • curves (Curve, LineCurve, str or list of such) –

    A single Curve, LineCurve or id or a list of such. A list defines the following curves in the order:

  • solver (Solver, optional) – The numerical Solver that constructs Curves from calibrating instruments.

  • fx (float, FXRates, FXForwards, optional) – The immediate settlement FX rate that will be used to convert values into another currency. A given float is used directly. If giving a FXRates or FXForwards object, converts from local currency into base.

  • base (str, optional) – The base currency to convert cashflows into (3-digit code). Only used if fx is an FXRates or FXForwards object. If not given defaults to fx.base.

  • local (bool, optional) – If True will return a dict identifying NPV by local currencies on each leg. Useful for multi-currency derivatives and for ensuring risk sensitivities are allocated to local currencies without conversion.

Return type:

float, Dual or Dual2, or dict of such.

Notes

If only one curve is given this is used as all four curves.

If two curves are given the forecasting curve is used as the forecasting curve on both legs and the discounting curve is used as the discounting curve for both legs.

If three curves are given the single discounting curve is used as the discounting curve for both legs.

Examples

In [1]: irs.npv(curve)
Out[1]: -1801917.2427669652

In [2]: irs.npv([curve], fx=fxr)
Out[2]: <Dual: -2252396.553459, (fx_gbpusd), [-1801917.2]>

In [3]: irs.npv([curve], fx=fxr, base="gbp")
Out[3]: -1801917.2427669652
rate(curves=NoInput.blank, solver=NoInput.blank, fx=NoInput.blank, base=NoInput.blank)#

Return the mid-market IRR rate of the ZCIS.

Parameters:

  • curves (Curve, str or list of such) –

    A single Curve or id or a list of such. A list defines the following curves in the order:

    • Forecasting Curve for floating leg.

    • Discounting Curve for both legs.

  • solver (Solver, optional) –

    The numerical Solver that constructs Curve from calibrating instruments.

    Note

    The arguments fx and base are unused by single currency derivatives rates calculations.

Return type:

float, Dual or Dual2

Notes

The arguments fx and base are unused by single currency derivatives rates calculations.