ZCS#

class rateslib.instruments.ZCS(*args, fixed_rate=NoInput.blank, leg2_float_spread=NoInput.blank, leg2_spread_compound_method=NoInput.blank, leg2_fixings=NoInput.blank, leg2_fixing_method=NoInput.blank, leg2_method_param=NoInput.blank, **kwargs)#

Bases: BaseDerivative

Create a zero coupon swap (ZCS) composing a ZeroFixedLeg and a ZeroFloatLeg.

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.

  • leg2_float_spread (float, optional) – The spread applied to the FloatLeg. Can be set to None and designated later, perhaps after a mid-market spread for all periods has been calculated.

  • leg2_spread_compound_method (str, optional) – The method to use for adding a floating spread to compounded rates. Available options are {“none_simple”, “isda_compounding”, “isda_flat_compounding”}.

  • leg2_fixings (float, list, or Series optional) – If a float scalar, will be applied as the determined fixing for the first period. If a list of n fixings will be used as the fixings for the first n periods. If any sublist of length m is given, is used as the first m RFR fixings for that FloatPeriod. If a datetime indexed Series will use the fixings that are available in that object, and derive the rest from the curve.

  • leg2_fixing_method (str, optional) – The method by which floating rates are determined, set by default. See notes.

  • leg2_method_param (int, optional) – A parameter that is used for the various fixing_method s. See notes.

  • 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): 0.70,
   ...:     },
   ...:     id="usd"
   ...: )
   ...:

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

In [2]: zcs = ZCS(
   ...:     effective=dt(2022, 1, 1),
   ...:     termination="10Y",
   ...:     frequency="Q",
   ...:     calendar="nyc",
   ...:     currency="usd",
   ...:     fixed_rate=4.0,
   ...:     convention="Act360",
   ...:     notional=100e6,
   ...:     curves=["usd"],
   ...: )
   ...: 

In [3]: zcs.rate(curves=usd)
Out[3]: 3.5307483757290647

In [4]: zcs.npv(curves=usd)
Out[4]: -4825959.828579076

In [5]: zcs.analytic_delta(curve=usd)
Out[5]: 105226.66099084073

A DataFrame of cashflows().

In [6]: zcs.cashflows(curves=usd)
Out[6]: 
                Type Period  Ccy  Acc Start    Acc End    Payment Convention   DCF      Notional   DF  Rate  Spread     Cashflow          NPV  FX Rate      NPV Ccy Collateral
leg1 0  ZeroFixedLeg   None  USD 2022-01-01 2032-01-01 2032-01-06     Act360 10.14  100000000.00 0.70  4.00     NaN -49744798.25 -34802851.16     1.00 -34802851.16       None
leg2 0  ZeroFloatLeg   None  USD 2022-01-03 2032-01-02 2032-01-06     Act360 10.14 -100000000.00 0.70  4.22    0.00  42846903.68  29976891.34     1.00  29976891.34       None

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

In [7]: sofr_kws = dict(
   ...:     effective=dt(2022, 1, 1),
   ...:     frequency="A",
   ...:     convention="Act360",
   ...:     calendar="nyc",
   ...:     currency="usd",
   ...:     curves=["usd"]
   ...: )
   ...: 

In [8]: instruments = [
   ...:     IRS(termination="5Y", **sofr_kws),
   ...:     IRS(termination="10Y", **sofr_kws),
   ...: ]
   ...: 

In [9]: solver = Solver(
   ...:     curves=[usd],
   ...:     instruments=instruments,
   ...:     s=[3.40, 3.60],
   ...:     instrument_labels=["5Y", "10Y"],
   ...:     id="sofr",
   ...: )
   ...: 
SUCCESS: `func_tol` reached after 5 iterations (levenberg_marquardt), `f_val`: 2.2942031400260264e-15, `time`: 0.0121s

In [10]: zcs.delta(solver=solver)
Out[10]: 
local_ccy                      usd
display_ccy                    usd
type        solver label          
instruments sofr   5Y    -10155.74
                   10Y   112851.29

In [11]: zcs.gamma(solver=solver)
Out[11]: 
type                                           instruments       
solver                                                sofr       
label                                                   5Y    10Y
local_ccy display_ccy type        solver label                   
usd       usd         instruments sofr   5Y           4.24 -23.45
                                         10Y        -23.45 -68.59

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, **kwargs)

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 by summing legs.

rate([curves, solver, fx, base])

Return the mid-market rate of the ZCS.

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

analytic_delta(*args, **kwargs)#

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

See BaseDerivative.analytic_delta.

cashflows(curves=NoInput.blank, solver=NoInput.blank, fx=NoInput.blank, base=NoInput.blank)#

Return the properties of all legs used in calculating cashflows.

See BaseDerivative.cashflows().

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 by summing legs.

See BaseDerivative.npv().

rate(curves=NoInput.blank, solver=NoInput.blank, fx=NoInput.blank, base=NoInput.blank)#

Return the mid-market rate of the ZCS.

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.

The ‘irr’ fixed_rate defines a cashflow by:

\[-notional * ((1 + irr / f)^{f \times dcf} - 1)\]

where \(f\) is associated with the compounding frequency.