FRA

class rateslib.instruments.FRA(effective=NoInput.blank, termination=NoInput.blank, frequency=NoInput.blank, roll=NoInput.blank, eom=NoInput.blank, modifier=NoInput.blank, calendar=NoInput.blank, payment_lag=NoInput.blank, notional=NoInput.blank, currency=NoInput.blank, convention=NoInput.blank, method_param=NoInput.blank, fixed_rate=NoInput.blank, fixings=NoInput.blank, curves=NoInput.blank, spec=NoInput.blank)

Bases: Sensitivities, BaseMixin

Create a forward rate agreement composing single period FixedLeg and FloatLeg valued in a customised manner.

Parameters:

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

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

• fixings (float or list, 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 as the first m RFR fixings within individual curve and composed into the overall rate.

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

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

Notes

FRAs are a legacy derivative whose FloatLeg fixing_method is set to “ibor”.

Examples

Construct curves to price the example.

In [1]: eur3m = Curve(
   ...:     nodes={
   ...:         dt(2022, 1, 1): 1.0,
   ...:         dt(2023, 1, 1): 0.965,
   ...:         dt(2024, 1, 1): 0.94
   ...:     },
   ...:     id="eur3m",
   ...: )
   ...: 

Create the FRA, and demonstrate the rate(), npv(), analytic_delta().

In [2]: fra = FRA(
   ...:     effective=dt(2023, 2, 15),
   ...:     termination="3M",
   ...:     frequency="Q",
   ...:     calendar="tgt",
   ...:     currency="eur",
   ...:     method_param=2,
   ...:     convention="Act360",
   ...:     notional=100e6,
   ...:     fixed_rate=2.617,
   ...:     curves=["eur3m"],
   ...: )
   ...: 

In [3]: fra.rate(curves=eur3m)
Out[3]: 2.5971685347783104

In [4]: fra.npv(curves=eur3m)
Out[4]: -4685.809351368945

In [5]: fra.analytic_delta(curve=eur3m)
Out[5]: 2362.815505051087

A DataFrame of cashflows().

In [6]: fra.cashflows(curves=eur3m)
Out[6]: 
  Type   Period  Ccy  Acc Start    Acc End    Payment Convention  DCF     Notional   DF Collateral  Rate  Spread  Cashflow      NPV  FX Rate  NPV Ccy
0  FRA  Regular  EUR 2023-02-15 2023-05-15 2023-02-15     ACT360 0.25 100000000.00 0.96       None -2.62 -259.72  -4871.50 -4685.81     1.00 -4685.81

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

In [7]: irs_kws = dict(
   ...:     effective=dt(2022, 1, 1),
   ...:     frequency="A",
   ...:     leg2_frequency="Q",
   ...:     convention="30E360",
   ...:     leg2_convention="Act360",
   ...:     leg2_fixing_method="ibor",
   ...:     leg2_method_param=2,
   ...:     calendar="tgt",
   ...:     currency="eur",
   ...:     curves=["eur3m", "eur3m"],
   ...: )
   ...: 

In [8]: instruments = [
   ...:     IRS(termination="1Y", **irs_kws),
   ...:     IRS(termination="2Y", **irs_kws),
   ...: ]
   ...: 

In [9]: solver = Solver(
   ...:     curves=[eur3m],
   ...:     instruments=instruments,
   ...:     s=[1.55, 1.6],
   ...:     instrument_labels=["1Y", "2Y"],
   ...:     id="eur",
   ...: )
   ...: 
SUCCESS: `func_tol` reached after 4 iterations (levenberg_marquardt), `f_val`: 8.531977771337697e-16, `time`: 0.0102s

In [10]: fra.delta(solver=solver)
Out[10]: 
local_ccy                     eur
display_ccy                   eur
type        solver label         
instruments eur    1Y    -2375.63
                   2Y     4766.74

In [11]: fra.gamma(solver=solver)
Out[11]: 
type                                           instruments      
solver                                                 eur      
label                                                   1Y    2Y
local_ccy display_ccy type        solver label                  
eur       eur         instruments eur    1Y           0.60 -0.48
                                         2Y          -0.48 -0.45

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(curve[, disc_curve, fx, base])	Return the analytic delta of the FRA.
cashflow(curve)	Calculate the local currency cashflow on the FRA from current floating rate and fixed rate.
cashflows([curves, solver, fx, base])	Return the properties of the leg 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.
rate([curves, solver, fx, base])	Return the mid-market rate of the FRA.

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(curve, disc_curve=NoInput.blank, fx=NoInput.blank, base=NoInput.blank)

Return the analytic delta of the FRA.

For arguments see analytic_delta().

cashflow(curve)

Calculate the local currency cashflow on the FRA from current floating rate and fixed rate.

Parameters:

curve (Curve or LineCurve,) – The forecasting curve for determining the floating rate.

Return type:

float, Dual or Dual2

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

Return the properties of the leg used in calculating cashflows.

Parameters:

• args – Positional arguments supplied to cashflows().

• kwargs – Keyword arguments supplied to cashflows().

Return type:

DataFrame

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.

See BaseDerivative.npv().

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

Return the mid-market rate of the FRA.

Only the forecasting curve is required to price an FRA.

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 floating leg.

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

• fx (unused)

• base (unused)

Return type:

float, Dual or Dual2