FloatRateNote#

class rateslib.instruments.FloatRateNote(effective=NoInput.blank, termination=NoInput.blank, frequency=NoInput.blank, stub=NoInput.blank, front_stub=NoInput.blank, back_stub=NoInput.blank, roll=NoInput.blank, eom=NoInput.blank, modifier=NoInput.blank, calendar=NoInput.blank, payment_lag=NoInput.blank, notional=NoInput.blank, currency=NoInput.blank, amortization=NoInput.blank, convention=NoInput.blank, float_spread=NoInput.blank, fixings=NoInput.blank, fixing_method=NoInput.blank, method_param=NoInput.blank, spread_compound_method=NoInput.blank, ex_div=NoInput.blank, settle=NoInput.blank, calc_mode=NoInput.blank, curves=NoInput.blank, spec=NoInput.blank, metric='clean_price')#

Bases: Sensitivities, BondMixin, Metrics

Create a floating rate note (FRN) security.

Parameters:

  • effective (datetime) – The adjusted or unadjusted effective date.

  • termination (datetime or str) – The adjusted or unadjusted termination date. If a string, then a tenor must be given expressed in days (“D”), months (“M”) or years (“Y”), e.g. “48M”.

  • frequency (str in {"M", "B", "Q", "T", "S", "A"}, optional) – The frequency of the schedule. “Z” is not permitted.

  • stub (str combining {"SHORT", "LONG"} with {"FRONT", "BACK"}, optional) – The stub type to enact on the swap. Can provide two types, for example “SHORTFRONTLONGBACK”.

  • front_stub (datetime, optional) – An adjusted or unadjusted date for the first stub period.

  • back_stub (datetime, optional) – An adjusted or unadjusted date for the back stub period. See notes for combining stub, front_stub and back_stub and any automatic stub inference.

  • roll (int in [1, 31] or str in {"eom", "imm", "som"}, optional) – The roll day of the schedule. Inferred if not given.

  • eom (bool, optional) – Use an end of month preference rather than regular rolls for inference. Set by default. Not required if roll is specified.

  • modifier (str, optional) – The modification rule, in {“F”, “MF”, “P”, “MP”}

  • calendar (calendar or str, optional) – The holiday calendar object to use. If str, looks up named calendar from static data.

  • payment_lag (int, optional) – The number of business days to lag payments by.

  • notional (float, optional) – The leg notional, which is applied to each period.

  • currency (str, optional) – The currency of the leg (3-digit code).

  • amortization (float, optional) – The amount by which to adjust the notional each successive period. Should have sign equal to that of notional if the notional is to reduce towards zero.

  • convention (str, optional) – The day count convention applied to calculations of period accrual dates. See dcf().

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

  • 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”}.

  • 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.

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

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

  • ex_div (int) – The number of business days prior to a cashflow which determines the last settlement date for which a coupon payment is still receivable. See BondMixin.ex_div().

  • settle (int) – The number of business days for regular settlement time, i.e, 1 is T+1.

  • calc_mode (str) – A calculation mode for dealing with bonds under different conventions. See notes.

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

    A single Curve or string id or a list of such.

    A list defines the following curves in the order:

    • Forecasting Curve for leg1.

    • Discounting Curve for leg1.

  • spec (str, optional) – An identifier to pre-populate many field with conventional values. See here for more info and available values.

  • metric (str, optional) – The pricing metric returned by the rate method of the Instrument.

Notes

Warning

FRNs based on RFR rates which have ex-div days must ensure that fixings are available to define the entire period. This means that ex_div days must be less than the fixing_method method_param lag minus the time to settlement time.

That is, a bond with a method_param of 5 and a settlement time of 2 days can have an ex_div period of at maximum 3.

A bond with a method_param of 2 and a settlement time of 1 day cnan have an ex_div period of at maximum 1.

ex_div_days#
Type:

int

leg1#
Type:

FloatLeg

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

accrued(settlement[, curve])

Calculate the accrued amount per nominal par value of 100.

analytic_delta([curve, disc_curve, fx, base])

Return the analytic delta of the security via summing all periods.

cashflows([curves, solver, fx, base, settlement])

Return the properties of the security used in calculating cashflows.

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

Aggregate the values derived from a cashflows() method on an Instrument.

delta(*args, **kwargs)

Calculate the delta of the Instrument.

ex_div(settlement)

Return a boolean whether the security is ex-div at the given settlement.

exo_delta(vars[, curves, solver, fx, base, ...])

Calculate delta risk of an Instrument against some exogenous user created Variables.

fixings_table([curves, solver, fx, base, ...])

Return a DataFrame of fixing exposures on the FloatLeg.

fwd_from_repo(price, settlement, ...[, ...])

Return a forward price implied by a given repo rate.

gamma(*args, **kwargs)

Calculate the gamma of the Instrument.

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

Return the NPV of the security by summing cashflow valuations.

oaspread([curves, solver, fx, base, price, ...])

The option adjusted spread added to the discounting Curve to value the security at price.

rate([curves, solver, fx, base, metric, ...])

Return various pricing metrics of the security calculated from Curve s.

repo_from_fwd(price, settlement, ...[, ...])

Return an implied repo rate from a forward price.

ytm(price, settlement[, curve, dirty])

Calculate the yield-to-maturity of the security given its price.

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

accrued(settlement, curve=NoInput.blank)#

Calculate the accrued amount per nominal par value of 100.

Parameters:

  • settlement (datetime) – The settlement date which to measure accrued interest against.

  • curve (Curve, optional) – If forecast is True and fixings are future based then must provide a forecast curve.

Notes

The settlement of an FRN will always be a definite amount. The fixing_method, method_param and ex_div will contain a valid combination of parameters such that when payments need to be cleared these definitive amounts can be calculated via previously published fixings.

If the coupon is IBOR based then the accrued fractionally apportions the coupon payment based on calendar days, including negative accrued during ex div periods. This rarely poses a problem since IBOR is fixed well in advance of settlement.

\[\text{Accrued} = \text{Coupon} \times \frac{\text{Settle - Last Coupon}}{\text{Next Coupon - Last Coupon}}\]

With RFR rates, however, and since settlement typically occurs in the future, e.g. T+2, it may be possible, particularly if the bond is ex-div that some fixings are not known today, but they will be known by settlement. This is also true if we wish to calculate the forward dirty price of a bond and need to forecast the accrued amount (and also for a forecast IBOR period).

Thus, there are two options:

  • In the analogue mode where very few fixings might be missing, and we require these values to calculate negative accrued in an ex-div period we do not require a curve but repeat the last historic fixing.

  • In the digital mode where the settlement is likely in the future we use a curve to forecast rates,

Examples

An RFR based FRN where the fixings are known up to the end of period.

In [1]: fixings = Series(2.0, index=date_range(dt(1999, 12, 1), dt(2000, 6, 2)))

In [2]: frn = FloatRateNote(
   ...:     effective=dt(1998, 12, 7),
   ...:     termination=dt(2015, 12, 7),
   ...:     frequency="S",
   ...:     currency="gbp",
   ...:     convention="Act365F",
   ...:     ex_div=3,
   ...:     fixings=fixings,
   ...:     fixing_method="rfr_observation_shift",
   ...:     method_param=5,
   ...: )
   ...: 

In [3]: frn.accrued(dt(2000, 3, 27))
Out[3]: np.float64(0.6100558220310195)

In [4]: frn.accrued(dt(2000, 6, 4))
Out[4]: np.float64(0.9911540636168727)

An IBOR based FRN where the coupon is known in advance.

In [5]: fixings = Series(2.0, index=[dt(1999, 12, 5)])

In [6]: frn = FloatRateNote(
   ...:     effective=dt(1998, 12, 7),
   ...:     termination=dt(2015, 12, 7),
   ...:     frequency="S",
   ...:     currency="gbp",
   ...:     convention="Act365F",
   ...:     ex_div=7,
   ...:     fixings=fixings,
   ...:     fixing_method="ibor",
   ...:     method_param=2,
   ...: )
   ...: 

In [7]: frn.accrued(dt(2000, 3, 27))
Out[7]: np.float64(0.608219178082192)

In [8]: frn.accrued(dt(2000, 6, 4))
Out[8]: np.float64(-0.016438356164383584)
analytic_delta(curve=NoInput.blank, disc_curve=NoInput.blank, fx=NoInput.blank, base=NoInput.blank)#

Return the analytic delta of the security via summing all periods.

For arguments see analytic_delta().

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

Return the properties of the security used in calculating cashflows.

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 leg1.

    • Discounting Curve for leg1.

  • 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), set by default. Only used if fx_rate is an FXRates or FXForwards object.

  • settlement (datetime, optional) – The settlement date of the security. If None adds the regular settle time to the initial node date of the given discount curves.

Return type:

DataFrame

cashflows_table(curves=NoInput.blank, solver=NoInput.blank, fx=NoInput.blank, base=NoInput.blank, **kwargs)#

Aggregate the values derived from a cashflows() method on an Instrument.

Parameters:

  • curves (CurveType, str or list of such, optional) – Argument input to the underlying cashflows method of the Instrument.

  • solver (Solver, optional) – Argument input to the underlying cashflows method of the Instrument.

  • fx (float, FXRates, FXForwards, optional) – Argument input to the underlying cashflows method of the Instrument.

  • base (str, optional) – Argument input to the underlying cashflows method of the Instrument.

  • kwargs (dict) – Additional arguments input the underlying cashflows method of the Instrument.

Return type:

DataFrame

delta(*args, **kwargs)#

Calculate the delta of the Instrument.

For arguments see Sensitivities.delta().

ex_div(settlement)#

Return a boolean whether the security is ex-div at the given settlement.

Parameters:

settlement (datetime) – The settlement date to test.

Return type:

bool

Notes

By default uses the UK DMO convention of returning False if settlement is on or before the ex-div date.

Ex-div dates are determined as measured by the number of ex_div business days prior to the unadjusted coupon end date.

With an ex_div of 1, a settlement that occurs on the coupon payment date will be classified as ex-dividend and not receive that coupon.

With an ex_div of 0, a settlement that occurs on the coupon payment date will not be classified as ex-dividend and will receive that coupon.

Most bonds under this convention have a ex_div parameter of 1. They will still receive the coupon if they settle 1 business day before the coupon end date, and will not receive the coupon if they settle on or after the coupon end date.

exo_delta(vars, curves=NoInput.blank, solver=NoInput.blank, fx=NoInput.blank, base=NoInput.blank, local=False, vars_scalar=NoInput.blank, vars_labels=NoInput.blank, **kwargs)#

Calculate delta risk of an Instrument against some exogenous user created Variables.

See What are exogenous variables? in the cookbook.

Parameters:

  • vars (list[str]) – The variable tags which to determine sensitivities for.

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

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

    • Forecasting Curve for leg1.

    • Discounting Curve for leg1.

    • Forecasting Curve for leg2.

    • Discounting Curve for leg2.

  • solver (Solver, optional) – The Solver that calibrates Curves from given 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), set by default. Only used if fx_rate is an FXRates or FXForwards object.

  • local (bool, optional) – If True will ignore base - this is equivalent to setting base to None. Included only for argument signature consistent with npv.

  • vars_scalar (list[float], optional) – Scaling factors for each variable, for example converting rates to basis point etc. Defaults to ones.

  • vars_labels (list[str], optional) – Alternative names to relabel variables in DataFrames.

Return type:

DataFrame

fixings_table(curves=NoInput.blank, solver=NoInput.blank, fx=NoInput.blank, base=NoInput.blank, approximate=False, right=NoInput.blank)#

Return a DataFrame of fixing exposures on the FloatLeg.

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 Instruments rates calculations.

  • approximate (bool, optional) – Perform a calculation that is broadly 10x faster but potentially loses precision upto 0.1%.

  • right (datetime, optional) – Only calculate fixing exposures upto and including this date.

Return type:

DataFrame

fwd_from_repo(price, settlement, forward_settlement, repo_rate, convention=NoInput.blank, dirty=False, method='proceeds')#

Return a forward price implied by a given repo rate.

Parameters:

  • price (float, Dual, or Dual2) – The initial price of the security at settlement.

  • settlement (datetime) – The settlement date of the bond

  • forward_settlement (datetime) – The forward date for which to calculate the forward price.

  • repo_rate (float, Dual or Dual2) – The rate which is used to calculate values.

  • convention (str, optional) – The day count convention applied to the rate. If not given uses default values.

  • dirty (bool, optional) – Whether the input and output price are specified including accrued interest.

  • method (str in {"proceeds", "compounded"}, optional) – The method for determining the forward price.

Return type:

float, Dual or Dual2

Notes

Any intermediate (non ex-dividend) cashflows between settlement and forward_settlement will also be assumed to accrue at repo_rate.

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 security by summing cashflow valuations.

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 leg1.

    • Discounting Curve for leg1.

  • 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), set by default. Only used if fx is an FXRates or FXForwards object.

  • local (bool, optional) – If True will ignore the base request and return a dict identifying local currency NPV.

Return type:

float, Dual, Dual2 or dict of such

Notes

The settlement date of the bond is inferred from the objects settle days parameter and the initial date of the supplied curves. The NPV returned is for immediate settlement.

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.

oaspread(curves=NoInput.blank, solver=NoInput.blank, fx=NoInput.blank, base=NoInput.blank, price=NoInput.blank, metric=NoInput.blank, func_tol=NoInput.blank, conv_tol=NoInput.blank)#

The option adjusted spread added to the discounting Curve to value the security at price.

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 leg1.

    • Discounting Curve for leg1.

  • 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), set by default. Only used if fx is an FXRates or FXForwards object.

  • price (float, Dual, Dual2) – The price of the bond to match.

  • metric (str, optional) – The metric to use when evaluating the price/rate of the instrument. If not given uses the instrument’s rate() method default.

  • func_tol (float, optional) – The tolerance for the objective function value when iteratively solving. If not given uses defaults.oaspread_func_tol.

  • conv_tol (float, optional) – The tolerance used for stopping criteria of successive iteration values. If not given uses defaults.oaspread_conv_tol.

Return type:

float, Dual, Dual2

Notes

The discount curve must be of type _BaseCurve with a provided shift() method available.

Warning

The sensitivity of variables is preserved for the input argument price, but this function does not preserve AD towards variables associated with the curves or solver.

Examples

In [9]: bond = FixedRateBond(dt(2000, 1, 1), "3Y", fixed_rate=2.5, spec="us_gb")

In [10]: curve = Curve({dt(2000, 7, 1): 1.0, dt(2005, 7, 1): 0.80})

# Add AD variables to the curve without a Solver
In [11]: curve._set_ad_order(1)

In [12]: bond.oaspread(curves=curve, price=Variable(95.0, ["price"], []))
Out[12]: <Dual: 11.809041, (price), [-42.6]>

This result excludes curve sensitivities but includes sensitivity to the constructed ‘price’ variable. Accuracy can be observed through numerical simulation.

In [13]: bond.oaspread(curves=curve, price=96.0)
Out[13]: -30.541959250658007

In [14]: bond.oaspread(curves=curve, price=94.0)
Out[14]: 54.615566044867904
rate(curves=NoInput.blank, solver=NoInput.blank, fx=NoInput.blank, base=NoInput.blank, metric=NoInput.blank, forward_settlement=NoInput.blank)#

Return various pricing metrics of the security calculated from Curve s.

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 leg1.

    • Discounting Curve for leg1.

  • 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), set by default. Only used if fx is an FXRates or FXForwards object.

  • metric (str, optional) – Metric returned by the method. Available options are {“clean_price”, “dirty_price”, “spread”, “ytm”}. Uses the Instrument default if not given.

  • forward_settlement (datetime, optional) – The forward settlement date. If not give uses the discount Curve and the bond’s settle attribute.}.

Return type:

float, Dual, Dual2

repo_from_fwd(price, settlement, forward_settlement, forward_price, convention=NoInput.blank, dirty=False)#

Return an implied repo rate from a forward price.

Parameters:

  • price (float, Dual, or Dual2) – The initial price of the security at settlement.

  • settlement (datetime) – The settlement date of the bond

  • forward_settlement (datetime) – The forward date for which to calculate the forward price.

  • forward_price (float, Dual or Dual2) – The forward price which iplies the repo rate

  • convention (str, optional) – The day count convention applied to the rate. If not given uses default values.

  • dirty (bool, optional) – Whether the input and output price are specified including accrued interest.

Return type:

float, Dual or Dual2

Notes

Any intermediate (non ex-dividend) cashflows between settlement and forward_settlement will also be assumed to accrue at repo_rate.

ytm(price, settlement, curve=NoInput.blank, dirty=False)#

Calculate the yield-to-maturity of the security given its price.

Parameters:

  • price (float, Dual, Dual2) – The price, per 100 nominal, against which to determine the yield.

  • settlement (datetime) – The settlement date on which to determine the price.

  • curve (Curve, dict[str, Curve]) – Curve used to forecast cashflows.

  • dirty (bool, optional) – If True will assume the accrued() is included in the price.

Return type:

float, Dual, Dual2

Notes

If price is given as Dual or Dual2 input the result of the yield will be output as the same type with the variables passed through accordingly.