FloatLeg#
- class rateslib.legs.FloatLeg(*args, float_spread=NoInput.blank, fixings=NoInput.blank, fixing_method=NoInput.blank, method_param=NoInput.blank, spread_compound_method=NoInput.blank, **kwargs)#
Bases:
_FloatLegMixin,BaseLegCreate a floating leg composed of
FloatPeriods.- Parameters:
args (tuple) – Required positional args to
BaseLeg.float_spread (float, optional) – The spread applied to determine cashflows in bps (i.e. 100 = 1%). 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, list, Series, 2-tuple, 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 indexedSerieswill use the fixings that are available in that object, and derive the rest from thecurve. If a 2-tuple of value and Series, the first scalar value is applied to the first period and latter periods handled as with Series.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_methods. See notes.kwargs (dict) – Required keyword arguments to
BaseLeg.
Notes
The NPV of a FloatLeg is the sum of the period NPVs.
\[P = \underbrace{- \sum_{i=1}^n {N_i r_i(r_j, z) d_i v_i(m_i)}}_{\text{regular flows}} \underbrace{+ N_1 v(m_0) - \sum_{i=1}^{n-1}v(m_i)(N_{i}-N_{i+1}) - N_n v(m_n)}_{\text{exchange flows}}\]The analytic delta is the sum of the period analytic deltas.
\[A = -\frac{\partial P}{\partial z} = \sum_{i=1}^n {\frac{\partial r_i}{\partial z} N_i d_i v_i(m_i)}\]Warning
When floating rates are determined from historical fixings the forecast
Curvecalendarwill be used to determine fixing dates. If this calendar does not align with theLegcalendarthen spurious results or errors may be generated.Including the curve calendar within a Leg multi-holiday calendar is acceptable, i.e. a Leg calendar of “nyc,ldn,tgt” and a curve calendar of “ldn” is valid. A Leg calendar of just “nyc,tgt” may give errors.
Examples
Set the first fixing on an historic IBOR leg.
In [1]: float_leg = FloatLeg( ...: schedule=Schedule(dt(2021, 12, 1), "9M", "Q"), ...: fixing_method="ibor", ...: fixings=2.00, ...: ) ...: In [2]: float_leg.cashflows(curve) Out[2]: Type Period Ccy Acc Start Acc End Payment Convention DCF Notional DF Collateral Rate Spread Cashflow NPV FX Rate NPV Ccy 0 FloatPeriod Regular USD 2021-12-01 2022-03-01 2022-03-03 Act360 0.250000 1000000.0 0.996629 None 2.000000 0.0 -5000.000000 -4983.146753 1.0 -4983.146753 1 FloatPeriod Regular USD 2022-03-01 2022-06-01 2022-06-03 Act360 0.255556 1000000.0 0.991567 None 1.997678 0.0 -5105.176472 -5062.125667 1.0 -5062.125667 2 FloatPeriod Regular USD 2022-06-01 2022-09-01 2022-09-03 Act360 0.255556 1000000.0 0.986531 None 1.997678 0.0 -5105.176472 -5036.413886 1.0 -5036.413886
Set multiple fixings on an historic IBOR leg.
In [3]: float_leg = FloatLeg( ...: schedule=Schedule(dt(2021, 9, 1), "12M", "Q"), ...: fixing_method="ibor", ...: fixings=[1.00, 2.00], ...: ) ...: In [4]: float_leg.cashflows(curve) Out[4]: Type Period Ccy Acc Start Acc End Payment Convention DCF Notional DF Collateral Rate Spread Cashflow NPV FX Rate NPV Ccy 0 FloatPeriod Regular USD 2021-09-01 2021-12-01 2021-12-03 Act360 0.252778 1000000.0 0.000000 None 1.000000 0.0 -2527.777778 0.000000 1.0 0.000000 1 FloatPeriod Regular USD 2021-12-01 2022-03-01 2022-03-03 Act360 0.250000 1000000.0 0.996629 None 2.000000 0.0 -5000.000000 -4983.146753 1.0 -4983.146753 2 FloatPeriod Regular USD 2022-03-01 2022-06-01 2022-06-03 Act360 0.255556 1000000.0 0.991567 None 1.997678 0.0 -5105.176472 -5062.125667 1.0 -5062.125667 3 FloatPeriod Regular USD 2022-06-01 2022-09-01 2022-09-03 Act360 0.255556 1000000.0 0.986531 None 1.997678 0.0 -5105.176472 -5036.413886 1.0 -5036.413886
It is not best practice to supply fixings as a list of values. It is better to supply a Series indexed by IBOR publication date (in this case lagged by zero days).
In [5]: float_leg = FloatLeg( ...: schedule=Schedule(dt(2021, 9, 1), "12M", "Q"), ...: fixing_method="ibor", ...: method_param=0, ...: fixings=Series([1.00, 2.00], index=[dt(2021, 9, 1), dt(2021, 12, 1)]) ...: ) ...: In [6]: float_leg.cashflows(curve) Out[6]: Type Period Ccy Acc Start Acc End Payment Convention DCF Notional DF Collateral Rate Spread Cashflow NPV FX Rate NPV Ccy 0 FloatPeriod Regular USD 2021-09-01 2021-12-01 2021-12-03 Act360 0.252778 1000000.0 0.000000 None 1.000000 0.0 -2527.777778 0.000000 1.0 0.000000 1 FloatPeriod Regular USD 2021-12-01 2022-03-01 2022-03-03 Act360 0.250000 1000000.0 0.996629 None 2.000000 0.0 -5000.000000 -4983.146753 1.0 -4983.146753 2 FloatPeriod Regular USD 2022-03-01 2022-06-01 2022-06-03 Act360 0.255556 1000000.0 0.991567 None 1.997678 0.0 -5105.176472 -5062.125667 1.0 -5062.125667 3 FloatPeriod Regular USD 2022-06-01 2022-09-01 2022-09-03 Act360 0.255556 1000000.0 0.986531 None 1.997678 0.0 -5105.176472 -5036.413886 1.0 -5036.413886
Set the initial RFR fixings in the first period of an RFR leg (notice the sublist and the implied -10% year end turn spread).
In [7]: swestr_curve = Curve({dt(2023, 1, 2): 1.0, dt(2023, 7, 2): 0.99}, calendar="stk") In [8]: float_leg = FloatLeg( ...: schedule=Schedule(dt(2022, 12, 28), "2M", "M", calendar="stk"), ...: fixings=[[1.19, 1.19, -8.81]], ...: currency="SEK", ...: ) ...: In [9]: float_leg.cashflows(swestr_curve) Out[9]: Type Period Ccy Acc Start Acc End Payment Convention DCF Notional DF Collateral Rate Spread Cashflow NPV FX Rate NPV Ccy 0 FloatPeriod Regular SEK 2022-12-28 2023-01-30 2023-02-01 Act360 0.091667 1000000.0 0.998336 None 0.967434 0.0 -886.814795 -885.338768 1.0 -885.338768 1 FloatPeriod Regular SEK 2023-01-30 2023-02-28 2023-03-02 Act360 0.080556 1000000.0 0.996729 None 2.000572 0.0 -1611.571994 -1606.301000 1.0 -1606.301000 In [10]: float_leg.fixings_table(swestr_curve)[dt(2022,12,28):dt(2023,1,4)] Out[10]: 15722 notional risk dcf rates obs_dates 2022-12-28 0.000000 0.000000 0.002778 1.190000 2022-12-29 0.000000 0.000000 0.002778 1.190000 2022-12-30 0.000000 0.000000 0.008333 -8.810000 2023-01-02 -999220.923922 -0.277546 0.002778 1.999017 2023-01-03 -999276.408920 -0.277546 0.002778 1.999017 2023-01-04 -999331.897000 -0.277546 0.002778 1.999017
Again, this is poor practice. It is best practice to supply a Series of RFR rates by reference value date.
In [11]: float_leg = FloatLeg( ....: schedule=Schedule(dt(2022, 12, 28), "2M", "M", calendar="stk"), ....: fixings=Series([1.19, 1.19, -8.81], index=[dt(2022, 12, 28), dt(2022, 12, 29), dt(2022, 12, 30)]), ....: currency="SEK", ....: ) ....: In [12]: float_leg.cashflows(swestr_curve) Out[12]: Type Period Ccy Acc Start Acc End Payment Convention DCF Notional DF Collateral Rate Spread Cashflow NPV FX Rate NPV Ccy 0 FloatPeriod Regular SEK 2022-12-28 2023-01-30 2023-02-01 Act360 0.091667 1000000.0 0.998336 None 0.967434 0.0 -886.814795 -885.338768 1.0 -885.338768 1 FloatPeriod Regular SEK 2023-01-30 2023-02-28 2023-03-02 Act360 0.080556 1000000.0 0.996729 None 2.000572 0.0 -1611.571994 -1606.301000 1.0 -1606.301000 In [13]: float_leg.fixings_table(swestr_curve)[dt(2022,12,28):dt(2023,1,4)] Out[13]: 15722 notional risk dcf rates obs_dates 2022-12-28 0.000000 0.000000 0.002778 1.190000 2022-12-29 0.000000 0.000000 0.002778 1.190000 2022-12-30 0.000000 0.000000 0.008333 -8.810000 2023-01-02 -999220.923922 -0.277546 0.002778 1.999017 2023-01-03 -999276.408920 -0.277546 0.002778 1.999017 2023-01-04 -999331.897000 -0.277546 0.002778 1.999017
Methods Summary
analytic_delta(*args, **kwargs)Return the analytic delta of the FloatLeg via summing all periods.
cashflows(*args, **kwargs)Return the properties of the FloatLeg used in calculating cashflows.
fixings_table(curve[, disc_curve, fx, base, ...])Return a DataFrame of fixing exposures on a
FloatLeg.npv(*args, **kwargs)Return the NPV of the FloatLeg via summing all periods.
Methods Documentation
- analytic_delta(*args, **kwargs)#
Return the analytic delta of the FloatLeg via summing all periods.
For arguments see
BasePeriod.analytic_delta().
- cashflows(*args, **kwargs)#
Return the properties of the FloatLeg used in calculating cashflows.
For arguments see
BasePeriod.cashflows().
- fixings_table(curve, disc_curve=NoInput.blank, fx=NoInput.blank, base=NoInput.blank, approximate=False, right=NoInput.blank)#
Return a DataFrame of fixing exposures on a
FloatLeg.- Parameters:
curve (Curve, optional) – The forecasting curve object.
disc_curve (Curve, optional) – The discounting curve object used in calculations. Set equal to
curveif not given andcurveis discount factor based.fx (float, FXRates, FXForwards, optional) – Only used in the case of
FloatLegMtmto derive FX fixings.base (str, optional) – Not used by
fixings_table.approximate (bool) – Whether to use a faster (3x) but marginally less accurate (0.1% error) calculation.
right (datetime, optional) – Only calculate fixing exposures upto and including this date.
- Return type:
DataFrame
- npv(*args, **kwargs)#
Return the NPV of the FloatLeg via summing all periods.
For arguments see
BasePeriod.npv().