FixedRateBond#

class rateslib.instruments.FixedRateBond(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, fixed_rate=NoInput.blank, ex_div=NoInput.blank, settle=NoInput.blank, calc_mode=NoInput.blank, curves=NoInput.blank, spec=NoInput.blank)#

Bases: Sensitivities, BondMixin, BaseMixin

Create a fixed rate bond 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. For zero-coupon-bonds use a fixed_rate of zero and set the frequency according to the yield-to-maturity convention required.

  • 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().

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

  • ex_div (int) – The number of days prior to a cashflow during which the bond is considered ex-dividend.

  • 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.

ex_div_days#
Type:

int

settle#
Type:

int

curves#
Type:

str, list, CurveType

leg1#
Type:

FixedLeg

Notes

Calculation Modes

The calc_mode parameter allows the calculation for yield-to-maturity and accrued interest to branch depending upon the particular convention of different bonds.

The following modes are currently available with a brief description of its particular action:

  • “ukg”: UK Gilt convention. Accrued is linearly proportioned, as are stub periods. Stub yields are compounded.

  • “ust”: US Treasury street convention. Same as “ukg” except long stub periods have linear proportioning only in the segregated short stub part.

  • “ust_31bii”: US Treasury convention that reprices examples in federal documents: Section 31-B-ii). Otherwise referred to as the ‘Treasury’ method.

  • “sgb”: Swedish government bond convention. Accrued ignores the convention and calculates using 30e360, also for back stubs.

  • “cadgb” Canadian government bond convention. Accrued is calculated using an ACT365F convention. Yield calculations are still derived with linearly proportioned compounded coupons.

More details available in supplementary materials. The table below outlines the rateslib price result relative to the calculation examples provided from official sources.

In [1]: from pandas import option_context

In [2]: with option_context("display.float_format", lambda x: '%.6f' % x):
   ...:     print(data)
   ...: 
                    Source       Example  Expected clean  Expected dirty  Calc mode  Rateslib clean  Rateslib dirty
0       Riksgalden Website  Nominal Bond      116.514000      119.868393        sgb      116.514226      119.868393
1           UK DMO Website  Ex 1, Scen 1             NaN      145.012268        ukg      141.319961      145.012268
2           UK DMO Website  Ex 1, Scen 2             NaN      145.047301        ukg      141.311037      145.047301
3           UK DMO Website  Ex 1, Scen 3             NaN      141.070132        ukg      141.311890      141.070132
4           UK DMO Website  Ex 1, Scen 4             NaN      141.257676        ukg      141.257676      141.257676
5           UK DMO Website  Ex 2, Scen 1             NaN      113.315543        ukg      110.238886      113.315543
6           UK DMO Website  Ex 2, Scen 2             NaN      113.415969        ukg      110.208786      113.415969
7           UK DMO Website  Ex 2, Scen 3             NaN      110.058738        ukg      110.207909      110.058738
8           UK DMO Website  Ex 2, Scen 4             NaN      110.170218        ukg      110.170218      110.170218
9   Title-31 Subtitle-B II    Ex A (reg)       99.057893       99.057893  ust_31bii       99.057893       99.057893
10  Title-31 Subtitle-B II   Ex B (stub)       99.838183       99.838183  ust_31bii       99.838183       99.838183
11  Title-31 Subtitle-B II   Ex C (stub)       99.805118       99.805118  ust_31bii       99.805118       99.805118
12  Title-31 Subtitle-B II    Ex D (reg)       99.730918      100.098321  ust_31bii       99.730918      100.098321
13  Title-31 Subtitle-B II   Ex E (stub)      102.214586      105.887384  ust_31bii      102.214586      105.887384
14  Title-31 Subtitle-B II   Ex F (stub)       99.777074      102.373541  ust_31bii       99.777073      102.373541
15  Title-31 Subtitle-B II   Ex G (stub)       99.738045      100.563865  ust_31bii       99.738045      100.563865

Examples

This example is taken from the UK debt management office (DMO) website. A copy of which is available here.

We demonstrate the use of analogue methods which do not need Curves or Solvers, price(), ytm(), ex_div(), accrued(), repo_from_fwd() fwd_from_repo() duration(), convexity().

In [3]: gilt = FixedRateBond(
   ...:     effective=dt(1998, 12, 7),
   ...:     termination=dt(2015, 12, 7),
   ...:     frequency="S",
   ...:     calendar="ldn",
   ...:     currency="gbp",
   ...:     convention="ActActICMA",
   ...:     ex_div=7,
   ...:     settle=1,
   ...:     fixed_rate=8.0,
   ...:     notional=-1e6,  # negative notional receives fixed, i.e. buys a bond
   ...:     curves="gilt_curve",
   ...: )
   ...: 

In [4]: gilt.ex_div(dt(1999, 5, 27))
Out[4]: True

In [5]: gilt.price(ytm=4.445, settlement=dt(1999, 5, 27), dirty=True)
Out[5]: 141.07013154004537

In [6]: gilt.ytm(price=141.070132, settlement=dt(1999, 5, 27), dirty=True)
Out[6]: 4.444999968624668

In [7]: gilt.accrued(dt(1999, 5, 27))
Out[7]: -0.24175824175824176

In [8]: gilt.fwd_from_repo(
   ...:     price=141.070132,
   ...:     settlement=dt(1999, 5, 27),
   ...:     forward_settlement=dt(2000, 2, 27),
   ...:     repo_rate=4.5,
   ...:     convention="Act365F",
   ...:     dirty=True,
   ...: )
   ...: 
Out[8]: 141.82994306695892

In [9]: gilt.repo_from_fwd(
   ...:     price=141.070132,
   ...:     settlement=dt(1999, 5, 27),
   ...:     forward_settlement=dt(2000, 2, 27),
   ...:     forward_price=141.829943,
   ...:     convention="Act365F",
   ...:     dirty=True,
   ...: )
   ...: 
Out[9]: 4.499999936695988

In [10]: gilt.duration(settlement=dt(1999, 5, 27), ytm=4.445, metric="risk")
Out[10]: 14.65975398077815

In [11]: gilt.duration(settlement=dt(1999, 5, 27), ytm=4.445, metric="modified")
Out[11]: 10.39181988471933

In [12]: gilt.convexity(settlement=dt(1999, 5, 27), ytm=4.445)
Out[12]: 2.03673015861093

The following digital methods consistent with the library’s ecosystem are also available, analytic_delta(), rate(), npv(), cashflows(), delta(), gamma().

In [13]: gilt_curve = Curve({dt(1999, 5, 26): 1.0, dt(2019, 5, 26): 1.0}, id="gilt_curve")

In [14]: instruments = [
   ....:     (gilt, (), {"metric": "ytm"}),
   ....: ]
   ....: 

In [15]: solver = Solver(
   ....:     curves=[gilt_curve],
   ....:     instruments=instruments,
   ....:     s=[4.445],
   ....:     instrument_labels=["8% Dec15"],
   ....:     id="gilt_solver",
   ....: )
   ....: 
SUCCESS: `func_tol` reached after 6 iterations (levenberg_marquardt), `f_val`: 2.6605195631838073e-17, `time`: 0.0475s

In [16]: gilt.npv(solver=solver)
Out[16]: <Dual: 1410531.560143, (gilt_curve0, gilt_curve1), [660978.5, 1805464.9]>

In [17]: gilt.analytic_delta(disc_curve=gilt_curve)
Out[17]: <Dual: -1158.813446, (gilt_curve0, gilt_curve1), [-721.5, -1053.4]>

In [18]: gilt.rate(solver=solver, metric="clean_price")
Out[18]: <Dual: 141.311890, (gilt_curve0, gilt_curve1), [-74.9, 180.5]>

The sensitivities are also available. In this case the Solver is calibrated with instruments priced in yield terms so sensitivities are measured in basis points (bps).

In [19]: gilt.delta(solver=solver)
Out[19]: 
local_ccy                             gbp
display_ccy                           gbp
type        solver      label            
instruments gilt_solver 8% Dec15 -1466.18

In [20]: gilt.gamma(solver=solver)
Out[20]: 
type                                                   instruments
solver                                                 gilt_solver
label                                                     8% Dec15
local_ccy display_ccy type        solver      label               
gbp       gbp         instruments gilt_solver 8% Dec15        2.04

The DataFrame of cashflows.

In [21]: gilt.cashflows(solver=solver)
Out[21]: 
           Type    Period  Ccy  Acc Start    Acc End    Payment  Convention  DCF    Notional   DF Collateral  Rate Spread   Cashflow       NPV  FX Rate   NPV Ccy
0   FixedPeriod   Regular  GBP 1998-12-07 1999-06-07 1999-06-07  ActActICMA 0.50 -1000000.00 1.00       None  8.00   None   40000.00      0.00     1.00      0.00
1   FixedPeriod   Regular  GBP 1999-06-07 1999-12-07 1999-12-07  ActActICMA 0.50 -1000000.00 0.98       None  8.00   None   40000.00  39072.26     1.00  39072.26
2   FixedPeriod   Regular  GBP 1999-12-07 2000-06-07 2000-06-07  ActActICMA 0.50 -1000000.00 0.96       None  8.00   None   40000.00  38221.20     1.00  38221.20
3   FixedPeriod   Regular  GBP 2000-06-07 2000-12-07 2000-12-07  ActActICMA 0.50 -1000000.00 0.93       None  8.00   None   40000.00  37388.67     1.00  37388.67
4   FixedPeriod   Regular  GBP 2000-12-07 2001-06-07 2001-06-07  ActActICMA 0.50 -1000000.00 0.91       None  8.00   None   40000.00  36578.68     1.00  36578.68
5   FixedPeriod   Regular  GBP 2001-06-07 2001-12-07 2001-12-07  ActActICMA 0.50 -1000000.00 0.89       None  8.00   None   40000.00  35781.93     1.00  35781.93
6   FixedPeriod   Regular  GBP 2001-12-07 2002-06-07 2002-06-07  ActActICMA 0.50 -1000000.00 0.88       None  8.00   None   40000.00  35006.75     1.00  35006.75
7   FixedPeriod   Regular  GBP 2002-06-07 2002-12-09 2002-12-09  ActActICMA 0.50 -1000000.00 0.86       None  8.00   None   40000.00  34236.00     1.00  34236.00
8   FixedPeriod   Regular  GBP 2002-12-09 2003-06-09 2003-06-09  ActActICMA 0.50 -1000000.00 0.84       None  8.00   None   40000.00  33494.30     1.00  33494.30
9   FixedPeriod   Regular  GBP 2003-06-09 2003-12-08 2003-12-08  ActActICMA 0.50 -1000000.00 0.82       None  8.00   None   40000.00  32768.68     1.00  32768.68
10  FixedPeriod   Regular  GBP 2003-12-08 2004-06-07 2004-06-07  ActActICMA 0.50 -1000000.00 0.80       None  8.00   None   40000.00  32058.78     1.00  32058.78
11  FixedPeriod   Regular  GBP 2004-06-07 2004-12-07 2004-12-07  ActActICMA 0.50 -1000000.00 0.78       None  8.00   None   40000.00  31360.48     1.00  31360.48
12  FixedPeriod   Regular  GBP 2004-12-07 2005-06-07 2005-06-07  ActActICMA 0.50 -1000000.00 0.77       None  8.00   None   40000.00  30681.08     1.00  30681.08
13  FixedPeriod   Regular  GBP 2005-06-07 2005-12-07 2005-12-07  ActActICMA 0.50 -1000000.00 0.75       None  8.00   None   40000.00  30012.79     1.00  30012.79
14  FixedPeriod   Regular  GBP 2005-12-07 2006-06-07 2006-06-07  ActActICMA 0.50 -1000000.00 0.73       None  8.00   None   40000.00  29362.59     1.00  29362.59
15  FixedPeriod   Regular  GBP 2006-06-07 2006-12-07 2006-12-07  ActActICMA 0.50 -1000000.00 0.72       None  8.00   None   40000.00  28723.02     1.00  28723.02
16  FixedPeriod   Regular  GBP 2006-12-07 2007-06-07 2007-06-07  ActActICMA 0.50 -1000000.00 0.70       None  8.00   None   40000.00  28100.77     1.00  28100.77
17  FixedPeriod   Regular  GBP 2007-06-07 2007-12-07 2007-12-07  ActActICMA 0.50 -1000000.00 0.69       None  8.00   None   40000.00  27488.68     1.00  27488.68
18  FixedPeriod   Regular  GBP 2007-12-07 2008-06-09 2008-06-09  ActActICMA 0.50 -1000000.00 0.67       None  8.00   None   40000.00  26883.46     1.00  26883.46
19  FixedPeriod   Regular  GBP 2008-06-09 2008-12-08 2008-12-08  ActActICMA 0.50 -1000000.00 0.66       None  8.00   None   40000.00  26301.05     1.00  26301.05
20  FixedPeriod   Regular  GBP 2008-12-08 2009-06-08 2009-06-08  ActActICMA 0.50 -1000000.00 0.64       None  8.00   None   40000.00  25731.26     1.00  25731.26
21  FixedPeriod   Regular  GBP 2009-06-08 2009-12-07 2009-12-07  ActActICMA 0.50 -1000000.00 0.63       None  8.00   None   40000.00  25173.82     1.00  25173.82
22  FixedPeriod   Regular  GBP 2009-12-07 2010-06-07 2010-06-07  ActActICMA 0.50 -1000000.00 0.62       None  8.00   None   40000.00  24628.45     1.00  24628.45
23  FixedPeriod   Regular  GBP 2010-06-07 2010-12-07 2010-12-07  ActActICMA 0.50 -1000000.00 0.60       None  8.00   None   40000.00  24092.00     1.00  24092.00
24  FixedPeriod   Regular  GBP 2010-12-07 2011-06-07 2011-06-07  ActActICMA 0.50 -1000000.00 0.59       None  8.00   None   40000.00  23570.07     1.00  23570.07
25  FixedPeriod   Regular  GBP 2011-06-07 2011-12-07 2011-12-07  ActActICMA 0.50 -1000000.00 0.58       None  8.00   None   40000.00  23056.67     1.00  23056.67
26  FixedPeriod   Regular  GBP 2011-12-07 2012-06-07 2012-06-07  ActActICMA 0.50 -1000000.00 0.56       None  8.00   None   40000.00  22554.45     1.00  22554.45
27  FixedPeriod   Regular  GBP 2012-06-07 2012-12-07 2012-12-07  ActActICMA 0.50 -1000000.00 0.55       None  8.00   None   40000.00  22063.18     1.00  22063.18
28  FixedPeriod   Regular  GBP 2012-12-07 2013-06-07 2013-06-07  ActActICMA 0.50 -1000000.00 0.54       None  8.00   None   40000.00  21585.20     1.00  21585.20
29  FixedPeriod   Regular  GBP 2013-06-07 2013-12-09 2013-12-09  ActActICMA 0.50 -1000000.00 0.53       None  8.00   None   40000.00  21109.95     1.00  21109.95
30  FixedPeriod   Regular  GBP 2013-12-09 2014-06-09 2014-06-09  ActActICMA 0.50 -1000000.00 0.52       None  8.00   None   40000.00  20652.62     1.00  20652.62
31  FixedPeriod   Regular  GBP 2014-06-09 2014-12-08 2014-12-08  ActActICMA 0.50 -1000000.00 0.51       None  8.00   None   40000.00  20205.20     1.00  20205.20
32  FixedPeriod   Regular  GBP 2014-12-08 2015-06-08 2015-06-08  ActActICMA 0.50 -1000000.00 0.49       None  8.00   None   40000.00  19767.48     1.00  19767.48
33  FixedPeriod   Regular  GBP 2015-06-08 2015-12-07 2015-12-07  ActActICMA 0.50 -1000000.00 0.48       None  8.00   None   40000.00  19339.23     1.00  19339.23
34     Cashflow  Exchange  GBP        NaT        NaT 2015-12-07        None  NaN -1000000.00 0.48       None   NaN   None 1000000.00 483480.80     1.00 483480.80

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)

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])

convexity(ytm, settlement)

Return the second derivative of price w.r.t.

delta(*args, **kwargs)

Calculate the delta of the Instrument.

duration(ytm, settlement[, metric])

Return the (negated) derivative of price w.r.t.

ex_div(settlement)

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

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.

price(ytm, settlement[, dirty])

Calculate the price of the security per nominal value of 100, given yield-to-maturity.

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[, 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)#

Calculate the accrued amount per nominal par value of 100.

Parameters:

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

Notes

Fractionally apportions the coupon payment based on calendar days.

\[\text{Accrued} = \text{Coupon} \times \frac{\text{Settle - Last Coupon}}{\text{Next Coupon - Last Coupon}}\]
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)#
convexity(ytm, settlement)#

Return the second derivative of price w.r.t. ytm.

Parameters:

  • ytm (float) – The yield-to-maturity for the bond.

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

Return type:

float

Examples

In [22]: gilt = FixedRateBond(
   ....:     effective=dt(1998, 12, 7),
   ....:     termination=dt(2015, 12, 7),
   ....:     frequency="S",
   ....:     calendar="ldn",
   ....:     currency="gbp",
   ....:     convention="ActActICMA",
   ....:     ex_div=7,
   ....:     fixed_rate=8.0
   ....: )
   ....: 

In [23]: gilt.convexity(4.445, dt(1999, 5, 27))
Out[23]: 2.03673015861093

This number is interpreted as hundredths of a cent. For a 1bp increase in yield the duration will decrease by 2 hundredths of a cent.

In [24]: gilt.duration(4.445, dt(1999, 5, 27))
Out[24]: 14.65975398077815

In [25]: gilt.duration(4.455, dt(1999, 5, 27))
Out[25]: 14.63940251353963
delta(*args, **kwargs)#

Calculate the delta of the Instrument.

For arguments see Sensitivities.delta().

duration(ytm, settlement, metric='risk')#

Return the (negated) derivative of price w.r.t. ytm.

Parameters:

  • ytm (float) – The yield-to-maturity for the bond.

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

  • metric (str) – The specific duration calculation to return. See notes.

Return type:

float

Notes

The available metrics are:

  • “risk”: the derivative of price w.r.t. ytm, scaled to -1bp.

    \[risk = - \frac{\partial P }{\partial y}\]

  • “modified”: the modified duration which is risk divided by price.

    \[mduration = \frac{risk}{P} = - \frac{1}{P} \frac{\partial P }{\partial y}\]

  • “duration”: the duration which is modified duration reverse modified.

    \[duration = mduration \times (1 + y / f)\]

Examples

In [26]: gilt = FixedRateBond(
   ....:     effective=dt(1998, 12, 7),
   ....:     termination=dt(2015, 12, 7),
   ....:     frequency="S",
   ....:     calendar="ldn",
   ....:     currency="gbp",
   ....:     convention="ActActICMA",
   ....:     ex_div=7,
   ....:     fixed_rate=8.0
   ....: )
   ....: 

In [27]: gilt.duration(4.445, dt(1999, 5, 27), "risk")
Out[27]: 14.65975398077815

In [28]: gilt.duration(4.445, dt(1999, 5, 27), "modified")
Out[28]: 10.39181988471933

In [29]: gilt.duration(4.445, dt(1999, 5, 27), "duration")
Out[29]: 10.622778081657216

This result is interpreted as cents. If the yield is increased by 1bp the price will fall by 14.65 cents.

In [30]: gilt.price(4.445, dt(1999, 5, 27))
Out[30]: 141.31188978180361

In [31]: gilt.price(4.455, dt(1999, 5, 27))
Out[31]: 141.16539402571507
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.

Some calc_mode options return True if settlement is on 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 (in the default calculation mode).

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, dirty=False)#

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.

  • dirty (bool) – Whether the price is given clean or dirty.

Return type:

float, Dual, Dual2

price(ytm, settlement, dirty=False)#

Calculate the price of the security per nominal value of 100, given yield-to-maturity.

Parameters:

  • ytm (float) – The yield-to-maturity against which to determine the price.

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

  • dirty (bool, optional) – If True will include the rateslib.instruments.FixedRateBond.accrued() in the price.

Return type:

float, Dual, Dual2

Examples

This example is taken from the UK debt management office website. The result should be 141.070132 and the bond is ex-div.

In [1]: gilt = FixedRateBond(
   ...:     effective=dt(1998, 12, 7),
   ...:     termination=dt(2015, 12, 7),
   ...:     frequency="S",
   ...:     calendar="ldn",
   ...:     currency="gbp",
   ...:     convention="ActActICMA",
   ...:     ex_div=7,
   ...:     fixed_rate=8.0
   ...: )
   ...: 

In [2]: gilt.ex_div(dt(1999, 5, 27))
Out[2]: True

In [3]: gilt.price(
   ...:     ytm=4.445,
   ...:     settlement=dt(1999, 5, 27),
   ...:     dirty=True
   ...: )
   ...: 
Out[3]: 141.07013154004537

This example is taken from the Swedish national debt office website. The result of accrued should, apparently, be 0.210417 and the clean price should be 99.334778.

In [4]: bond = FixedRateBond(
   ...:     effective=dt(2017, 5, 12),
   ...:     termination=dt(2028, 5, 12),
   ...:     frequency="A",
   ...:     calendar="stk",
   ...:     currency="sek",
   ...:     convention="ActActICMA",
   ...:     ex_div=5,
   ...:     fixed_rate=0.75
   ...: )
   ...: 

In [5]: bond.ex_div(dt(2017, 8, 23))
Out[5]: False

In [6]: bond.accrued(dt(2017, 8, 23))
Out[6]: 0.21164383561643835

In [7]: bond.price(
   ...:     ytm=0.815,
   ...:     settlement=dt(2017, 8, 23),
   ...:     dirty=False
   ...: )
   ...: 
Out[7]: 99.3348737576038
rate(curves=NoInput.blank, solver=NoInput.blank, fx=NoInput.blank, base=NoInput.blank, metric='clean_price', 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”, “ytm”}

  • forward_settlement (datetime, optional) – The forward settlement date. If not given the settlement date is inferred from the discount Curve and the 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, dirty=False)#

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

Parameters:

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

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

  • 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.

Examples

In [1]: gilt = FixedRateBond(
   ...:     effective=dt(1998, 12, 7),
   ...:     termination=dt(2015, 12, 7),
   ...:     frequency="S",
   ...:     calendar="ldn",
   ...:     currency="gbp",
   ...:     convention="ActActICMA",
   ...:     ex_div=7,
   ...:     fixed_rate=8.0
   ...: )
   ...: 

In [2]: gilt.ytm(
   ...:     price=141.0701315,
   ...:     settlement=dt(1999,5,27),
   ...:     dirty=True
   ...: )
   ...: 
Out[2]: 4.445000002731656

In [3]: gilt.ytm(Dual(141.0701315, ["price", "a", "b"], [1, -0.5, 2]), dt(1999, 5, 27), True)
Out[3]: <Dual: 4.445000, (price, a, b), [-0.1, 0.0, -0.1]>

In [4]: gilt.ytm(Dual2(141.0701315, ["price", "a", "b"], [1, -0.5, 2], []), dt(1999, 5, 27), True)
Out[4]: <Dual2: 4.445000, (price, a, b), [-0.1, 0.0, -0.1], [[...]]>