FloatBond
FloatBond
instrument object
Description
Create and price a FloatBond
instrument object using this
workflow:
Use
fininstrument
to create aFloatBond
instrument object.Use
ratecurve
to specify a curve model for theFloatBond
instrument or use aHullWhite
,BlackKarasinski
,BlackDermanToy
,BraceGatarekMusiela
,SABRBraceGatarekMusiela
,CoxIngersollRoss
, orLinearGaussian2F
model.Choose a pricing method.
When using a
ratecurve
, usefinpricer
to specify aDiscount
pricing method for one or moreFloatBond
instruments.When using a
HullWhite
,BlackKarasinski
,CoxIngersollRoss
, orBlackDermanToy
model, usefinpricer
to specify anIRTree
pricing method for one or moreFloatBond
instruments.When using a
HullWhite
,BlackKarasinski
,BraceGatarekMusiela
,SABRBraceGatarekMusiela
, orLinearGaussian2F
model, usefinpricer
to specify anIRMonteCarlo
pricing method for one or moreFloatBond
instruments.
For more information on this workflow, see Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments.
For more information on the available models and pricing methods for a
FloatBond
instrument, see Choose Instruments, Models, and Pricers.
Creation
Syntax
Description
creates a FloatBondObj
= fininstrument(InstrumentType
,'Spread
',spread_value,'Maturity
',maturity_date)FloatBond
object by specifying
InstrumentType
and sets the properties for the
required name-value pair arguments Spread
and
Maturity
.
The FloatBond
instrument supports a vanilla floating
rate note and an amortizing floating rate note. For more information, see
Floating-Rate Note.
sets optional properties using
additional name-value pairs in addition to the required arguments in the
previous syntax. For example, FloatBondObj
= fininstrument(___,Name,Value
)FloatBondObj =
fininstrument("FloatBond",'Spread',0.6,'Maturity',datetime(2019,1,30),'Basis',1,'Principal',100,'FirstCouponDate',datetime(2016,1,30),'EndMonthRule',true,'Name',"float_bond_instrument")
creates a FloatBond
instrument with a spread of 0.6 and a
maturity of January 30, 2019. You can specify multiple name-value pair
arguments.
Input Arguments
Instrument type, specified as a string with the value of
"FloatBond"
, a character vector with the value of
'FloatBond'
, an
NINST
-by-1
string array with
values of "FloatBond"
, or an
NINST
-by-1
cell array of
character vectors with values of 'FloatBond'
.
Data Types: char
| cell
| string
Name-Value Arguments
Specify required
and optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where
Name
is the argument name and Value
is
the corresponding value. Name-value arguments must appear after other arguments,
but the order of the pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.
Example: FloatBondObj =
fininstrument("FloatBond",'Spread',0.6,'Maturity',datetime(2019,1,30),'Basis',1,'Principal',100,'FirstCouponDate',datetime(2016,1,30),'EndMonthRule',true,'Name',"float_bond_instrument")
Required FloatBond
Name-Value Pair Arguments
Decimal value over the reference rate, specified as the
comma-separated pair consisting of 'Spread'
and a
scalar nonnegative decimal or an
NINST
-by-1
vector of
nonnegative decimals.
Data Types: double
Maturity date, specified as the comma-separated pair consisting of
'Maturity'
and a scalar or an
NINST
-by-1
vector using a
datetime array, string array, or date character vectors.
To support existing code, FloatBond
also
accepts serial date numbers as inputs, but they are not recommended.
If you use date character vectors or strings, the format must be
recognizable by datetime
because
the Maturity
property is stored as a
datetime.
Optional FloatBond
Name-Value Pair Arguments
Frequency of payments per year, specified as the comma-separated
pair consisting of 'Reset'
and a scalar integer
or an NINST
-by-1
vector of
integers. Values for Reset
are:
1
, 2
,
3
, 4
, 6
, or
12
.
Data Types: double
Day count basis, specified as the comma-separated pair consisting
of 'Basis'
and a scalar integer or an
NINST
-by-1
using the
following values:
0 — actual/actual
1 — 30/360 (SIA)
2 — actual/360
3 — actual/365
4 — 30/360 (PSA)
5 — 30/360 (ISDA)
6 — 30/360 (European)
7 — actual/365 (Japanese)
8 — actual/actual (ICMA)
9 — actual/360 (ICMA)
10 — actual/365 (ICMA)
11 — 30/360E (ICMA)
12 — actual/365 (ISDA)
13 — BUS/252
For more information, see Basis.
Data Types: double
Notional principal amount or principal value schedule, specified
as the comma-separated pair consisting of
'Principal'
and a scalar numeric or an
NINST
-by-1
numeric vector
or a timetable.
Principal
accepts a timetable
, where the
first column is dates and the second column is the associated
notional principal value. The date indicates the last day that the
principal value is valid.
Note
If you are creating one or more FloatBond
instruments and use a timetable, the timetable specification
applies to all of the FloatBond
instruments.
Principal
does not accept an
NINST
-by-1
cell array
of timetables as input.
Data Types: double
| timetable
Rate curve for projecting floating cash flows, specified as the
comma-separated pair consisting of
'ProjectionCurve'
and a scalar
ratecurve
object or an
NINST
-by-1
vector of
ratecurve
objects. You must create this
object using ratecurve
.
Data Types: object
Lag in rate setting, specified as the comma-separated pair
consisting of 'ResetOffset'
and a scalar numeric
or an NINST
-by-1
numeric
vector.
Data Types: double
Latest floating rate for the FloatBond
object,
specified as the comma-separated pair consisting of
'LatestFloatingRate'
and a scalar decimal or
an NINST
-by-1
vector of
decimals.
Data Types: double
Flag to adjust cash flows based on actual period day count,
specified as the comma-separated pair consisting of
'DaycountAdjustedCashFlow'
and a scalar
logical or an NINST
-by-1
vector of logicals with values of true
or
false
.
Data Types: logical
Business day conventions, specified as the comma-separated pair
consisting of 'BusinessDayConvention'
and a
scalar string or character vector or an
NINST
-by-1
cell array of
character vectors or string array. The selection for business day
convention determines how nonbusiness days are treated. Nonbusiness
days are defined as weekends plus any other date that businesses are
not open (for example, statutory holidays). Values are:
"actual"
— Nonbusiness days are effectively ignored. Cash flows that fall on nonbusiness days are assumed to be distributed on the actual date."follow"
— Cash flows that fall on a nonbusiness day are assumed to be distributed on the following business day."modifiedfollow"
— Cash flows that fall on a nonbusiness day are assumed to be distributed on the following business day. However if the following business day is in a different month, the previous business day is adopted instead."previous"
— Cash flows that fall on a nonbusiness day are assumed to be distributed on the previous business day."modifiedprevious"
— Cash flows that fall on a nonbusiness day are assumed to be distributed on the previous business day. However if the previous business day is in a different month, the following business day is adopted instead.
Data Types: char
| cell
| string
Holidays used in computing business days, specified as the
comma-separated pair consisting of 'Holidays'
and
dates using an NINST
-by-1
vector of a datetime array, string array, or date character vectors.
For
example:
H = holidays(datetime('today'),datetime(2025,12,15)); FloatBondObj = fininstrument("floatbond",'Spread',100,'Maturity',datetime(2025,12,15),'Holidays',H)
To support existing code, FloatBond
also
accepts serial date numbers as inputs, but they are not recommended.
End-of-month rule flag for generating dates when
Maturity
is an end-of-month date for a month
with 30 or fewer days, specified as the comma-separated pair
consisting of 'EndMonthRule'
and a scalar logical
or an NINST
-by-1
vector of
logicals with values of true
or
false
.
If you set
EndMonthRule
tofalse
, the software ignores the rule, meaning that a payment date is always the same numerical day of the month.If you set
EndMonthRule
totrue
, the software sets the rule on, meaning that a payment date is always the last actual day of the month.
Data Types: logical
Bond issue date, specified as the comma-separated pair consisting
of 'IssueDate'
and a scalar or an
NINST
-by-1
vector using a
datetime array, string array, or date character vectors.
To support existing code, FloatBond
also
accepts serial date numbers as inputs, but they are not recommended.
If you use date character vectors or strings, the format must be
recognizable by datetime
because
the IssueDate
property is stored as a
datetime.
Irregular first coupon date, specified as the comma-separated pair
consisting of 'FirstCouponDate'
and a scalar or
an NINST
-by-1
vector using a
datetime array, string array, or date character vectors.
To support existing code, FloatBond
also
accepts serial date numbers as inputs, but they are not recommended.
When FirstCouponDate
and
LastCouponDate
are both specified,
FirstCouponDate
takes precedence in
determining the coupon payment structure. If you do not specify
FirstCouponDate
, the cash flow payment dates
are determined from other inputs.
If you use date character vectors or strings, the format must be
recognizable by datetime
because
the FirstCouponDate
property is stored as a
datetime.
Irregular last coupon date, specified as the comma-separated pair
consisting of 'LastCouponDate'
and a scalar or an
NINST
-by-1
vector using a
datetime array, string array, or date character vectors.
To support existing code, FloatBond
also
accepts serial date numbers as inputs, but they are not recommended.
If you specify LastCouponDate
but not
FirstCouponDate
,
LastCouponDate
determines the coupon
structure of the bond. The coupon structure of a bond is truncated
at LastCouponDate
, regardless of where it falls,
and is followed only by the bond's maturity cash flow date. If you
do not specify LastCouponDate
, the cash flow
payment dates are determined from other inputs.
If you use date character vectors or strings, the format must be
recognizable by datetime
because
the LastCouponDate
property is stored as a
datetime.
Forward starting date of payments, specified as the
comma-separated pair consisting of 'StartDate'
and a scalar or an NINST
-by-1
vector using a datetime array, string array, or date character
vectors.
To support existing code, FloatBond
also
accepts serial date numbers as inputs, but they are not recommended.
If you use date character vectors or strings, the format must be
recognizable by datetime
because
the StartDate
property is stored as a
datetime.
User-defined name for one of more instruments, specified as the
comma-separated pair consisting of 'Name'
and a
scalar string or character vector or an
NINST
-by-1
cell array of
character vectors or string array.
Data Types: char
| cell
| string
Output Arguments
Float Bond instrument, returned as a FloatBond
object.
Properties
Number of basis points over the reference rate, returned as a scalar
nonnegative numeric or an NINST
-by-1
nonnegative numeric vector.
Data Types: double
Maturity date, returned as a scalar datetime or an
NINST
-by-1
vector of
datetimes.
Data Types: datetime
Coupons per year, returned as a scalar integer or an
NINST
-by-1
vector of
integers.
Data Types: double
Day count basis, returned as a scalar integer or an
NINST
-by-1
vector of integers.
Data Types: double
Notional principal amount or principal value schedules, returned as a
scalar numeric or an NINST
-by-1
numeric vector or a timetable.
Data Types: timetable
| double
Rate curve to be used in projecting the future cash flows, returned as a
scalar ratecurve
object or an
NINST
-by-1
vector of
ratecurve
objects.
Data Types: object
Lag in rate setting, returned as a scalar numeric or an
NINST
-by-1
numeric vector.
Data Types: double
Latest floating rate for FloatBond
, returned as a
scalar decimal or an NINST
-by-1
vector
of decimals.
Data Types: double
Flag to adjust cash flows based on actual period day count, returned as
scalar logical or an NINST
-by-1
vector
of logicals with values of true
or
false
.
Data Types: logical
Business day conventions, returned as a scalar string or an
NINST
-by-1
string array.
Data Types: string
Holidays used in computing business days, returned as an
NINST
-by-1
vector of
datetimes.
Data Types: datetime
End-of-month rule flag for generating dates when
Maturity
is an end-of-month date for a month with 30
or fewer days, returned as a scalar logical or an
NINST
-by-1
vector of logical
values.
Data Types: logical
Bond issue date, returned as a scalar datetime or an
NINST
-by-1
vector of
datetimes.
Data Types: datetime
Irregular first coupon date, returned as a scalar datetime or an
NINST
-by-1
vector of datetimes.
Data Types: datetime
Irregular last coupon date, returned as a scalar datetime or an
NINST
-by-1
vector of
datetimes.
Data Types: datetime
Forward starting date of payments, returned as a scalar datetime or an
NINST
-by-1
vector of datetimes.
Data Types: datetime
User-defined name for the instrument, returned as a string or an
NINST
-by-1
string array.
Data Types: string
Object Functions
cashflows | Compute cash flow for FixedBond , FloatBond ,
Swap , FRA , STIRFuture ,
OISFuture , OvernightIndexedSwap , or
Deposit instrument |
Examples
This example shows the workflow to price a vanilla FloatBond
instrument when you use a ratecurve
and a Discount
pricing method.
Create FloatBond
Instrument Object
Use fininstrument
to create a vanilla FloatBond
instrument object.
FloatB = fininstrument("FloatBond",'Maturity',datetime(2022,9,15),'Spread',0.025,'Reset',2,'Basis',1,'Principal',100,'EndMonthRule',false,'Name',"float_bond_instrument")
FloatB = FloatBond with properties: Spread: 0.0250 ProjectionCurve: [0×0 ratecurve] ResetOffset: 0 Reset: 2 Basis: 1 EndMonthRule: 0 Principal: 100 DaycountAdjustedCashFlow: 0 BusinessDayConvention: "actual" LatestFloatingRate: NaN Holidays: NaT IssueDate: NaT FirstCouponDate: NaT LastCouponDate: NaT StartDate: NaT Maturity: 15-Sep-2022 Name: "float_bond_instrument"
Create ratecurve
Object
Create a ratecurve
object using ratecurve
.
Settle = datetime(2018,9,15); Type = 'zero'; ZeroTimes = [calmonths(6) calyears([1 2 3 4 5 7 10 20 30])]'; ZeroRates = [0.0052 0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307]'; ZeroDates = Settle + ZeroTimes; myRC = ratecurve('zero',Settle,ZeroDates,ZeroRates)
myRC = ratecurve with properties: Type: "zero" Compounding: -1 Basis: 0 Dates: [10×1 datetime] Rates: [10×1 double] Settle: 15-Sep-2018 InterpMethod: "linear" ShortExtrapMethod: "next" LongExtrapMethod: "previous"
Create Discount
Pricer Object
Use finpricer
to create a Discount
pricer object and use the ratecurve
object for the 'DiscountCurve'
name-value pair argument.
outPricer = finpricer("Discount",'DiscountCurve',myRC)
outPricer = Discount with properties: DiscountCurve: [1×1 ratecurve]
Price FloatBond
Instrument
Use price
to compute the price and sensitivities for the vanilla FloatBond
instrument.
[Price, outPR] = price(outPricer, FloatB,["all"])
Price = 109.8322
outPR = priceresult with properties: Results: [1×2 table] PricerData: []
outPR.Results
ans=1×2 table
Price DV01
______ _________
109.83 0.0021981
This example shows the workflow to price multiple vanilla FloatBond
instruments when you use a ratecurve
and a Discount
pricing method.
Create FloatBond
Instrument Object
Use fininstrument
to create a vanilla FloatBond
instrument object for three Float Bond instruments.
FloatB = fininstrument("FloatBond",'Maturity',datetime([2022,9,15 ; 2022,9,15 ; 2022,9,15]),'Spread',0.025,'Reset',2,'Basis',1,'Principal',[100 ; 200 ; 300],'EndMonthRule',false,'Name',"float_bond_instrument")
FloatB=3×1 FloatBond array with properties:
Spread
ProjectionCurve
ResetOffset
Reset
Basis
EndMonthRule
Principal
DaycountAdjustedCashFlow
BusinessDayConvention
LatestFloatingRate
Holidays
IssueDate
FirstCouponDate
LastCouponDate
StartDate
Maturity
Name
Create ratecurve
Object
Create a ratecurve
object using ratecurve
.
Settle = datetime(2018,9,15); Type = 'zero'; ZeroTimes = [calmonths(6) calyears([1 2 3 4 5 7 10 20 30])]'; ZeroRates = [0.0052 0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307]'; ZeroDates = Settle + ZeroTimes; myRC = ratecurve('zero',Settle,ZeroDates,ZeroRates)
myRC = ratecurve with properties: Type: "zero" Compounding: -1 Basis: 0 Dates: [10×1 datetime] Rates: [10×1 double] Settle: 15-Sep-2018 InterpMethod: "linear" ShortExtrapMethod: "next" LongExtrapMethod: "previous"
Create Discount
Pricer Object
Use finpricer
to create a Discount
pricer object and use the ratecurve
object for the 'DiscountCurve'
name-value pair argument.
outPricer = finpricer("Discount",'DiscountCurve',myRC)
outPricer = Discount with properties: DiscountCurve: [1×1 ratecurve]
Price FloatBond
Instruments
Use price
to compute the prices and sensitivities for the vanilla FloatBond
instruments.
[Price, outPR] = price(outPricer, FloatB,["all"])
Price = 3×1
109.8322
219.6644
329.4965
outPR=1×3 priceresult array with properties:
Results
PricerData
outPR.Results
ans=1×2 table
Price DV01
______ _________
109.83 0.0021981
ans=1×2 table
Price DV01
______ _________
219.66 0.0043961
ans=1×2 table
Price DV01
_____ _________
329.5 0.0065942
This example shows the workflow to price an amortizing FloatBond
instrument when you use a ratecurve
and a Discount
pricing method.
Create ratecurve
Object
Create a ratecurve
object using ratecurve
.
Settle = datetime(2018,1,1); ZeroTimes = calyears(1:10)'; ZeroRates = [0.0052 0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307]'; ZeroDates = Settle + ZeroTimes; Compounding = 1; ZeroCurve = ratecurve("zero",Settle,ZeroDates,ZeroRates, "Compounding",Compounding);
Create FloatBond
Instrument Object
Use fininstrument
to create an amortizing FloatBond
instrument object.
Maturity = datetime(2024,1,1); Spread = 0.02; Reset = 1; ADates = datetime([2020,1,1 ; 2024,1,1]); APrincipal = [100; 80]; Principal = timetable(ADates,APrincipal); Floatamort = fininstrument("FloatBond",'Maturity',Maturity,'Spread',Spread,'Reset',Reset,'ProjectionCurve',ZeroCurve,'Principal',Principal)
Floatamort = FloatBond with properties: Spread: 0.0200 ProjectionCurve: [1×1 ratecurve] ResetOffset: 0 Reset: 1 Basis: 0 EndMonthRule: 1 Principal: [2×1 timetable] DaycountAdjustedCashFlow: 0 BusinessDayConvention: "actual" LatestFloatingRate: NaN Holidays: NaT IssueDate: NaT FirstCouponDate: NaT LastCouponDate: NaT StartDate: NaT Maturity: 01-Jan-2024 Name: ""
Create Discount
Pricer Object
Use finpricer
to create an Discount
pricer object and use the ratecurve
object with the 'DiscountCurve'
name-value pair argument.
outPricer = finpricer("Discount",'DiscountCurve',ZeroCurve)
outPricer = Discount with properties: DiscountCurve: [1×1 ratecurve]
Price FloatBond
Instrument
Use price
to compute the price and sensitivities for the vanilla FloatBond
instrument.
[Price, outPR] = price(outPricer,Floatamort,["all"])
Price = 110.1101
outPR = priceresult with properties: Results: [1×2 table] PricerData: []
outPR.Results
ans=1×2 table
Price DV01
______ _________
110.11 0.0033187
This example shows the workflow to price a FloatBond
instrument when using a HullWhite
model and an IRMonteCarlo
pricing method.
Create FloatBond
Instrument Object
Use fininstrument
to create a FloatBond
instrument object.
FloatB = fininstrument("FloatBond",'Maturity',datetime(2022,9,15),'Spread',0.025,'Reset',2,'Basis',1,'Principal',100,'EndMonthRule',false,'Name',"float_bond_instrument")
FloatB = FloatBond with properties: Spread: 0.0250 ProjectionCurve: [0×0 ratecurve] ResetOffset: 0 Reset: 2 Basis: 1 EndMonthRule: 0 Principal: 100 DaycountAdjustedCashFlow: 0 BusinessDayConvention: "actual" LatestFloatingRate: NaN Holidays: NaT IssueDate: NaT FirstCouponDate: NaT LastCouponDate: NaT StartDate: NaT Maturity: 15-Sep-2022 Name: "float_bond_instrument"
Create HullWhite
Model Object
Use finmodel
to create a HullWhite
model object.
HullWhiteModel = finmodel("HullWhite",'Alpha',0.32,'Sigma',0.49)
HullWhiteModel = HullWhite with properties: Alpha: 0.3200 Sigma: 0.4900
Create ratecurve
Object
Create a ratecurve
object using ratecurve
.
Settle = datetime(2019,1,1); Type = 'zero'; ZeroTimes = [calmonths(6) calyears([1 2 3 4 5 7 10 20 30])]'; ZeroRates = [0.0052 0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307]'; ZeroDates = Settle + ZeroTimes; myRC = ratecurve('zero',Settle,ZeroDates,ZeroRates)
myRC = ratecurve with properties: Type: "zero" Compounding: -1 Basis: 0 Dates: [10×1 datetime] Rates: [10×1 double] Settle: 01-Jan-2019 InterpMethod: "linear" ShortExtrapMethod: "next" LongExtrapMethod: "previous"
Create IRMonteCarlo
Pricer Object
Use finpricer
to create an IRMonteCarlo
pricer object and use the ratecurve
object for the 'DiscountCurve'
name-value pair argument.
outPricer = finpricer("IRMonteCarlo",'Model',HullWhiteModel,'DiscountCurve',myRC,'SimulationDates',ZeroDates)
outPricer = HWMonteCarlo with properties: NumTrials: 1000 RandomNumbers: [] DiscountCurve: [1×1 ratecurve] SimulationDates: [01-Jul-2019 01-Jan-2020 01-Jan-2021 01-Jan-2022 01-Jan-2023 01-Jan-2024 01-Jan-2026 01-Jan-2029 01-Jan-2039 01-Jan-2049] Model: [1×1 finmodel.HullWhite]
Price FloatBond
Instrument
Use price
to compute the price and sensitivities for the FloatBond
instrument.
[Price,outPR] = price(outPricer,FloatB,["all"])
Price = 109.1227
outPR = priceresult with properties: Results: [1×4 table] PricerData: [1×1 struct]
outPR.Results
ans=1×4 table
Price Delta Gamma Vega
______ _______ ______ ____
109.12 -19.033 50.224 0
This example shows the workflow to price a vanilla FloatBond
instrument when using a HullWhite
model and an IRTree pricing method.
Create ratecurve
Object
Create a ratecurve
object using ratecurve
.
Settle = datetime(2018,1,1); ZeroTimes = calyears(1:10)'; ZeroRates = [0.0052 0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307]'; ZeroDates = Settle + ZeroTimes; Compounding = 1; ZeroCurve = ratecurve("zero",Settle,ZeroDates,ZeroRates, "Compounding",Compounding);
Create FloatBond Instrument Object
Use fininstrument
to create a vanilla FloatdBond
instrument object.
Spread = 0.03; Reset = 1; Maturity = datetime(2024,1,1); Period = 1; Float = fininstrument("FloatBond",'Maturity',Maturity,'Spread',Spread,'Reset',Reset,'ProjectionCurve',ZeroCurve)
Float = FloatBond with properties: Spread: 0.0300 ProjectionCurve: [1×1 ratecurve] ResetOffset: 0 Reset: 1 Basis: 0 EndMonthRule: 1 Principal: 100 DaycountAdjustedCashFlow: 0 BusinessDayConvention: "actual" LatestFloatingRate: NaN Holidays: NaT IssueDate: NaT FirstCouponDate: NaT LastCouponDate: NaT StartDate: NaT Maturity: 01-Jan-2024 Name: ""
Create HullWhite Model Object
Use finmodel
to create a HullWhite
model object.
VolCurve = 0.01; AlphaCurve = 0.1; HWModel = finmodel("HullWhite",'alpha',AlphaCurve,'sigma',VolCurve);
Create IRTree Pricer Object
Use finpricer
to create an IRTree
pricer object and use the ratecurve
object with the 'DiscountCurve'
name-value pair argument.
HWTreePricer = finpricer("IRTree",'Model',HWModel,'DiscountCurve',ZeroCurve,'TreeDates',ZeroDates)
HWTreePricer = HWBKTree with properties: Tree: [1×1 struct] TreeDates: [10×1 datetime] Model: [1×1 finmodel.HullWhite] DiscountCurve: [1×1 ratecurve]
Price FloatBond Instrument
Use price
to compute the price and sensitivities for the vanilla FloatBond
instrument.
[Price, outPR] = price(HWTreePricer,Float,["all"])
Price = 117.4686
outPR = priceresult with properties: Results: [1×4 table] PricerData: [1×1 struct]
outPR.Results
ans=1×4 table
Price Delta Gamma Vega
______ _______ ______ ____
117.47 -60.007 315.09 0
This example shows the workflow to price a FloatBond
instrument when you use a CoxIngersollRoss
model and an IRTree
pricing method.
Create FloatBond
Instrument Object
Use fininstrument
to create a FloatBond
instrument object.
Maturity = datetime(2027,1,1); Spread = 0.0020; Reset = 1; FloatBond = fininstrument("FloatBond",Maturity=Maturity,Spread=Spread,Reset=Reset,Name="FloatBond_inst")
FloatBond = FloatBond with properties: Spread: 0.0020 ProjectionCurve: [0×0 ratecurve] ResetOffset: 0 Reset: 1 Basis: 0 EndMonthRule: 1 Principal: 100 DaycountAdjustedCashFlow: 0 BusinessDayConvention: "actual" LatestFloatingRate: NaN Holidays: NaT IssueDate: NaT FirstCouponDate: NaT LastCouponDate: NaT StartDate: NaT Maturity: 01-Jan-2027 Name: "FloatBond_inst"
Create CoxIngersollRoss
Model Object
Use finmodel
to create a CoxIngersollRoss
model object.
alpha = 0.03;
theta = 0.02;
sigma = 0.1;
CIRModel = finmodel("CoxIngersollRoss",Sigma=sigma,Alpha=alpha,Theta=theta)
CIRModel = CoxIngersollRoss with properties: Sigma: 0.1000 Alpha: 0.0300 Theta: 0.0200
Create ratecurve
Object
Create a ratecurve
object using ratecurve
.
Times= [calyears([1 2 3 4 ])]';
Settle = datetime(2023,1,1);
ZRates = [0.035; 0.042147; 0.047345; 0.052707]';
ZDates = Settle + Times;
Compounding = -1;
Basis = 1;
ZeroCurve = ratecurve("zero",Settle,ZDates,ZRates,Compounding = Compounding, Basis = Basis);
Create IRTree
Pricer Object
Use finpricer
to create an IRTree
pricer object for the CoxIngersollRoss
model and use the ratecurve
object for the 'DiscountCurve'
name-value argument.
CIRPricer = finpricer("irtree",Model=CIRModel,DiscountCurve=ZeroCurve,Maturity=ZDates(end),NumPeriods=length(ZDates))
CIRPricer = CIRTree with properties: Tree: [1×1 struct] TreeDates: [4×1 datetime] Model: [1×1 finmodel.CoxIngersollRoss] DiscountCurve: [1×1 ratecurve]
Price FloatBond
Instrument
Use price
to compute the price for the FloatBond
instrument.
[Price,outPR] = price(CIRPricer,FloatBond,"all")
Price = 100.7125
outPR = priceresult with properties: Results: [1×4 table] PricerData: [1×1 struct]
outPR.Results
ans=1×4 table
Price Delta Gamma Vega
______ _______ ______ __________
100.71 -1.7293 5.0818 2.8422e-10
More About
A floating-rate note (FRN) is a security like a bond, but the interest rate of the note is reset periodically, relative to a reference index rate, to reflect fluctuations in market interest rates.
A FRN has an interest rate tied to a benchmark like LIBOR or the U.S. Treasury bill rate, with interest payments calculated by adding a spread to the reference rate. FRNs offer protection against interest rate fluctuations, with interest payments increasing or decreasing in line with the reference rate. Typically issued with a fixed maturity date, FRNs make regular interest payments and repay the principal at maturity.
Version History
Introduced in R2020aYou can price FloatBond
instruments using a CoxIngersollRoss
model object
and an IRTree
pricing
method.
Although FloatBond
supports serial date numbers,
datetime
values are recommended instead. The
datetime
data type provides flexible date and time
formats, storage out to nanosecond precision, and properties to account for time
zones and daylight saving time.
To convert serial date numbers or text to datetime
values, use the datetime
function. For example:
t = datetime(738427.656845093,"ConvertFrom","datenum"); y = year(t)
y = 2021
There are no plans to remove support for serial date number inputs.
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