FixedBond
Description
Create and price a FixedBond
instrument object for one of
more Fixed Bond instruments using this workflow:
Use
fininstrument
to create aFixedBond
instrument object for one of more Fixed Bond instruments.Use
ratecurve
to specify a curve model for theFixedBond
instrument object 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 moreFixedBond
instruments.When using a
HullWhite
,BlackKarasinski
,CoxIngersollRoss
, orBlackDermanToy
model, usefinpricer
to specify anIRTree
pricing method for one or moreFixedBond
instruments.When using a
HullWhite
,BlackKarasinski
,BraceGatarekMusiela
,SABRBraceGatarekMusiela
, orLinearGaussian2F
model, usefinpricer
to specify anIRMonteCarlo
pricing method for one or moreFixedBond
instruments.
For more detailed 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
FixedBond
instrument, see Choose Instruments, Models, and Pricers.
Creation
Syntax
Description
creates a FixedBondObj
= fininstrument(InstrumentType
,'CouponRate
',couponrate_value,'Maturity
',maturity_date)FixedBond
object for one of more Fixed Bond
instruments by specifying InstrumentType
and sets the
properties for the
required name-value pair arguments CouponRate
and
Maturity
.
The FixedBond
instrument supports a vanilla bond, a
stepped coupon bond, and an amortizing bond. For more information, see More About.
sets optional properties using
additional name-value pairs in addition to the required arguments in the
previous syntax. For example, FixedBondObj
= fininstrument(___,Name,Value
)FixedBondObj =
fininstrument("FixedBond",'CouponRate',0.34,'Maturity',datetime(2019,1,30),'Period',4,'Basis',1,'Principal',100,'FirstCouponDate',datetime(2016,1,30),'EndMonthRule',true,'Name',"fixedbond_instrument")
creates a FixedBond
option with a coupon rate of 0.34 and
a maturity of January 30, 2019. You can specify multiple name-value pair
arguments.
Input Arguments
InstrumentType
— Instrument type
string with value "Fixedbond"
| string array with values of "Fixedbond"
| character vector with value 'FixedBond'
| cell array of character vectors with values of
'FixedBond'
Instrument type, specified as a string with the value of
"FixedBond"
, a character vector with the value of
'FixedBond'
, an
NINST
-by-1
string array with
values of "FixedBond"
, or an
NINST
-by-1
cell array of
character vectors with values of 'FixedBond'
.
Data Types: char
| cell
| string
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: FixedBondObj =
fininstrument("FixedBond",'CouponRate',0.34,'Maturity',datetime(2019,1,30),'Period',4,'Basis',1,'Principal',100,'FirstCouponDate',datetime(2016,1,30),'EndMonthRule',true,'Name',"fixedbond_instrument")
FixedBond
Name-Value Pair ArgumentsCouponRate
— FixedBond
coupon rate
scalar decimal | vector of decimals | timetable
FixedBond
coupon rate, specified as the
comma-separated pair consisting of 'CouponRate'
and a scalar decimal or an
NINST
-by-1
vector of
decimals for an annual rate or a timetable where the first column is
dates and the second column is associated rates. The date indicates
the last day that the coupon rate is valid.
Note
If you are creating one or more FixedBond
instruments and use a timetable, the timetable specification
applies to all of the FixedBond
instruments.
CouponRate
does not accept an
NINST
-by-1
cell array
of timetables as input.
Data Types: double
| timetable
Maturity
— FixedBond
maturity date
datetime array | string array | date character vector
FixedBond
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, FixedBond
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.
FixedBond
Name-Value Pair ArgumentsPeriod
— Frequency of payments per year
2
(default) | scalar numeric value of 0
,
1
, 2
,
3
, 4
, 6
, or
12
| numeric vector with values of 0
,
1
, 2
,
3
, 4
, 6
, or
12
Frequency of payments, specified as the comma-separated pair
consisting of 'Period'
and a scalar integer or an
NINST
-by-1
vector of
integers. Values for Period
are
1
, 2
,
3
, 4
, 6
, or
12
.
Data Types: double
Basis
— Day count basis
0
(actual/actual) (default) | scalar integer from 0
to
13
| vector of integers from 0
to
13
Day count basis, specified as the comma-separated pair consisting
of 'Basis'
and scalar integer or an
NINST
-by-1
vector of
integers 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
Principal
— Principal amount or principal value schedule
100
(default) | scalar numeric | numeric vector | timetable
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 FixedBond
instruments and use a timetable, the timetable specification
applies to all of the FixedBond
instruments.
Principal
does not accept an
NINST
-by-1
cell array
of timetables as input.
Data Types: double
| timetable
DaycountAdjustedCashFlow
— Flag indicating whether cash flow adjusts for day count convention
false
(default) | scalar logical value of true
or
false
| vector of logical values of true
or
false
Flag indicating whether cash flow is adjusted by day count
convention, 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
BusinessDayConvention
— Business day conventions for cash flow dates
"actual"
(default) | string | string array | character vector | cell array of character vectors
Business day conventions for cash flow dates, 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
— Holidays used in computing business days
NaT
(default) | datetime array | string array | date character vector
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)); FixedBondObj = fininstrument("FixedBond",'CouponRate',0.34,'Maturity',datetime(2025,12,15),'Holidays',H)
To support existing code, FixedBond
also
accepts serial date numbers as inputs, but they are not recommended.
EndMonthRule
— End-of-month rule flag for generating dates when Maturity
is end-of-month date for month with 30
or fewer days
true
(in effect) (default) | scalar logical value of true
or
false
| vector of logical values of true
or
false
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
value 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
IssueDate
— Bond issue date
NaT
(default) | datetime array | string array | date character vector
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, FixedBond
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.
FirstCouponDate
— Irregular first coupon date
NaT
(default) | datetime array | string array | date character vector
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, FixedBond
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.
LastCouponDate
— Irregular last coupon date
NaT
(default) | datetime array | string array | date character vector
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, FixedBond
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.
StartDate
— Forward starting date of payments
NaT
(default) | datetime array | string array | date character vector
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, FixedBond
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.
Name
— User-defined name for instrument
" "
(default) | string | string array | character vector | cell array of character vectors
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
Properties
CouponRate
— FixedBond
coupon annual rate
scalar decimal | vector of decimals | timetable
FixedBond
coupon annual rate, returned as a scalar
decimal or an NINST
-by-1
vector of
decimals or a timetable.
Data Types: double
| timetable
Maturity
— FixedBond
maturity date
scalar datetime | vector of datetimes
FixedBond
maturity date, returned as a scalar datetime
or NINST
-by-1
vector of
datetimes.
Data Types: datetime
Period
— Frequency of payments per year
2
(default) | scalar integer | vector of integers
Frequency of payments per year, returned as a scalar integer or an
NINST
-by-1
vector of
integers.
Data Types: double
Basis
— Day count basis
0
(actual/actual) (default) | scalar integer from 0
to 13
| vector of integers from 0
to
13
Day count basis, returned as a scalar integer or an
NINST
-by-1
vector of integers.
Data Types: double
Principal
— Principal amount or principal value schedules
100
(default) | scalar numeric | numeric vector | timetable
Principal amount or principal value schedules, returned as a scalar
numeric or an NINST
-by-1
numeric
vector or a timetable.
Data Types: double
DaycountAdjustedCashFlow
— Flag indicating whether cash flow adjusts for day count convention
false
(default) | scalar logical value of true
or
false
| vector of logicals with values of true
or
false
Flag indicating whether cash flow adjusts for day count convention,
returned as scalar logical or an
NINST
-by-1
vector of logicals with
values of true
or false
.
Data Types: logical
BusinessDayConvention
— Business day conventions
"actual"
(default) | string | string array
Business day conventions, returned as a scalar string or an
NINST
-by-1
string array.
Data Types: string
Holidays
— Holidays used in computing business days
NaT
(default) | datetimes
Holidays used in computing business days, returned as an
NINST
-by-1
vector of
datetimes.
Data Types: datetime
EndMonthRule
— End-of-month rule flag for generating dates when Maturity
is end-of-month date for month with 30 or fewer
days
true
(in effect) (default) | scalar logical value of true
or
false
| vector of logicals with values of true
or
false
End-of-month rule flag for generating dates when
Maturity
is an end-of-month date for a month having
30 or fewer days, returned as a scalar logical or an
NINST
-by-1
vector of logical
values.
Data Types: logical
IssueDate
— Bond issue date
NaT
(default) | datetime | vector of datetimes
Bond issue date, returned as a scalar datetime or an
NINST
-by-1
vector of
datetimes.
Data Types: datetime
FirstCouponDate
— Irregular first coupon date
NaT
(default) | datetime | vector of datetimes
Irregular first coupon date, returned as a scalar datetime or an
NINST
-by-1
vector of datetimes.
Data Types: datetime
LastCouponDate
— Irregular last coupon date
NaT
(default) | datetime | vector of datetimes
Irregular last coupon date, returned as a scalar datetime or an
NINST
-by-1
vector of
datetimes.
Data Types: datetime
StartDate
— Forward starting date of payments
NaT
(default) | datetime | vector of datetimes
Forward starting date of payments, returned as a scalar datetime or an
NINST
-by-1
vector of datetimes.
Data Types: datetime
Name
— User-defined name for instrument
" "
(default) | string | string array
User-defined name for the instrument, returned as a scalar 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
Price Vanilla FixedBond
Instrument Using ratecurve
and Discount
Pricer
This example shows the workflow to price a vanilla FixedBond
instrument when you use a ratecurve
and a Discount
pricing method.
Create FixedBond
Instrument Object
Use fininstrument
to create a FixedBond
instrument object.
FixB = fininstrument("FixedBond",'Maturity',datetime(2022,9,15),'CouponRate',0.021,'Period',2,'Basis',1,'Principal',100,'Name',"fixed_bond_instrument")
FixB = FixedBond with properties: CouponRate: 0.0210 Period: 2 Basis: 1 EndMonthRule: 1 Principal: 100 DaycountAdjustedCashFlow: 0 BusinessDayConvention: "actual" Holidays: NaT IssueDate: NaT FirstCouponDate: NaT LastCouponDate: NaT StartDate: NaT Maturity: 15-Sep-2022 Name: "fixed_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: [10x1 datetime] Rates: [10x1 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 with the 'DiscountCurve'
name-value pair argument.
outPricer = finpricer("Discount",'DiscountCurve',myRC)
outPricer = Discount with properties: DiscountCurve: [1x1 ratecurve]
Price FixedBond
Instrument
Use price
to compute the price and sensitivities for the FixedBond
instrument.
[Price, outPR] = price(outPricer, FixB,["all"])
Price = 104.5679
outPR = priceresult with properties: Results: [1x2 table] PricerData: []
outPR.Results
ans=1×2 table
Price DV01
______ ________
104.57 0.040397
Price Vanilla FixedBond
Instrument Using ratecurve
and Discount
Pricer and Perform Bond Analytics
This example shows how to create a FixedBond
instrument and then use any of the following Financial Toolbox™ functions to perform bond analytics: bnddurp
, bnddury
, bndconvp
, bndconvy
, bndkrdur
, cfdur
, and cfconv
.
Create FixedBond
Instrument Object
Use fininstrument
to create a FixedBond
instrument object.
MaturityDate = datetime(2027,12,16); CouponRate = 0.01; FixedBondObj = fininstrument('FixedBond','CouponRate',CouponRate,'Maturity',MaturityDate);
Create ratecurve
Object
Create a ratecurve
object using ratecurve
.
Settle = datetime(2022,10,10);
MarketDates = datetime([2023,9,15 ; 2024,9,15 ; 2025,9,15 ; 2026,9,15 ; 2027,9,15 ; 2028,9,15]);
ZeroDates = datetime([2023,10,15 ; 2024,10,15 ; 2025,10,15 ; 2026,10,15 ; 2027,10,15 ; 2028,10,15]);
ZeroRates = [4.2520 4.1081 3.8801 3.7170 3.6060 3.5250]'/100;
MarketSpreads = [97.9825 97.9825 97.9825 97.9825 97.9825 97.9825]';
RateObjB = ratecurve('zero',Settle,ZeroDates,ZeroRates+MarketSpreads(1)/10000);
Create Discount
Pricer Object
Use finpricer
to create a Discount
pricer object and use the ratecurve
object with the 'DiscountCurve'
name-value argument.
Pricer1 = finpricer("Discount",'DiscountCurve',RateObjB);
Price FixedBond
Instrument
Use price
to compute the price and sensitivities for the FixedBond
instrument.
[Price1, outPR] = price(Pricer1, FixedBondObj,["all"])
Price1 = 83.4210
outPR = priceresult with properties: Results: [1x2 table] PricerData: []
Compute Bond Durations for FixedBond
Instrument
Use bnddurp
to compute the bond durations given the bond price.
[ModDuration, YearDuration, PerDuration] = bnddurp(Price1,FixedBondObj.CouponRate, Settle, FixedBondObj.Maturity,Period=FixedBondObj.Period)
ModDuration = 4.9169
YearDuration = 5.0308
PerDuration = 10.0616
Compute Key Rate Durations for FixedBond
Instrument
Use bndkrdur
to compute the FixedBond
instrument key rate duration given a zero curve.
ZeroData1 = [datenum(RateObjB.Dates) RateObjB.Rates]; KeyRateDuration = bndkrdur(ZeroData1,FixedBondObj.CouponRate,Settle,FixedBondObj.Maturity)
KeyRateDuration = 1×6
0.0133 0.0212 0.0304 0.0389 4.0226 0.8164
Price Multiple Vanilla FixedBond
Instruments Using ratecurve
and Discount
Pricer
This example shows the workflow to price multiple vanilla FixedBond
instruments when you use a ratecurve
and a Discount
pricing method.
Create FixedBond
Instrument Object
Use fininstrument
to create a FixedBond
instrument object for three Fixed Bond instruments.
FixB = fininstrument("FixedBond",'Maturity',datetime([2022,9,15 ; 2022,10,15 ; 2022,11,15]),'CouponRate',0.021,'Period',2,'Basis',1,'Principal',[100 ; 250 ; 500],'Name',"fixed_bond_instrument")
FixB=3×1 FixedBond array with properties:
CouponRate
Period
Basis
EndMonthRule
Principal
DaycountAdjustedCashFlow
BusinessDayConvention
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: [10x1 datetime] Rates: [10x1 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 with the 'DiscountCurve'
name-value pair argument.
outPricer = finpricer("Discount",'DiscountCurve',myRC)
outPricer = Discount with properties: DiscountCurve: [1x1 ratecurve]
Price FixedBond
Instruments
Use price
to compute the prices and sensitivities for the FixedBond
instruments.
[Price, outPR] = price(outPricer, FixB,["all"])
Price = 3×1
104.5679
261.4498
522.9174
outPR=1×3 priceresult array with properties:
Results
PricerData
outPR.Results
ans=1×2 table
Price DV01
______ ________
104.57 0.040397
ans=1×2 table
Price DV01
______ _____
261.45 0.103
ans=1×2 table
Price DV01
______ _______
522.92 0.21013
Price Stepped FixedBond
Instrument Using ratecurve
and Discount
Pricer
This example shows the workflow to price a stepped FixedBond
instrument when you use a ratecurve
and a Discount
pricing method.
Create FixedBond
Instrument Object
Use fininstrument
to create a stepped FixedBond
instrument object.
Maturity = datetime(2024,1,1); Period = 1; CDates = datetime([2020,1,1 ; 2024,1,1]); CRates = [.025; .03]; CouponRate = timetable(CDates,CRates); SBond = fininstrument("FixedBond",'Maturity',Maturity,'CouponRate',CouponRate,'Period',Period)
SBond = FixedBond with properties: CouponRate: [2x1 timetable] Period: 1 Basis: 0 EndMonthRule: 1 Principal: 100 DaycountAdjustedCashFlow: 0 BusinessDayConvention: "actual" Holidays: NaT IssueDate: NaT FirstCouponDate: NaT LastCouponDate: NaT StartDate: NaT Maturity: 01-Jan-2024 Name: ""
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)
ZeroCurve = ratecurve with properties: Type: "zero" Compounding: 1 Basis: 0 Dates: [10x1 datetime] Rates: [10x1 double] Settle: 01-Jan-2018 InterpMethod: "linear" ShortExtrapMethod: "next" LongExtrapMethod: "previous"
Create Discount
Pricer Object
Use finpricer
to create a 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: [1x1 ratecurve]
Price FixedBond
Instrument
Use price
to compute the price and sensitivities for the vanilla FixedBond
instrument.
[Price, outPR] = price(outPricer, SBond,["all"])
Price = 109.6218
outPR = priceresult with properties: Results: [1x2 table] PricerData: []
outPR.Results
ans=1×2 table
Price DV01
______ ________
109.62 0.061108
Price Amortizing FixedBond
Instrument Using ratecurve
and Discount
Pricer
This example shows the workflow to price an amortizing FixedBond
instrument when you use a ratecurve
and a Discount
pricing method.
Create FixedBond
Instrument Object
Use fininstrument
to create an amortizing FixedBond
instrument object.
Maturity = datetime(2024,1,1); Period = 1; ADates = datetime([2020,1,1 ; 2024,1,1]); APrincipal = [100; 85]; Principal = timetable(ADates,APrincipal); Bondamort = fininstrument("FixedBond",'Maturity',Maturity,'CouponRate',0.025,'Period',Period,'Principal',Principal)
Bondamort = FixedBond with properties: CouponRate: 0.0250 Period: 1 Basis: 0 EndMonthRule: 1 Principal: [2x1 timetable] DaycountAdjustedCashFlow: 0 BusinessDayConvention: "actual" Holidays: NaT IssueDate: NaT FirstCouponDate: NaT LastCouponDate: NaT StartDate: NaT Maturity: 01-Jan-2024 Name: ""
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 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',ZeroCurve)
outPricer = Discount with properties: DiscountCurve: [1x1 ratecurve]
Price FixedBond
Instrument
Use price
to compute the price and sensitivities for the vanilla FixedBond
instrument.
[Price, outPR] = price(outPricer,Bondamort,["all"])
Price = 107.1273
outPR = priceresult with properties: Results: [1x2 table] PricerData: []
outPR.Results
ans=1×2 table
Price DV01
______ ________
107.13 0.054279
Price FixedBond
Instrument Using HullWhite
Model and IRMonteCarlo
Pricer
This example shows the workflow to price a FixedBond
instrument when using a HullWhite
model and an IRMonteCarlo
pricing method.
Create FixedBond
Instrument Object
Use fininstrument
to create a FixedBond
instrument object.
FixB = fininstrument("FixedBond","Maturity",datetime(2022,9,15),"CouponRate",0.05,'Name',"fixed_bond")
FixB = FixedBond with properties: CouponRate: 0.0500 Period: 2 Basis: 0 EndMonthRule: 1 Principal: 100 DaycountAdjustedCashFlow: 0 BusinessDayConvention: "actual" Holidays: NaT IssueDate: NaT FirstCouponDate: NaT LastCouponDate: NaT StartDate: NaT Maturity: 15-Sep-2022 Name: "fixed_bond"
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: [10x1 datetime] Rates: [10x1 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: [1x1 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: [1x1 finmodel.HullWhite]
Price FixedBond
Instrument
Use price
to compute the price and sensitivities for the FixedBond
instrument.
[Price,outPR] = price(outPricer,FixB,["all"])
Price = 115.0303
outPR = priceresult with properties: Results: [1x4 table] PricerData: [1x1 struct]
outPR.Results
ans=1×4 table
Price Delta Gamma Vega
______ _______ ______ ____
115.03 -397.13 1430.4 0
Price FixedBond
Instrument Using HullWhite
Model and IRTree
Pricer
This example shows the workflow to price a FixedBond
instrument when using a HullWhite
model and a IRTree pricing method.
Create FixedBond Instrument Object
Use fininstrument
to create a FixedBond
instrument object.
FixB = fininstrument("FixedBond","Maturity",datetime(2029,9,15),"CouponRate",.05,"Period",1,"Name","fixed_bond_instrument")
FixB = FixedBond with properties: CouponRate: 0.0500 Period: 1 Basis: 0 EndMonthRule: 1 Principal: 100 DaycountAdjustedCashFlow: 0 BusinessDayConvention: "actual" Holidays: NaT IssueDate: NaT FirstCouponDate: NaT LastCouponDate: NaT StartDate: NaT Maturity: 15-Sep-2029 Name: "fixed_bond_instrument"
Create ratecurve
Object
Create a ratecurve
object using ratecurve
.
Settle = datetime(2019,9,15); Type = "zero"; ZeroTimes = [calyears([1:10])]'; ZeroRates = [0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307 0.0310]'; ZeroDates = Settle + ZeroTimes; myRC = ratecurve('zero',Settle,ZeroDates,ZeroRates)
myRC = ratecurve with properties: Type: "zero" Compounding: -1 Basis: 0 Dates: [10x1 datetime] Rates: [10x1 double] Settle: 15-Sep-2019 InterpMethod: "linear" ShortExtrapMethod: "next" LongExtrapMethod: "previous"
Create HullWhite Model Object
Use finmodel
to create a HullWhite
model object.
HullWhiteModel = finmodel("hullwhite",'Alpha',0.052,'Sigma',0.34)
HullWhiteModel = HullWhite with properties: Alpha: 0.0520 Sigma: 0.3400
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",HullWhiteModel,"DiscountCurve",myRC,"TreeDates",ZeroDates)
HWTreePricer = HWBKTree with properties: Tree: [1x1 struct] TreeDates: [10x1 datetime] Model: [1x1 finmodel.HullWhite] DiscountCurve: [1x1 ratecurve]
HWTreePricer.Tree
ans = struct with fields:
tObs: [0 1 1.9973 2.9945 3.9918 4.9918 5.9891 6.9863 7.9836 8.9836]
dObs: [15-Sep-2019 15-Sep-2020 15-Sep-2021 15-Sep-2022 15-Sep-2023 15-Sep-2024 15-Sep-2025 15-Sep-2026 15-Sep-2027 15-Sep-2028]
CFlowT: {[10x1 double] [9x1 double] [8x1 double] [7x1 double] [6x1 double] [5x1 double] [4x1 double] [3x1 double] [2x1 double] [9.9809]}
Probs: {[3x1 double] [3x3 double] [3x5 double] [3x7 double] [3x9 double] [3x11 double] [3x13 double] [3x15 double] [3x17 double]}
Connect: {[2] [2 3 4] [2 3 4 5 6] [2 3 4 5 6 7 8] [2 3 4 5 6 7 8 9 10] [2 3 4 5 6 7 8 9 10 11 12] [2 3 4 5 6 7 8 9 10 11 12 13 14] [2 3 4 5 6 7 8 9 10 11 12 13 14 15 16] [2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18]}
FwdTree: {1x10 cell}
RateTree: {1x10 cell}
Price FixedBond Instrument
Use price
to compute the price and sensitivities for the FixedBond
instrument.
[Price, outPR] = price(HWTreePricer, FixB,["all"])
Price = 117.9440
outPR = priceresult with properties: Results: [1x4 table] PricerData: [1x1 struct]
outPR.Results
ans=1×4 table
Price Delta Gamma Vega
______ _______ ______ ___________
117.94 -964.01 8868.6 -4.2633e-10
Price FixedBond
Instrument Using CoxIngersollRoss
Model and IRTree
Pricer
This example shows the workflow to price a FixedBond
instrument when you use a CoxIngersollRoss
model and an IRTree
pricing method.
Create FixedBond
Instrument Object
Use fininstrument
to create a FixedBond
instrument object.
Period = 1; Maturity = datetime(2027,1,1); CouponRate = 0.035; FixedBond = fininstrument("FixedBond",'Maturity',Maturity,'CouponRate',CouponRate,'Period',Period,Name="fixed_bond")
FixedBond = FixedBond with properties: CouponRate: 0.0350 Period: 1 Basis: 0 EndMonthRule: 1 Principal: 100 DaycountAdjustedCashFlow: 0 BusinessDayConvention: "actual" Holidays: NaT IssueDate: NaT FirstCouponDate: NaT LastCouponDate: NaT StartDate: NaT Maturity: 01-Jan-2027 Name: "fixed_bond"
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: [1x1 struct] TreeDates: [4x1 datetime] Model: [1x1 finmodel.CoxIngersollRoss] DiscountCurve: [1x1 ratecurve]
Price FixedBond
Instrument
Use price
to compute the price for the FixedBond
instrument.
[Price,outPR] = price(CIRPricer,FixedBond,"all")
Price = 93.4593
outPR = priceresult with properties: Results: [1x4 table] PricerData: [1x1 struct]
outPR.Results
ans=1×4 table
Price Delta Gamma Vega
______ _______ ______ ___________
93.459 -354.23 1384.8 -1.4211e-10
Use FixedBond
Instruments to Fit Svensson Model to Bond Data
This example shows the workflow for using FixedBond
instruments that are fit to a Svensson model using fitSvensson
.
Define the bond data and use fininstrument
to create FixedBond
instrument objects.
settle = datetime(2009,11,24)
settle = datetime
24-Nov-2009
maturity = settle + calyears([1;2;3;5;7;10;20;30])
maturity = 8x1 datetime
24-Nov-2010
24-Nov-2011
24-Nov-2012
24-Nov-2014
24-Nov-2016
24-Nov-2019
24-Nov-2029
24-Nov-2039
price = [100.1; 100.1; 100.2; 99.0; ... 100.8; 99.2; 101.7; 100.2]; coupon = [0.020; 0.0275; 0.035; 0.042; ... 0.0475; 0.0525; 0.055; 0.052]; Bonds = fininstrument("FixedBond",'Maturity',maturity,'CouponRate',coupon)
Bonds=8×1 FixedBond array with properties:
CouponRate
Period
Basis
EndMonthRule
Principal
DaycountAdjustedCashFlow
BusinessDayConvention
Holidays
IssueDate
FirstCouponDate
LastCouponDate
StartDate
Maturity
Name
Use fitSvensson
to create a parameter curve object.
lb = [-Inf -Inf -Inf -Inf 0 0]; ub = [Inf Inf Inf Inf 5 20]; x0 = [.5 .5 .5 .5 2 5]; SvenModel = fitSvensson(settle,Bonds,price,'x0',x0,'lb',lb,'ub',ub)
Local minimum possible. lsqnonlin stopped because the final change in the sum of squares relative to its initial value is less than the value of the function tolerance.
SvenModel = parametercurve with properties: Type: "zero" Settle: 24-Nov-2009 Compounding: -1 Basis: 0 FunctionHandle: @(t)fitF(Params,t) Parameters: [0.0290 -0.0217 0.0025 0.0973 1.7821 7.5297]
p = SvenModel.Parameters
p = 1×6
0.0290 -0.0217 0.0025 0.0973 1.7821 7.5297
maturities = settle(1) + calmonths(1:360)
maturities = 1x360 datetime
24-Dec-2009 24-Jan-2010 24-Feb-2010 24-Mar-2010 24-Apr-2010 24-May-2010 24-Jun-2010 24-Jul-2010 24-Aug-2010 24-Sep-2010 24-Oct-2010 24-Nov-2010 24-Dec-2010 24-Jan-2011 24-Feb-2011 24-Mar-2011 24-Apr-2011 24-May-2011 24-Jun-2011 24-Jul-2011 24-Aug-2011 24-Sep-2011 24-Oct-2011 24-Nov-2011 24-Dec-2011 24-Jan-2012 24-Feb-2012 24-Mar-2012 24-Apr-2012 24-May-2012 24-Jun-2012 24-Jul-2012 24-Aug-2012 24-Sep-2012 24-Oct-2012 24-Nov-2012 24-Dec-2012 24-Jan-2013 24-Feb-2013 24-Mar-2013 24-Apr-2013 24-May-2013 24-Jun-2013 24-Jul-2013 24-Aug-2013 24-Sep-2013 24-Oct-2013 24-Nov-2013 24-Dec-2013 24-Jan-2014 24-Feb-2014 24-Mar-2014 24-Apr-2014 24-May-2014 24-Jun-2014 24-Jul-2014 24-Aug-2014 24-Sep-2014 24-Oct-2014 24-Nov-2014 24-Dec-2014 24-Jan-2015 24-Feb-2015 24-Mar-2015 24-Apr-2015 24-May-2015 24-Jun-2015 24-Jul-2015 24-Aug-2015 24-Sep-2015 24-Oct-2015 24-Nov-2015 24-Dec-2015 24-Jan-2016 24-Feb-2016 24-Mar-2016 24-Apr-2016 24-May-2016 24-Jun-2016 24-Jul-2016 24-Aug-2016 24-Sep-2016 24-Oct-2016 24-Nov-2016 24-Dec-2016 24-Jan-2017 24-Feb-2017 24-Mar-2017 24-Apr-2017 24-May-2017 24-Jun-2017 24-Jul-2017 24-Aug-2017 24-Sep-2017 24-Oct-2017 24-Nov-2017 24-Dec-2017 24-Jan-2018 24-Feb-2018 24-Mar-2018 24-Apr-2018 24-May-2018 24-Jun-2018 24-Jul-2018 24-Aug-2018 24-Sep-2018 24-Oct-2018 24-Nov-2018 24-Dec-2018 24-Jan-2019 24-Feb-2019 24-Mar-2019 24-Apr-2019 24-May-2019 24-Jun-2019 24-Jul-2019 24-Aug-2019 24-Sep-2019 24-Oct-2019 24-Nov-2019 24-Dec-2019 24-Jan-2020 24-Feb-2020 24-Mar-2020 24-Apr-2020 24-May-2020 24-Jun-2020 24-Jul-2020 24-Aug-2020 24-Sep-2020 24-Oct-2020 24-Nov-2020 24-Dec-2020 24-Jan-2021 24-Feb-2021 24-Mar-2021 24-Apr-2021 24-May-2021 24-Jun-2021 24-Jul-2021 24-Aug-2021 24-Sep-2021 24-Oct-2021 24-Nov-2021 24-Dec-2021 24-Jan-2022 24-Feb-2022 24-Mar-2022 24-Apr-2022 24-May-2022 24-Jun-2022 24-Jul-2022 24-Aug-2022 24-Sep-2022 24-Oct-2022 24-Nov-2022 24-Dec-2022 24-Jan-2023 24-Feb-2023 24-Mar-2023 24-Apr-2023 24-May-2023 24-Jun-2023 24-Jul-2023 24-Aug-2023 24-Sep-2023 24-Oct-2023 24-Nov-2023 24-Dec-2023 24-Jan-2024 24-Feb-2024 24-Mar-2024 24-Apr-2024 24-May-2024 24-Jun-2024 24-Jul-2024 24-Aug-2024 24-Sep-2024 24-Oct-2024 24-Nov-2024 24-Dec-2024 24-Jan-2025 24-Feb-2025 24-Mar-2025 24-Apr-2025 24-May-2025 24-Jun-2025 24-Jul-2025 24-Aug-2025 24-Sep-2025 24-Oct-2025 24-Nov-2025 24-Dec-2025 24-Jan-2026 24-Feb-2026 24-Mar-2026 24-Apr-2026 24-May-2026 24-Jun-2026 24-Jul-2026 24-Aug-2026 24-Sep-2026 24-Oct-2026 24-Nov-2026 24-Dec-2026 24-Jan-2027 24-Feb-2027 24-Mar-2027 24-Apr-2027 24-May-2027 24-Jun-2027 24-Jul-2027 24-Aug-2027 24-Sep-2027 24-Oct-2027 24-Nov-2027 24-Dec-2027 24-Jan-2028 24-Feb-2028 24-Mar-2028 24-Apr-2028 24-May-2028 24-Jun-2028 24-Jul-2028 24-Aug-2028 24-Sep-2028 24-Oct-2028 24-Nov-2028 24-Dec-2028 24-Jan-2029 24-Feb-2029 24-Mar-2029 24-Apr-2029 24-May-2029 24-Jun-2029 24-Jul-2029 24-Aug-2029 24-Sep-2029 24-Oct-2029 24-Nov-2029 24-Dec-2029 24-Jan-2030 24-Feb-2030 24-Mar-2030 24-Apr-2030 24-May-2030 24-Jun-2030 24-Jul-2030 24-Aug-2030 24-Sep-2030 24-Oct-2030 24-Nov-2030 24-Dec-2030 24-Jan-2031 24-Feb-2031 24-Mar-2031 24-Apr-2031 24-May-2031 24-Jun-2031 24-Jul-2031 24-Aug-2031 24-Sep-2031 24-Oct-2031 24-Nov-2031 24-Dec-2031 24-Jan-2032 24-Feb-2032 24-Mar-2032 24-Apr-2032 24-May-2032 24-Jun-2032 24-Jul-2032 24-Aug-2032 24-Sep-2032 24-Oct-2032 24-Nov-2032 24-Dec-2032 24-Jan-2033 24-Feb-2033 24-Mar-2033 24-Apr-2033 24-May-2033 24-Jun-2033 24-Jul-2033 24-Aug-2033 24-Sep-2033 24-Oct-2033 24-Nov-2033 24-Dec-2033 24-Jan-2034 24-Feb-2034 24-Mar-2034 24-Apr-2034 24-May-2034 24-Jun-2034 24-Jul-2034 24-Aug-2034 24-Sep-2034 24-Oct-2034 24-Nov-2034 24-Dec-2034 24-Jan-2035 24-Feb-2035 24-Mar-2035 24-Apr-2035 24-May-2035 24-Jun-2035 24-Jul-2035 24-Aug-2035 24-Sep-2035 24-Oct-2035 24-Nov-2035 24-Dec-2035 24-Jan-2036 24-Feb-2036 24-Mar-2036 24-Apr-2036 24-May-2036 24-Jun-2036 24-Jul-2036 24-Aug-2036 24-Sep-2036 24-Oct-2036 24-Nov-2036 24-Dec-2036 24-Jan-2037 24-Feb-2037 24-Mar-2037 24-Apr-2037 24-May-2037 24-Jun-2037 24-Jul-2037 24-Aug-2037 24-Sep-2037 24-Oct-2037 24-Nov-2037 24-Dec-2037 24-Jan-2038 24-Feb-2038 24-Mar-2038 24-Apr-2038 24-May-2038 24-Jun-2038 24-Jul-2038 24-Aug-2038 24-Sep-2038 24-Oct-2038 24-Nov-2038 24-Dec-2038 24-Jan-2039 24-Feb-2039 24-Mar-2039 24-Apr-2039 24-May-2039 24-Jun-2039 24-Jul-2039 24-Aug-2039 24-Sep-2039 24-Oct-2039 24-Nov-2039
rates = zerorates(SvenModel,maturities)
rates = 1×360
0.0083 0.0094 0.0105 0.0114 0.0124 0.0134 0.0143 0.0153 0.0162 0.0171 0.0179 0.0188 0.0196 0.0204 0.0212 0.0219 0.0226 0.0234 0.0241 0.0248 0.0255 0.0262 0.0268 0.0275 0.0281 0.0287 0.0293 0.0299 0.0304 0.0310 0.0316 0.0321 0.0326 0.0332 0.0336 0.0342 0.0346 0.0351 0.0356 0.0360 0.0365 0.0369 0.0373 0.0377 0.0382 0.0386 0.0389 0.0393 0.0397 0.0401
Plot the zero coupon rate.
plot(maturities,rates) xtickformat('yyyy') grid('on') xlabel('Time in Years') ylabel('Zero Coupon Rate')
More About
Fixed-Rate Note
A fixed-rate note is a long-term debt security with a preset interest rate and maturity, by which the interest must be paid.
The principal might or might not be paid at maturity. In Financial Instruments Toolbox™, the principal is always paid at maturity. For more information, see Fixed-Rate Note.
Vanilla Bond
A vanilla coupon bond is a security representing an obligation to repay a borrowed amount at a designated time and to make periodic interest payments until that time.
The issuer of a bond makes the periodic interest payments until the bond matures. At maturity, the issuer pays to the holder of the bond the principal amount owed (face value) and the last interest payment.
Stepped Coupon Bond
A step-up bond and a step-down bond are debt securities with a predetermined coupon structure over time.
With these instruments, coupons increase (step up) or decrease (step down) at specific times during the life of the bond.
Bond with an Amortization Schedule
An amortized bond is treated as an asset, with the discount amount being amortized to interest expense over the life of the bond.
Version History
Introduced in R2020aR2023b: Support for Pricing FixedBond
Instruments Using CoxIngersollRoss
Model and IRTree
Pricer
You can price FixedBond
instruments using a CoxIngersollRoss
model object
and an IRTree
pricing
method.
R2022b: Serial date numbers not recommended
Although FixedBond
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.
See Also
Functions
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