bondbyzero
Price bond from set of zero curves
Syntax
Description
[
prices
a bond from a set of zero curves. Price
,DirtyPrice
,CFlowAmounts
,CFlowDates
]
= bondbyzero(RateSpec
,CouponRate
,Settle
,Maturity
)bondbyzero
computes
prices of vanilla bonds, stepped coupon bonds and amortizing bonds.
[
adds
additional namevalue pair arguments.Price
,DirtyPrice
,CFlowAmounts
,CFlowDates
]
= bondbyzero(___,Name,Value
)
Examples
Price a Vanilla Bond
Price a 4% bond using a zero curve.
Load deriv.mat
, which provides ZeroRateSpec
, the interestrate term structure, needed to price the bond.
load deriv.mat; CouponRate = 0.04; Settle = '01Jan2000'; Maturity = '01Jan2004'; Price = bondbyzero(ZeroRateSpec, CouponRate, Settle, Maturity)
Price = 97.5334
Price a Stepped Coupon Bond
Price single stepped coupon bonds using market data.
Define data for the interestrate term structure.
Rates = [0.035; 0.042147; 0.047345; 0.052707]; ValuationDate = 'Jan12010'; StartDates = ValuationDate; EndDates = {'Jan12011'; 'Jan12012'; 'Jan12013'; 'Jan12014'}; Compounding = 1;
Create the RateSpec
.
RS = intenvset('ValuationDate', ValuationDate, 'StartDates', StartDates,... 'EndDates', EndDates,'Rates', Rates, 'Compounding', Compounding)
RS = struct with fields:
FinObj: 'RateSpec'
Compounding: 1
Disc: [4x1 double]
Rates: [4x1 double]
EndTimes: [4x1 double]
StartTimes: [4x1 double]
EndDates: [4x1 double]
StartDates: 734139
ValuationDate: 734139
Basis: 0
EndMonthRule: 1
Create the stepped bond instrument.
Settle = '01Jan2010'; Maturity = {'01Jan2011';'01Jan2012';'01Jan2013';'01Jan2014'}; CouponRate = {{'01Jan2012' .0425;'01Jan2014' .0750}}; Period = 1;
Compute the price of the stepped coupon bonds.
PZero= bondbyzero(RS, CouponRate, Settle, Maturity ,Period)
PZero = 4×1
100.7246
100.0945
101.5900
102.0820
Price a Bond with an Amortizing Schedule
Price a bond with an amortizing schedule using the Face
input argument to define the schedule.
Define data for the interestrate term structure.
Rates = 0.065; ValuationDate = '1Jan2011'; StartDates = ValuationDate; EndDates= '1Jan2017'; Compounding = 1;
Create the RateSpec
.
RateSpec = intenvset('ValuationDate', ValuationDate,'StartDates', StartDates,... 'EndDates', EndDates,'Rates', Rates, 'Compounding', Compounding)
RateSpec = struct with fields:
FinObj: 'RateSpec'
Compounding: 1
Disc: 0.6853
Rates: 0.0650
EndTimes: 6
StartTimes: 0
EndDates: 736696
StartDates: 734504
ValuationDate: 734504
Basis: 0
EndMonthRule: 1
Create and price the amortizing bond instrument. The bond has a coupon rate of 7%, a period of one year, and matures on 1Jan2017.
CouponRate = 0.07; Settle ='1Jan2011'; Maturity = '1Jan2017'; Period = 1; Face = {{'1Jan2015' 100;'1Jan2016' 90;'1Jan2017' 80}}; Price = bondbyzero(RateSpec, CouponRate, Settle, Maturity, 'Period',... Period, 'Face', Face)
Price = 102.3155
Compare the results with price of a vanilla bond.
PriceVanilla = bondbyzero(RateSpec, CouponRate, Settle, Maturity,Period)
PriceVanilla = 102.4205
Price both the amortizing and vanilla bonds.
Face = {{'1Jan2015' 100;'1Jan2016' 90;'1Jan2017' 80}; 100}; PriceBonds = bondbyzero(RateSpec, CouponRate, Settle, Maturity, 'Period',... Period, 'Face', Face)
PriceBonds = 2×1
102.3155
102.4205
Price a Bond in a Holding Period
When a bond is first issued, it can be priced with bondbyzero
on that day by setting the Settle
date to the issue date. Later on, if the bond needs to be traded someday between the issue date and the maturity date, its new price can be computed by updating the Settle
date, as well as the RateSpec
input.
Note that the bond's price is determined by its remaining cash flows and the zerorate term structure, which can both change as the bond matures. While bondbyzero
automatically updates the bond's remaining cash flows with respect to the new Settle
date, you must supply a new RateSpec
input in order to reflect the new zerorate term structure for that new Settle
date.
Use the following Bond information.
IssueDate = datenum('20May2014'); CouponRate = 0.01; Maturity = datenum('20May2019');
Determine the bond price on 20May2014.
Settle1 = datenum('20May2014'); ZeroDates1 = datemnth(Settle1,12*[1 2 3 5 7 10 20]'); ZeroRates1 = [0.23 0.63 1.01 1.60 2.01 2.27 2.79]'/100; RateSpec1 = intenvset('StartDate',Settle1,'EndDates',ZeroDates1,'Rates',ZeroRates1); [Price1, ~, CFlowAmounts1, CFlowDates1] = bondbyzero(RateSpec1, ... CouponRate, Settle1, Maturity, 'IssueDate', IssueDate); Price1
Price1 = 97.1899
Determine the bond price on 10Aug2015.
Settle2 = datenum('10Aug2015'); ZeroDates2 = datemnth(Settle2,12*[1 2 3 5 7 10 20]'); ZeroRates2 = [0.40 0.73 1.09 1.62 1.98 2.24 2.58]'/100; RateSpec2 = intenvset('StartDate',Settle2,'EndDates',ZeroDates2,'Rates',ZeroRates2); [Price2, ~, CFlowAmounts2, CFlowDates2] = bondbyzero(RateSpec2, ... CouponRate, Settle2, Maturity, 'IssueDate', IssueDate); Price2
Price2 = 98.9384
Price Three Bonds Using Two Different Curves
To price three bonds using two different curves, define the RateSpec
:
StartDates = '01April2016'; EndDates = ['01April2017'; '01April2018';'01April2019';'01April2020']; Rates = [[0.0356;0.041185;0.04489;0.047741],[0.0325;0.0423;0.0437;0.0465]]; RateSpec = intenvset('Rates', Rates, 'StartDates',StartDates,... 'EndDates', EndDates, 'Compounding', 1)
RateSpec = struct with fields:
FinObj: 'RateSpec'
Compounding: 1
Disc: [4x2 double]
Rates: [4x2 double]
EndTimes: [4x1 double]
StartTimes: [4x1 double]
EndDates: [4x1 double]
StartDates: 736421
ValuationDate: 736421
Basis: 0
EndMonthRule: 1
Price three bonds with the same Maturity
and different coupons.
Settle = '01April2016'; Maturity = '01April2020'; Price = bondbyzero(RateSpec,[0.025;0.028;0.035],Settle,Maturity)
Price = 3×2
92.0766 92.4888
93.1680 93.5823
95.7145 96.1338
Price a Vanilla Bond Using the Optional Input Argument AdjustCashFlowsBasis
To adjust the cash flows according to the accrual amount, use the optional input argument AdjustCashFlowsBasis
when calling bondbyzero
.
Use the following data to define the interestrate term structure and to create a RateSpec
.
Rates = 0.065; ValuationDate = '1Jan2011'; StartDates = ValuationDate; EndDates= '1Jan2017'; Compounding = 1; RateSpec = intenvset('ValuationDate',ValuationDate,'StartDates',StartDates,... 'EndDates', EndDates,'Rates',Rates,'Compounding',Compounding); CouponRate = 0.07; Settle ='1Jan2011'; Maturity = '1Jan2017'; Period = 1; Face = {{'1Jan2015' 100;'1Jan2016' 90;'1Jan2017' 80}};
Use cfamounts
and cycle through the Basis
of 0
to 13
, using the optional argument AdjustCashFlowsBasis
to determine the cash flow amounts for accrued interest due at settlement.
AdjustCashFlowsBasis = true; CFlowAmounts = cfamounts(CouponRate,Settle,Maturity,'Period',Period,'Basis',0:13,'AdjustCashFlowsBasis',AdjustCashFlowsBasis)
CFlowAmounts = 14×7
0 7.0000 7.0000 7.0000 7.0000 7.0000 107.0000
0 7.0000 7.0000 7.0000 7.0000 7.0000 107.0000
0 7.0972 7.1167 7.0972 7.0972 7.0972 107.1167
0 7.0000 7.0192 7.0000 7.0000 7.0000 107.0192
0 7.0000 7.0000 7.0000 7.0000 7.0000 107.0000
0 7.0000 7.0000 7.0000 7.0000 7.0000 107.0000
0 7.0000 7.0000 7.0000 7.0000 7.0000 107.0000
0 7.0000 7.0000 7.0000 7.0000 7.0000 107.0000
0 7.0000 7.0000 7.0000 7.0000 7.0000 107.0000
0 7.0972 7.1167 7.0972 7.0972 7.0972 107.1167
⋮
Notice that the cash flow amounts have been adjusted according to Basis
.
Price a vanilla bond using the input argument AdjustCashFlowsBasis
.
PriceVanilla = bondbyzero(RateSpec,CouponRate,Settle,Maturity,'Period',Period,'Basis',0:13,'AdjustCashFlowsBasis',AdjustCashFlowsBasis)
PriceVanilla = 14×1
102.4205
102.4205
102.9216
102.4506
102.4205
102.4205
102.4205
102.4205
102.4205
102.9216
⋮
Input Arguments
RateSpec
— Interestrate structure
structure
Interestrate structure, specified using intenvset
to create a RateSpec
for
an annualized zero rate term structure.
Data Types: struct
CouponRate
— Bond coupon rate
positive decimal value
Bond coupon rate, specified as an NINST
by1
decimal
annual rate or NINST
by1
cell
array, where each element is a NumDates
by2
cell
array. The first column of the NumDates
by2
cell
array is dates and the second column is associated rates. The date
indicates the last day that the coupon rate is valid.
Data Types: double
 cell
Settle
— Settlement date
serial date number  character vector
Settlement date, specified either as a scalar or NINST
by1
vector
of serial date numbers or date character vectors.
Settle
must be earlier than Maturity
.
Data Types: char
 double
Maturity
— Maturity date
serial date number  character vector
Maturity date, specified as a NINST
by1
vector
of serial date numbers or date character vectors representing the
maturity date for each bond.
Data Types: char
 double
NameValue Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Namevalue 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: Price = bondbyzero(RateSpec,CouponRate,Settle,Maturity,'Period',4,'Face',10000)
Period
— Coupons per year
2
per year (default)  vector
Coupons per year, specified as the commaseparated pair consisting of
'Period'
and a
NINST
by1
vector. Values for
Period
are 1
,
2
, 3
, 4
,
6
, and 12
.
Data Types: double
Basis
— Daycount basis
0
(actual/actual) (default)  integer from 0
to 13
Daycount basis of the instrument, specified as the commaseparated pair consisting of
'Basis'
and a
NINST
by1
vector.
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
EndMonthRule
— Endofmonth rule flag for generating dates when Maturity
is endofmonth date for month having 30 or fewer days
1
(in effect) (default)  nonnegative integer [0,1]
Endofmonth rule flag for generating dates when Maturity
is an
endofmonth date for a month having 30 or fewer days, specified as the
commaseparated pair consisting of 'EndMonthRule'
and
a nonnegative integer [0
, 1
] using
a NINST
by1
vector.
0
= Ignore rule, meaning that a payment date is always the same numerical day of the month.1
= Set rule on, meaning that a payment date is always the last actual day of the month.
Data Types: logical
IssueDate
— Bond issue date
serial nonnegative date number  date character vector
Bond issue date, specified as the commaseparated pair consisting of
'IssueDate'
and a
NINST
by1
vector using a
serial nonnegative date number or date character vector.
Data Types: double
 char
FirstCouponDate
— Irregular first coupon date
serial nonnegative date number  date character vector
Irregular first coupon date, specified as the commaseparated pair consisting of
'FirstCouponDate'
and a
NINST
by1
vector using a
serial nonnegative date number or date character vector.
Data Types: double
 char
LastCouponDate
— Irregular last coupon date
serial nonnegative date number  date character vector
Irregular last coupon date, specified as the commaseparated pair consisting of
'LastCouponDate'
and a
NINST
by1
vector using a
serial nonnegative date number or date character vector.
Data Types: double
 char
StartDate
— Forward starting date of payments
Settle
date (default)  serial date number  date character vector
Forward starting date of payments (the date from which a bond cash flow is considered),
specified as the commaseparated pair consisting of
'StartDate'
and a
NINST
by1
vector using serial
date numbers or date character vectors.
If you do not specify StartDate
, the effective
start date is the Settle
date.
Data Types: char
 double
Face
— Face value
100
(default)  scalar of nonnegative value  cell array of nonnegative values
Face value, specified as the commaseparated pair consisting of 'Face'
and
a NINST
by1
scalar of nonnegative
face values or an NINST
by1
cell
array, where each element is a
NumDates
by2
cell array. The
first column of the NumDates
by2
cell array is dates and the second column is the associated face value.
The date indicates the last day that the face value is valid.
Data Types: cell
 double
Options
— Derivatives pricing options
structure
Derivatives pricing options, specified as the commaseparated pair consisting of
'Options'
and a structure that is created with
derivset
.
Data Types: struct
AdjustCashFlowsBasis
— Flag to adjust cash flows based on actual period day count
false
(default)  value of 0
(false) or 1
(true)
Flag to adjust cash flows based on actual period day count, specified as the commaseparated
pair consisting of 'AdjustCashFlowsBasis'
and a
NINST
by1
vector of logicals
with values of 0
(false) or 1
(true).
Data Types: logical
BusinessDayConvention
— Business day conventions
actual
(default)  character vector  cell array of character vectors
Business day conventions, specified as the commaseparated pair
consisting of 'BusinessDayConvention'
and a character
vector or a N
by1
(or
NINST
by2
if
BusinessDayConvention
is different for each leg)
cell array of character vectors of business day conventions. 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 (e.g. 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
Holidays
— Holidays used in computing business days
if not specified, the default is to use holidays.m
(default)  MATLAB^{®} date numbers
Holidays used in computing business days, specified as the commaseparated pair consisting of
'Holidays'
and MATLAB date numbers using a
NHolidays
by1
vector.
Data Types: double
Output Arguments
Price
— Fixedrate note prices
matrix
Floatingrate note prices, returned as a (NINST
)
by number of curves (NUMCURVES
) matrix. Each column
arises from one of the zero curves.
DirtyPrice
— Dirty bond price
matrix
Dirty bond price (clean + accrued interest), returned as a NINST

byNUMCURVES
matrix. Each column arises from one
of the zero curves.
CFlowAmounts
— Cash flow amounts
matrix
Cash flow amounts, returned as a NINST
 byNUMCFS
matrix
of cash flows for each bond.
CFlowDates
— Cash flow dates
matrix
Cash flow dates, returned as a NINST
 byNUMCFS
matrix
of payment dates for each bond.
More About
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 stepup and stepdown bond is a debt security 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
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