Price bond from set of zero curves
[
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
)
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 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 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
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
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
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
⋮
RateSpec
— Interestrate structureInterestrate structure, specified using intenvset
to create a RateSpec
for
an annualized zero rate term structure.
Data Types: struct
CouponRate
— Bond coupon rate 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 dateSettlement 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 dateMaturity 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
Specify optional
commaseparated pairs of Name,Value
arguments. Name
is
the argument name and Value
is the corresponding value.
Name
must appear inside quotes. You can specify several name and value
pair arguments in any order as
Name1,Value1,...,NameN,ValueN
.
Price = bondbyzero(RateSpec,CouponRate,Settle,Maturity,'Period',4,'Face',10000)
'Period'
— Coupons per year2
per year (default)  vectorCoupons 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 basis0
(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 days1
(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 dateBond 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 dateIrregular 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 dateIrregular 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 paymentsSettle
date (default)  serial date number  date character vectorForward 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 value100
(default)  scalar of nonnegative value  cell array of nonnegative valuesFace 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 optionsDerivatives 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 countfalse
(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 conventionsactual
(default)  character vector  cell array of character vectorsBusiness 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 daysholidays.m
(default)  MATLAB^{®} date numbersHolidays 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
Price
— Fixedrate note pricesFloatingrate note prices, returned as a (NINST
)
by number of curves (NUMCURVES
) matrix. Each column
arises from one of the zero curves.
DirtyPrice
— Dirty bond priceDirty bond price (clean + accrued interest), returned as a NINST

byNUMCURVES
matrix. Each column arises from one
of the zero curves.
CFlowAmounts
— Cash flow amountsCash flow amounts, returned as a NINST
 byNUMCFS
matrix
of cash flows for each bond.
CFlowDates
— Cash flow datesCash flow dates, returned as a NINST
 byNUMCFS
matrix
of payment dates for each 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.
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.
An amortized bond is treated as an asset, with the discount amount being amortized to interest expense over the life of the bond.
cfamounts
 cfbyzero
 fixedbyzero
 floatbyzero
 swapbyzero
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