fixedbyzero
Price fixedrate note from set of zero curves
Syntax
Description
[
prices a fixedrate note from a set of zero curves.Price
,DirtyPrice
,CFlowAmounts
,CFlowDates
]
= fixedbyzero(RateSpec
,CouponRate
,Settle
,Maturity
)
Note
Alternatively, you can use the FixedBond
object to price fixedrate
bond instruments. For more information, see Get Started with Workflows Using ObjectBased Framework for Pricing Financial Instruments.
[
adds
additional namevalue pair arguments.Price
,DirtyPrice
,CFlowAmounts
,CFlowDates
]
= fixedbyzero(___,Name,Value
)
Examples
Price a 4% FixedRate Note Using a Set of Zero Curves
This example shows how to price a 4% fixedrate note using a set of zero curves by loading the file deriv.mat
, which provides ZeroRateSpec
, the interestrate term structure needed to price the note.
load deriv.mat
CouponRate = 0.04;
Settle = datetime(2000,1,1);
Maturity = datetime(2003,1,1);
Price = fixedbyzero(ZeroRateSpec, CouponRate, Settle, Maturity)
Price = 98.7159
Pricing a FixedFixed Cross Currency Swap
Assume that a financial institution has an existing swap with three years left to maturity where they are receiving 5% per year in yen and paying 8% per year in USD. The reset frequency for the swap is annual, the principals for the two legs are 1200 million yen and $10 million USD, and both term structures are flat.
Settle = datetime(2015,8,15); Maturity = datetime(2018,8,15); Reset = 1; r_d = .09; r_f = .04; FixedRate_d = .08; FixedRate_f = .05; Principal_d = 10000000; Principal_f = 1200000000; S0 = 1/110;
Construct term structures.
RateSpec_d = intenvset('StartDate',Settle,'EndDate',Maturity,'Rates',r_d,'Compounding',1); RateSpec_f = intenvset('StartDate',Settle,'EndDate',Maturity,'Rates',r_f,'Compounding',1);
Use fixedbyzero:
B_d = fixedbyzero(RateSpec_d,FixedRate_d,Settle,Maturity,'Principal',Principal_d,'Reset',Reset); B_f = fixedbyzero(RateSpec_f,FixedRate_f,Settle,Maturity,'Principal',Principal_f,'Reset',Reset);
Compute swap price. Based on Hull (see References), a cross currency swap can be valued with the following formula V_swap
= S0*B_f
− B_d
.
V_swap = S0*B_f  B_d
V_swap = 1.5430e+06
Input Arguments
RateSpec
— Annualized zero rate term structure
structure
Annualized zero rate term structure, specified using intenvset
to create a RateSpec
.
Data Types: struct
CouponRate
— Annual rate
decimal
Annual rate, specified as NINST
by1
decimal
annual rate or a NINST
by1
cell
array where each element is a NumDates
by2
cell
array and the first column 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
datetime array  string array  date character vector
Settlement date, specified either as a scalar or a
NINST
by1
vector using a datetime array, string array, or date
character vectors.
To support existing code, fixedbyzero
also
accepts serial date numbers as inputs, but they are not recommended.
Settle
must be earlier than Maturity
.
Maturity
— Maturity date
datetime array  string array  date character vector
Maturity date, specified as a NINST
by1
vector using a
datetime array, string array, or date character
vectors representing the maturity date for each
fixedrate note.
To support existing code, fixedbyzero
also
accepts serial date numbers as inputs, but they are not recommended.
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,DirtyPrice,CFlowAmounts,CFlowDates]
= fixedbyzero(RateSpec,CouponRate,Settle,Maturity,'Principal',Principal)
FixedReset
— Frequency of payments per year
1
(default)  vector
Frequency of payments per year, specified as
the commaseparated pair consisting of
'FixedReset'
and a
NINST
by1
vector.
Data Types: double
Basis
— Day count basis
0
(actual/actual) (default)  integer from 0
to 13
Day count basis, 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
Principal
— Notional principal amounts or principal value schedules
100
(default)  vector or cell array
Notional principal amounts, specified as the commaseparated pair consisting of
'Principal'
and a vector or
cell array.
Principal
accepts a NINST
by1
vector
or NINST
by1
cell array, where
each element of the cell array is a NumDates
by2
cell
array and the first column is dates and the second column is its associated
notional principal value. The date indicates the last day that the
principal value is valid.
Data Types: cell
 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
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
Holidays
— Holidays used in computing business days
if not specified, the default
is to use holidays.m
(default)  MATLAB^{®} dates
Holidays used in computing business days, specified as the commaseparated pair consisting of
'Holidays'
and MATLAB dates using a
NHolidays
by1
vector.
Data Types: datetime
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
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
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
FixedRate Note
A fixedrate note is a longterm debt security with a preset interest rate and maturity, by which the interest must be paid.
The principal may or may not be paid at maturity. In Financial Instruments Toolbox™, the principal is always paid at maturity. For more information, see FixedRate Note.
References
[1] Hull, J. Options, Futures, and Other Derivatives. PrenticeHall, 2011.
Version History
Introduced before R2006aR2022b: Serial date numbers not recommended
Although fixedbyzero
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
bondbyzero
 cfbyzero
 floatbyzero
 swapbyzero
 FixedBond
Topics
 Pricing Using InterestRate Term Structure
 Price Portfolio of Bond and Bond Option Instruments
 Bond Portfolio Optimization Using Portfolio Object
 FixedRate Note
 Understanding InterestRate Tree Models
 Supported InterestRate Instrument Functions
 Mapping Financial Instruments Toolbox Functions for InterestRate Instrument Objects
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