floatbyzero
Price floatingrate note from set of zero curves
Syntax
Description
[
prices
a floatingrate note from a set of zero curves.Price
,DirtyPrice
,CFlowAmounts
,CFlowDates
]
= floatbyzero(RateSpec
,Spread
,Settle
,Maturity
)
floatbyzero
computes prices of vanilla floatingrate
notes and amortizing floatingrate notes.
[
adds
additional namevalue pair arguments.Price
,DirtyPrice
,CFlowAmounts
,CFlowDates
]
= floatbyzero(___,Name,Value
)
Examples
Price a FloatingRate Note Using a Set of Zero Curves
Price a 20basis point floatingrate note using a set of zero curves.
Load deriv.mat
, which provides ZeroRateSpec
, the interestrate term structure, needed to price the bond.
load deriv.mat;
Define the floatingrate note using the required arguments. Other arguments use defaults.
Spread = 20; Settle = '01Jan2000'; Maturity = '01Jan2003';
Use floatbyzero
to compute the price of the note.
Price = floatbyzero(ZeroRateSpec, Spread, Settle, Maturity)
Price = 100.5529
Price an Amortizing FloatingRate Note
Price an amortizing floatingrate note using the Principal
input argument to define the amortization schedule.
Create the RateSpec
.
Rates = [0.03583; 0.042147; 0.047345; 0.052707; 0.054302]; ValuationDate = '15Nov2011'; StartDates = ValuationDate; EndDates = {'15Nov2012';'15Nov2013';'15Nov2014' ;'15Nov2015';'15Nov2016'}; Compounding = 1; RateSpec = intenvset('ValuationDate', ValuationDate,'StartDates', StartDates,... 'EndDates', EndDates,'Rates', Rates, 'Compounding', Compounding)
RateSpec = struct with fields:
FinObj: 'RateSpec'
Compounding: 1
Disc: [5x1 double]
Rates: [5x1 double]
EndTimes: [5x1 double]
StartTimes: [5x1 double]
EndDates: [5x1 double]
StartDates: 734822
ValuationDate: 734822
Basis: 0
EndMonthRule: 1
Create the floatingrate instrument using the following data:
Settle ='15Nov2011'; Maturity = '15Nov2015'; Spread = 15;
Define the floatingrate note amortizing schedule.
Principal ={{'15Nov2012' 100;'15Nov2013' 70;'15Nov2014' 40;'15Nov2015' 10}};
Compute the price of the amortizing floatingrate note.
Price = floatbyzero(RateSpec, Spread, Settle, Maturity, 'Principal', Principal)
Price = 100.3059
Specify the Rate at the Instrument’s Starting Date When It Cannot Be Obtained from the RateSpec
If Settle
is not on a reset date of a floatingrate note,
floatbyzero
attempts to obtain the latest floating rate before
Settle
from RateSpec
or the
LatestFloatingRate
parameter. When the reset date for this rate is
out of the range of RateSpec
(and LatestFloatingRate
is not specified), floatbyzero
fails to obtain the rate for that date
and generates an error. This example shows how to use the
LatestFloatingRate
input parameter to avoid the error.
Create the error condition when a floatingrate instrument’s StartDate
cannot
be determined from the RateSpec
.
load deriv.mat; Spread = 20; Settle = '01Jan2000'; Maturity = '01Dec2003'; Price = floatbyzero(ZeroRateSpec, Spread, Settle, Maturity)
Error using floatbyzero (line 256) The rate at the instrument starting date cannot be obtained from RateSpec. Its reset date (01Dec1999) is out of the range of dates contained in RateSpec. This rate is required to calculate cash flows at the instrument starting date. Consider specifying this rate with the 'LatestFloatingRate' input parameter.
Here, the reset date for the rate at Settle
was
01Dec1999, which was earlier than the valuation date of ZeroRateSpec
(01Jan2000).
This error can be avoided by specifying the rate at the instrument’s
starting date using the LatestFloatingRate
namevalue
pair argument.
Define LatestFloatingRate
and calculate
the floatingrate price.
Price = floatbyzero(ZeroRateSpec, Spread, Settle, Maturity, 'LatestFloatingRate', 0.03)
Price = 100.0285
Price a FloatingRate Note Using a Different Curve to Generate Floating Cash Flows
Define the OIS and Libor rates.
Settle = datenum('15Mar2013');
CurveDates = daysadd(Settle,360*[1/12 2/12 3/12 6/12 1 2 3 4 5 7 10],1);
OISRates = [.0018 .0019 .0021 .0023 .0031 .006 .011 .017 .021 .026 .03]';
LiborRates = [.0045 .0047 .005 .0055 .0075 .011 .016 .022 .026 .030 .0348]';
Plot the dual curves.
figure,plot(CurveDates,OISRates,'r');hold on;plot(CurveDates,LiborRates,'b') datetick legend({'OIS Curve', 'Libor Curve'})
Create an associated RateSpec
for the OIS and Libor curves.
OISCurve = intenvset('Rates',OISRates,'StartDate',Settle,'EndDates',CurveDates); LiborCurve = intenvset('Rates',LiborRates,'StartDate',Settle,'EndDates',CurveDates);
Define the floatingrate note.
Maturity = datenum('15Mar2018');
Compute the price for the floatingrate note. The LiborCurve
term structure will be used to generate the floating cash flows of the floater instrument. The OISCurve
term structure will be used for discounting the cash flows.
Price = floatbyzero(OISCurve,0,Settle,Maturity,'ProjectionCurve',LiborCurve)
Price = 102.4214
Some instruments require using different interestrate curves for generating the floating cash flows and discounting. This is when the ProjectionCurve
parameter is useful. When you provide both RateSpec
and ProjectionCurve
, floatbyzero
uses the RateSpec
for the purpose of discounting and it uses the ProjectionCurve
for generating the floating cash flows.
Input Arguments
RateSpec
— Annualized zero rate term structure
structure
Annualized zero rate term structure, specified using intenvset
to create a RateSpec
.
Data Types: struct
Spread
— Number of basis points over the reference rate
vector
Number of basis points over the reference rate, specified as
a NINST
by1
vector.
Data Types: double
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
floatingrate note.
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,DirtyPrice,CFlowAmounts,CFlowDates]
= floatbyzero(RateSpec,Spread,Settle,Maturity,'Principal',Principal)
FloatReset
— Frequency of payments per year
1
(default)  vector
Frequency of payments per year, specified as the commaseparated pair consisting
of 'FloatReset'
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
LatestFloatingRate
— Rate for the next floating payment
if not specified, the floating rate at the previous
reset date is computed from RateSpec
(default)  numeric
Rate for the next floating payment set at the last reset date, specified as the
commaseparated pair consisting of 'LatestFloatingRate'
and a
NINST
by1
.
Data Types: double
ProjectionCurve
— Rate curve used in generating future forward rates
if not specified, then RateSpec
is
used both for discounting cash flows and projecting future forward
rates (default)  structure
The rate curve to be used in generating the future forward rates, specified as the
commaseparated pair consisting of 'ProjectionCurve'
and a
structure created using intenvset
. Use this optional input
if the forward curve is different from the discount curve.
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
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
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
— Floatingrate 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 note price
matrix
Dirty note 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 note. If there is more than one curve specified
in the RateSpec
input, then the first NCURVES
rows
correspond to the first note, the second NCURVES
rows
correspond to the second note, and so on.
CFlowDates
— Cash flow dates
matrix
Cash flow dates, returned as a NINST
 byNUMCFS
matrix
of payment dates for each note.
More About
FloatingRate Note
A floatingrate note 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.
Version History
See Also
bondbyzero
 cfbyzero
 fixedbyzero
 swapbyzero
 intenvset
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