floatbyzero
Price floating-rate note from set of zero curves
Syntax
Description
[
prices
a floating-rate note from a set of zero curves.Price
,DirtyPrice
,CFlowAmounts
,CFlowDates
]
= floatbyzero(RateSpec
,Spread
,Settle
,Maturity
)
floatbyzero
computes prices of vanilla floating-rate
notes and amortizing floating-rate notes.
Note
Alternatively, you can use the FloatBond
object to
price floating-rate bond instruments. For more information, see Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments.
[
adds
additional name-value pair arguments.Price
,DirtyPrice
,CFlowAmounts
,CFlowDates
]
= floatbyzero(___,Name,Value
)
Examples
Price a Floating-Rate Note Using a Set of Zero Curves
Price a 20-basis point floating-rate note using a set of zero curves.
Load deriv.mat
, which provides ZeroRateSpec
, the interest-rate term structure, needed to price the bond.
load deriv.mat;
Define the floating-rate note using the required arguments. Other arguments use defaults.
Spread = 20; Settle = datetime(2000,1,1); Maturity = datetime(2003,1,1);
Use floatbyzero
to compute the price of the note.
Price = floatbyzero(ZeroRateSpec, Spread, Settle, Maturity)
Price = 100.5529
Price an Amortizing Floating-Rate Note
Price an amortizing floating-rate 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 = datetime(2011,11,15); StartDates = ValuationDate; EndDates = [datetime(2012,11,15) ; datetime(2013,11,15) ; datetime(2014,11,15) ; datetime(2015,11,15) ; datetime(2016,11,15)]; 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 floating-rate instrument using the following data:
Settle = datetime(2011,11,15); Maturity = datetime(2015,11,15); Spread = 15;
Define the floating-rate note amortizing schedule.
Principal ={{datetime(2012,11,15) 100;datetime(2013,11,15) 70;datetime(2014,11,15) 40;datetime(2015,11,15) 10}};
Compute the price of the amortizing floating-rate 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 floating-rate 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 floating-rate instrument’s StartDate
cannot
be determined from the RateSpec
.
load deriv.mat;
Spread = 20;
Settle = datetime(2000,1,1);
Maturity = datetime(2003,12,1);
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 (01-Dec-1999) 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
01-Dec-1999, which was earlier than the valuation date of ZeroRateSpec
(01-Jan-2000).
This error can be avoided by specifying the rate at the instrument’s
starting date using the LatestFloatingRate
name-value
pair argument.
Define LatestFloatingRate
and calculate
the floating-rate price.
Price = floatbyzero(ZeroRateSpec, Spread, Settle, Maturity, 'LatestFloatingRate', 0.03)
Price = 100.0285
Price a Floating-Rate Note Using a Different Curve to Generate Floating Cash Flows
Define the OIS and Libor rates.
Settle = datetime(2013,3,15); 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') 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 floating-rate note.
Maturity = datetime(2018,3,15);
Compute the price for the floating-rate 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 interest-rate 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
-by-1
vector.
Data Types: double
Settle
— Settlement date
datetime array | string array | date character vector
Settlement date, specified either as a scalar or
NINST
-by-1
vector using a datetime array, string
array, or date character vectors.
To support existing code, floatbyzero
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
-by-1
vector using a
datetime array, string array, or date character vectors representing the maturity date
for each floating-rate note.
To support existing code, floatbyzero
also
accepts serial date numbers as inputs, but they are not recommended.
Name-Value Arguments
Specify 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: [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 comma-separated pair consisting
of 'FloatReset'
and a
NINST
-by-1
vector.
Data Types: double
Basis
— Day count basis
0
(actual/actual) (default) | integer from 0
to 13
Day count basis, specified as the comma-separated pair consisting of
'Basis'
and a NINST
-by-1
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 comma-separated pair consisting of
'Principal'
and a vector or cell array.
Principal
accepts a NINST
-by-1
vector
or NINST
-by-1
cell array, where
each element of the cell array is a NumDates
-by-2
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
— End-of-month rule flag for generating dates when Maturity
is end-of-month date for month having 30 or fewer days
1
(in effect) (default) | nonnegative integer [0,1]
End-of-month rule flag for generating dates when Maturity
is an
end-of-month date for a month having 30 or fewer days, specified as the
comma-separated pair consisting of 'EndMonthRule'
and a nonnegative
integer [0
, 1
] using a
NINST
-by-1
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
comma-separated pair consisting of 'LatestFloatingRate'
and a
NINST
-by-1
.
The LatestFloatingRate
is specified as the benchmark plus the
spread (for example, SOFR + spread).
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
comma-separated 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 comma-separated
pair consisting of 'AdjustCashFlowsBasis'
and a
NINST
-by-1
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 comma-separated pair consisting of
'Holidays'
and MATLAB dates using a NHolidays
-by-1
vector.
Data Types: datetime
BusinessDayConvention
— Business day conventions
actual
(default) | character vector | cell array of character vectors
Business day conventions, specified as the comma-separated pair consisting of
'BusinessDayConvention'
and a character vector or a
N
-by-1
cell array of character vectors of
business day conventions. The selection for business day convention determines how
non-business days are treated. Non-business days are defined as weekends plus any
other date that businesses are not open (e.g. statutory holidays). Values are:
actual
— Non-business days are effectively ignored. Cash flows that fall on non-business days are assumed to be distributed on the actual date.follow
— Cash flows that fall on a non-business day are assumed to be distributed on the following business day.modifiedfollow
— Cash flows that fall on a non-business 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 non-business day are assumed to be distributed on the previous business day.modifiedprevious
— Cash flows that fall on a non-business 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
— Floating-rate note prices
matrix
Floating-rate 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
-
by-NUMCURVES
matrix. Each column arises from one
of the zero curves.
CFlowAmounts
— Cash flow amounts
matrix
Cash flow amounts, returned as a NINST
- by-NUMCFS
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
- by-NUMCFS
matrix
of payment dates for each note.
More About
Floating-Rate Note
A floating-rate 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
Introduced before R2006aR2022b: Serial date numbers not recommended
Although floatbyzero
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
| fixedbyzero
| swapbyzero
| intenvset
| FloatBond
Topics
- Pricing Using Interest-Rate Term Structure
- Price Portfolio of Bond and Bond Option Instruments
- Compute LIBOR Fallback
- Floating-Rate Note
- Understanding Interest-Rate Tree Models
- Supported Interest-Rate Instrument Functions
- Mapping Financial Instruments Toolbox Functions for Interest-Rate Instrument Objects
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