floatbyzero

Price floating-rate note from set of zero curves

Syntax

[Price,DirtyPrice,CFlowAmounts,CFlowDates] = floatbyzero(RateSpec,Spread,Settle,Maturity)

[Price,DirtyPrice,CFlowAmounts,CFlowDates] = floatbyzero(___,Name,Value)

Description

[Price,DirtyPrice,CFlowAmounts,CFlowDates] = floatbyzero(RateSpec,Spread,Settle,Maturity) prices a floating-rate note from a set of zero curves.

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.

[Price,DirtyPrice,CFlowAmounts,CFlowDates] = floatbyzero(___,Name,Value) adds additional name-value pair arguments.

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 R2006a

R2022b: 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.