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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

example

[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.

example

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

Examples

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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 = '01-Jan-2000';
Maturity = '01-Jan-2003';

Use floatbyzero to compute the price of the note.

Price = floatbyzero(ZeroRateSpec, Spread, Settle, Maturity)
Price = 100.5529

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 = '15-Nov-2011';
StartDates = ValuationDate;
EndDates = {'15-Nov-2012';'15-Nov-2013';'15-Nov-2014' ;'15-Nov-2015';'15-Nov-2016'};
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 ='15-Nov-2011';
Maturity = '15-Nov-2015';
Spread = 15;

Define the floating-rate note amortizing schedule.

Principal ={{'15-Nov-2012' 100;'15-Nov-2013' 70;'15-Nov-2014' 40;'15-Nov-2015' 10}};

Compute the price of the amortizing floating-rate note.

Price  = floatbyzero(RateSpec, Spread, Settle, Maturity, 'Principal', Principal)
Price = 100.3059

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 = '01-Jan-2000';
Maturity = '01-Dec-2003';

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

Define the OIS and Libor rates.

Settle = datenum('15-Mar-2013');
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 floating-rate note.

Maturity = datenum('15-Mar-2018'); % Five year swap
FloatSpread = 0;
FixedRate = .025;
SwapRates = [FixedRate FloatSpread];

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.

floatbyzero(OISCurve,0,Settle,Maturity,'ProjectionCurve',LiborCurve)
ans = 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

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Annualized zero rate term structure, specified using intenvset to create a RateSpec.

Data Types: struct

Number of basis points over the reference rate, specified as a NINST-by-1 vector.

Data Types: double

Settlement date, specified either as a scalar or NINST-by-1 vector of serial date numbers or date character vectors.

Settle must be earlier than Maturity.

Data Types: char | double

Maturity date, specified as a NINST-by-1 vector of serial date numbers or date character vectors representing the maturity date for each swap.

Data Types: char | double

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: [Price,DirtyPrice,CFlowAmounts,CFlowDates] = floatbyzero(RateSpec,Spread,Settle,Maturity,'Principal',Principal)

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Frequency of payments per year, specified as NINST-by-1 vector.

Data Types: double

Day count basis, specified as 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

Notional principal amounts, specified as 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

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 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

Rate for the next floating payment set at the last reset date, specified as a NINST-by-1.

Data Types: double

The rate curve to be used in generating the future forward rates. This structure must be created using intenvset. Use this optional input if the forward curve is different from the discount curve.

Data Types: struct

Flag to adjust cash flows based on actual period day count, specified as a NINST-by-1 vector of logicals with values of 0 (false) or 1 (true).

Data Types: logical

Holidays used in computing business days, specified as MATLAB date numbers using a NHolidays-by-1 vector.

Data Types: double

Business day conventions, specified by 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

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Floating-rate note prices, returned as a (NINST) by number of curves (NUMCURVES) matrix. Each column arises from one of the zero curves.

Dirty note price (clean + accrued interest), returned as a NINST- by-NUMCURVES matrix. Each column arises from one of the zero curves.

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.

Cash flow dates, returned as a NINST- by-NUMCFS matrix of payment dates for each note.

Introduced before R2006a

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