floatbyzero

Price floating-rate note from set of zero curves

Syntax

[Price,DirtyPrice,OutputCashFlows,CFlowDates] =
floatbyzero(RateSpec,Spread,Settle,Maturity)
[Price,DirtyPrice,OutputCashFlows,CFlowDates] =
floatbyzero(RateSpec,Spread,Settle,Maturity,
Reset,Basis,Principal,EndMonthRule)
[Price,DirtyPrice,OutputCashFlows,CFlowDates] =
floatbyzero(RateSpec,Spread,Settle,Maturity,Name,Value)

Description

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

[Price,DirtyPrice,OutputCashFlows,CFlowDates] =
floatbyzero(RateSpec,Spread,Settle,Maturity,
Reset,Basis,Principal,EndMonthRule)
computes the price of a floating-rate note from a set of zero curves using optional input arguments.

[Price,DirtyPrice,OutputCashFlows,CFlowDates] =
floatbyzero(RateSpec,Spread,Settle,Maturity,Name,Value)
computes the price of a floating-rate note from a set of zero curves with additional options specified by one or more Name,Value pair arguments.

Input Arguments

RateSpec

Structure containing the properties of an interest-rate structure. See intenvset for information on creating RateSpec.

Spread

Number of basis points over the reference rate.

Settle

Settlement date. Settle must be either a scalar or NINST-by-1 vector of serial date numbers or date strings of the same value which represent the settlement date for each bond. Settle must be earlier than Maturity.

Maturity

Maturity date.

Ordered Input or Name-Value Pair Arguments

Enter the following optional inputs using an ordered syntax or as name-value pair arguments. You cannot mix ordered syntax with name-value pair arguments.

Reset

NINST-by-1 vector representing the frequency of payments per year.

Default: 1

Basis

Day-count basis of the instrument. A vector of integers.

  • 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 (ISMA)

  • 9 = actual/360 (ISMA)

  • 10 = actual/365 (ISMA)

  • 11 = 30/360E (ISMA)

  • 12 = actual/365 (ISDA)

  • 13 = BUS/252

For more information, see basis.

Default: 0 (actual/actual)

Principal

NINST-by-1 vector of notional principal amounts or NINST-by-1 cell array. For the latter case, each element of the cell array is a NumDates-by-2 matrix where the first column is dates and the second column is associated principal amount. The date indicates the last day that the principal value is valid.

Default: 100

EndMonthRule

End-of-month rule. NINST-by-1 vector. This rule applies only when Maturity is an end-of-month date for a month having 30 or fewer days.

  • 0 = Ignore rule, meaning that a bond coupon payment date is always the same numerical day of the month.

  • 1 = Set rule on, meaning that a bond coupon payment date is always the last actual day of the month.

Default: 1

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.

AdjustCashFlowsBasis

Adjust the cash flows based on the actual period day count. NINST-by-1 of logicals.

Default: false

BusinessDayConvention

Require payment dates to be business dates. NINST-by-1 cell array with possible choices of business day convention:

  • actual

  • follow

  • modifiedfollow

  • previous

  • modifiedprevious

Default: actual

Holidays

Holidays used for business day convention. NHOLIDAYS-by-1 of MATLAB® date numbers.

Default: If no dates are specified, holidays.m is used.

LatestFloatingRate

Rate for the next floating payment set at the last reset date. NINST-by-1 of scalars.

Default: If no LatestFloatingRate is specified, the floating rate at the previous reset date is computed from the RateSpec.

ProjectionCurve

The rate curve to be used in generating floating cash flows of the floater instruments. This structure must be created using intenvset.

Default: If no ProjectionCurve is specified, the RateSpec is used both for discounting and generating floating cash flows for the floater instrument.

Output Arguments

Price

Number of instruments (NINST) by number of curves (NUMCURVES) matrix of floating-rate note prices. Each column arises from one of the zero curves.

DirtyPrice

NINST-by-NUMCURVES matrix of dirty bond price (clean + accrued interest). Each column arises from one of the zero curves.

OutputCashFlows

NINST-by-NUMCFS matrix of cash flows for each bond.

    Note:   If there is more than one curve specified in the RateSpec input, then the first NCURVES rows correspond to the first bond, the second NCURVES rows correspond to the second bond, and so on.

CFlowDates

NINST-by-NUMCFS matrix of payment dates for each bond.

Examples

expand all

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 = '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

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 = 

           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

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 = '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

Price a Floating-Rate Note Using a Different Curve to Generate Floating Cash Flows

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.

SwapMaturity = 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, SwapMaturity,'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.

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