Creating an IRDataCurve Object

To create an IRDataCurve object, see the following options:

• IRDataCurve Constructor with Dates and Data

• IRDataCurve Bootstrapping Based on Market Instruments

IRDataCurve Constructor with Dates and Data

Use the IRDataCurve constructor with vectors of dates and data to create an interest-rate curve object. When constructing the IRDataCurve object, you can also use optional inputs to define how the interest-rate curve is constructed from the dates and data.

Example

In this example, you create the vectors for Dates and Data for an interest-rate curve:

Data = [2.09 2.47 2.71 3.12 3.43 3.85 4.57 4.58]/100;
Dates = daysadd(today,[360 2*360 3*360 5*360 7*360 10*360 20*360 30*360],1);

Use the IRDataCurve constructor to build interest-rate objects based on the constant and pchip interpolation methods:

irdc_const = IRDataCurve('Forward',today,Dates,Data,'InterpMethod','constant');
irdc_pchip = IRDataCurve('Forward',today,Dates,Data,'InterpMethod','pchip');

Plot the forward and zero rate curves for the two IRDataCurve objects based on constant and pchip interpolation methods:

PlottingDates = daysadd(today,180:10:360*30,1);
plot(PlottingDates, getForwardRates(irdc_const, PlottingDates),'b')
hold on
plot(PlottingDates, getForwardRates(irdc_pchip, PlottingDates),'r')
plot(PlottingDates, getZeroRates(irdc_const, PlottingDates),'g')
plot(PlottingDates, getZeroRates(irdc_pchip, PlottingDates),'yellow')
legend({'Constant Forward Rates','PCHIP Forward Rates','Constant Zero Rates',...
'PCHIP Zero Rates'},'location','SouthEast')
title('Interpolation methods for IRDataCurve objects')
datetick

The plot demonstrates the relationship of the forward and zero rate curves.

IRDataCurve Bootstrapping Based on Market Instruments

Use the bootstrapping method, based on market instruments, to create an interest-rate curve object. When bootstrapping, you also have the option to define a range of interpolation methods (linear, spline, constant, and pchip).

Example 1

In this example, you bootstrap a swap curve from deposits, Eurodollar Futures and swaps. The input market data for this example is hard-coded and specified as two cell arrays of data; one cell array indicates the type of instrument and the other contains the Settle, Maturity values and a market quote for the instrument. For deposits and swaps, the quote is a rate; for the EuroDollar futures, the quote is a price. Although bonds are not used in this example, a bond would also be quoted with a price.

InstrumentTypes = {'Deposit';'Deposit';'Deposit';'Deposit';'Deposit'; ...
    'Futures';'Futures'; ...
    'Futures';'Futures';'Futures'; ...
    'Futures';'Futures';'Futures'; ...
    'Futures';'Futures';'Futures'; ...
    'Futures';'Futures';'Futures'; ...
    'Futures';'Futures';'Futures'; ...
    'Swap';'Swap';'Swap';'Swap';'Swap';'Swap';'Swap'};

Instruments = [datenum('08/10/2007'),datenum('08/17/2007'),.0532063; ...
    datenum('08/10/2007'),datenum('08/24/2007'),.0532000; ...
    datenum('08/10/2007'),datenum('09/17/2007'),.0532000; ...
    datenum('08/10/2007'),datenum('10/17/2007'),.0534000; ...
    datenum('08/10/2007'),datenum('11/17/2007'),.0535866; ...
    datenum('08/08/2007'),datenum('19-Dec-2007'),9485; ...
    datenum('08/08/2007'),datenum('19-Mar-2008'),9502; ...
    datenum('08/08/2007'),datenum('18-Jun-2008'),9509.5; ...
    datenum('08/08/2007'),datenum('17-Sep-2008'),9509; ...
    datenum('08/08/2007'),datenum('17-Dec-2008'),9505.5; ...
    datenum('08/08/2007'),datenum('18-Mar-2009'),9501; ...
    datenum('08/08/2007'),datenum('17-Jun-2009'),9494.5; ...
    datenum('08/08/2007'),datenum('16-Sep-2009'),9489; ...
    datenum('08/08/2007'),datenum('16-Dec-2009'),9481.5; ...
    datenum('08/08/2007'),datenum('17-Mar-2010'),9478; ...
    datenum('08/08/2007'),datenum('16-Jun-2010'),9474; ...
    datenum('08/08/2007'),datenum('15-Sep-2010'),9469.5; ...
    datenum('08/08/2007'),datenum('15-Dec-2010'),9464.5; ...
    datenum('08/08/2007'),datenum('16-Mar-2011'),9462.5; ...
    datenum('08/08/2007'),datenum('15-Jun-2011'),9456.5; ...
    datenum('08/08/2007'),datenum('21-Sep-2011'),9454; ...
    datenum('08/08/2007'),datenum('21-Dec-2011'),9449.5; ...
    datenum('08/08/2007'),datenum('08/08/2014'),.0530; ...
    datenum('08/08/2007'),datenum('08/08/2017'),.0545; ...
    datenum('08/08/2007'),datenum('08/08/2019'),.0551; ...
    datenum('08/08/2007'),datenum('08/08/2022'),.0559; ...
    datenum('08/08/2007'),datenum('08/08/2027'),.0565; ...
    datenum('08/08/2007'),datenum('08/08/2032'),.0566; ...
    datenum('08/08/2007'),datenum('08/08/2037'),.0566];

The bootstrap method is called as a static method of the @IRDataCurve class. Inputs to this method include the curve Type (zero or forward), Settle date, InstrumentTypes, and Instrument data. The bootstrap method also supports optional arguments, including an interpolation method, compounding, basis, and an options structure for bootstrapping. For example, you are passing in an @IRBootstrapOptions object which includes information for the ConvexityAdjustment to forward rates.

IRsigma = .01;
CurveSettle = datenum('08/10/2007');
bootModel = IRDataCurve.bootstrap('Forward', CurveSettle, ...
InstrumentTypes, Instruments,'InterpMethod','pchip',...
'Compounding',-1,'IRBootstrapOptions',...
IRBootstrapOptions('ConvexityAdjustment',@(t) .5*IRsigma^2.*t.^2))

bootModel = 

IRDataCurve

			 Type: Forward
		   Settle: 733264 (10-Aug-2007)
	  Compounding: -1
			Basis: 0 (actual/actual)
	 InterpMethod: pchip
			Dates: [29x1 double]
			 Data: [29x1 double]

The bootstrap method uses an Optimization Toolbox™ function to solve for any bootstrapped rates.

Plot the forward and zero curves:

PlottingDates = (CurveSettle+20:30:CurveSettle+365*25)';
TimeToMaturity = yearfrac(CurveSettle,PlottingDates);
BootstrappedForwardRates = getForwardRates(bootModel, PlottingDates);
BootstrappedZeroRates = getZeroRates(bootModel, PlottingDates);

figure
hold on
plot(TimeToMaturity,BootstrappedForwardRates,'r')
plot(TimeToMaturity,BootstrappedZeroRates,'g')
title('Bootstrapped Curve')
xlabel('Time')
legend({'Forward','Zero'})

The plot demonstrates the forward and zero rate curves for the market data.

Example 2

In this example, you bootstrap a swap curve from deposits, Eurodollar futures, and swaps. The input market data for this example is hard-coded and specified as two cell arrays of data; one cell array indicates the type of instrument and the other cell array contains the Settle, Maturity values and a market quote for the instrument. This example of bootstrapping also demonstrates the use of an InstrumentBasis for each Instrument type:

InstrumentTypes = {'Deposit';'Deposit';...
'Futures';'Futures';'Futures';'Futures';'Futures';'Futures';...
'Swap';'Swap';'Swap';'Swap';};

Instruments = [datenum('08/10/2007'),datenum('09/17/2007'),.0532000; ...
datenum('08/10/2007'),datenum('11/17/2007'),.0535866; ...
datenum('08/08/2007'),datenum('19-Dec-2007'),9485; ...
datenum('08/08/2007'),datenum('19-Mar-2008'),9502; ...
datenum('08/08/2007'),datenum('18-Jun-2008'),9509.5; ...
datenum('08/08/2007'),datenum('17-Sep-2008'),9509; ...
datenum('08/08/2007'),datenum('17-Dec-2008'),9505.5; ...
datenum('08/08/2007'),datenum('18-Mar-2009'),9501; ...
datenum('08/08/2007'),datenum('08/08/2014'),.0530; ...
datenum('08/08/2007'),datenum('08/08/2019'),.0551; ...
datenum('08/08/2007'),datenum('08/08/2027'),.0565; ...
datenum('08/08/2007'),datenum('08/08/2037'),.0566];

CurveSettle = datenum('08/10/2007');

The bootstrap method is called as a static method of the @IRDataCurve class. Inputs to this method include the curve Type (zero or forward), Settle date, InstrumentTypes, and Instrument data. The bootstrap method also supports optional arguments, including an interpolation method, compounding, basis, and an options structure for bootstrapping. In this example, you are passing an additional Basis value for each instrument type:

bootModel=IRDataCurve.bootstrap('Forward',CurveSettle,InstrumentTypes, ...
Instruments,'InterpMethod','pchip','InstrumentBasis',[repmat(2,8,1);repmat(0,4,1)])

bootModel = 

	IRDataCurve

			 Type: Forward
		   Settle: 733264 (10-Aug-2007)
	  Compounding: 2
			Basis: 0 (actual/actual)
	 InterpMethod: pchip
			Dates: [12x1 double]
			 Data: [12x1 double]

The bootstrap method uses an Optimization Toolbox function to solve for any bootstrapped rates.

Plot the par yields curve using the getParYields method:

PlottingDates = (datenum('08/11/2007'):30:CurveSettle+365*25)';
plot(PlottingDates, getParYields(bootModel, PlottingDates),'r')
datetick

The plot demonstrates the par yields curve for the market data.