## Creating an `IRDataCurve` Object

To create an `IRDataCurve` object, see the following options:

### Use `IRDataCurve` with Dates and Data

Use `IRDataCurve` 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 `IRDataCurve` 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.

### Bootstrap `IRDataCurve` Based on Market Instruments

Use the bootstrapping function, 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]; ```

`bootstrap` is called as a function of the `IRDataCurve` object. Inputs to this function include the curve `Type` (`zero` or `forward`), `Settle` date, `InstrumentTypes`, and `Instrument` data. The `bootstrap` function 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` function 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` function is called as a function of the `IRBootstrapOptions` object. Inputs to the `bootstrap` function include the curve `Type` (`zero` or `forward`), `Settle` date, `InstrumentTypes`, and `Instrument` data. The `bootstrap` function 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` function uses an Optimization Toolbox function to solve for any bootstrapped rates.

Plot the par yields curve using the `getParYields` function.

```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.