bootstrap

Bootstrap interest-rate curve from market data

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Syntax

Dcurve = IRDataCurve.bootstrap(Type,Settle,InstrumentTypes,Instruments)

Dcurve = IRDataCurve.bootstrap(Type,Settle,InstrumentTypes,Instruments,'Parameter1',Value1,'Parameter2',Value2, ...)

Arguments

Type

Type of interest-rate curve. Type refers to the type of data in the curve that is bootstrapped from the market instruments. Acceptable values are: discount, forward, or zero.

When using the bootstrap method, the choice of the Type parameter can impact the curve construction because it will affect the type of data that will be interpolated on (that is, forward rates, zero rates or discount factors) during the bootstrapping process. So curves that are bootstrapped using different Type parameters undergo different bootstrapping algorithms with different interpolation methods, and they can sometimes produce different results when using the “get” methods (for example, getForwardRates).

Settle

Scalar or column vector of settlement dates.

InstrumentTypes

N-by-1 cell array (where N is the number of instruments) indicating what kind of instrument is in the Instruments matrix. Acceptable values are deposit, futures, swap, bond, and fra.

Instruments

N-by-3 data matrix for Instruments where the first column is Settle date, the second column is Maturity, and the third column is the market quote (dates must be MATLAB® date numbers). The market quote represents the following for each instrument:

  • deposit: rate

  • futures: price (e.g., 9628.54)

  • swap: rate

  • bond: clean price

  • fra: forward rate

    Note

    Instruments input for fra and for futures are different. Specifically, the forward rate underlying a fra starts on the start date (column 1 of Instruments) and ends on the end date (column 2 of Instruments). While the forward rate underlying a futures contract starts on the maturity date of the futures contract and ends on a date n months after the futures maturity, where n is the periodicity of the futures contract.

Compounding

(Optional) Scalar that sets the compounding frequency per year for an IRDataCurve object:

  • -1 = Continuous compounding

  • 0 = Simple interest (no compounding) for “zero” and “discount” curve types only, not supported for “forward” curves

  • 1 = Annual compounding

  • 2 = Semiannual compounding (default)

  • 3 = Compounding three times per year

  • 4 = Quarterly compounding

  • 6 = Bimonthly compounding

  • 12 = Monthly compounding

Basis

(Optional) Day-count basis of the interest-rate curve. A scalar of integers.

  • 0 = actual/actual (default)

  • 1 = 30/360 (SIA)

  • 2 = actual/360

  • 3 = actual/365

  • 4 = 30/360 (BMA)

  • 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.

InterpMethod

(Optional) Values are:

  • 'linear' — Linear interpolation (default).

  • 'constant' — Piecewise constant interpolation.

  • 'pchip' — Piecewise cubic Hermite interpolation.

  • 'spline' — Cubic spline interpolation.

IRBootstrapOptionsObj

(Optional) An IRBootstrapOptions object.

DiscountCurve

(Optional) RateSpec for a curve used to discount the cash flows.

Instrument Parameters

For each bond Instrument, you can specify the following additional instrument parameters as parameter/value pairs. For example, InstrumentBasis distinguishes a bond instrument's Basis value from the curve's Basis value. For instruments of type deposit, futures, or swap the Basis and Compounding values must be identical for each instance of the instrument.

InstrumentCouponRate

(Optional) Decimal number indicating the annual percentage rate used to determine the coupons payable on an instrument.

InstrumentPeriod

(Optional) Coupons per year of the instrument. A vector of integers. Allowed values are 0, 1, 2 (default), 3, 4, 6, and 12.

InstrumentBasis

(Optional) Day-count basis of the instrument. A vector of integers.

  • 0 = actual/actual (default)

  • 1 = 30/360 (SIA)

  • 2 = actual/360

  • 3 = actual/365

  • 4 = 30/360 (BMA)

  • 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.

InstrumentEndMonthRule

(Optional) End-of-month rule. A 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 an instrument's coupon payment date is always the same numerical day of the month. 1 = set rule on (default), meaning that an instrument's coupon payment date is always the last actual day of the month.

InstrumentIssueDate

(Optional) Date when an instrument was issued.

InstrumentFirstCouponDate

(Optional) Date when a bond makes its first coupon payment; used when bond has an irregular first coupon period. When FirstCouponDate and LastCouponDate are both specified, FirstCouponDate takes precedence in determining the coupon payment structure. If you do not specify a FirstCouponDate, the cash flow payment dates are determined from other inputs.

InstrumentLastCouponDate

(Optional) Last coupon date of a bond before the maturity date; used when bond has an irregular last coupon period. In the absence of a specified FirstCouponDate, a specified LastCouponDate determines the coupon structure of the bond. The coupon structure of a bond is truncated at the LastCouponDate, regardless of where it falls, and is followed only by the bond's maturity cash flow date. If you do not specify a LastCouponDate, the cash flow payment dates are determined from other inputs.

InstrumentFace

(Optional) Face or par value. Default = 100.

Note

When using Instrument parameter/value pairs, you can specify simple interest for an Instrument by specifying the InstrumentPeriod value as 0. If InstrumentBasis and InstrumentPeriod are not specified for an Instrument, the following default values are used:

  • deposit instrument uses InstrumentBasis as 2 (act/360) and InstrumentPeriod is 0 (simple interest).

  • futures instrument uses InstrumentBasis as 2 (act/360) and InstrumentPeriod is 4 (quarterly).

  • swap instrument uses InstrumentBasis as 2 (act/360) and InstrumentPeriod is 2.

  • bond instrument uses InstrumentBasis as 0 (act/act) and InstrumentPeriod is 2.

  • FRA instrument uses InstrumentBasis as 2 (act/360) and InstrumentPeriod is 4 (quarterly).

Description

Dcurve = IRDataCurve.bootstrap(Type, Settle, InstrumentTypes, Instruments, 'Parameter1', Value1, 'Parameter2', Value2, ...) bootstraps an interest-rate curve from market data. The dates of the bootstrapped curve correspond to the maturity dates of the input instruments. You must enter the optional arguments for Basis, Compounding, Interpmethod, IRBootstrapOptionsObj, and DiscountCurve as parameter/value pairs.

Examples

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Open Live Script

In this bootstrapping example, InstrumentTypes, Instruments, and a Settle date are defined: 

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');

Use the bootstrap method to create an IRDataCurve object. 

bootModel = IRDataCurve.bootstrap('Forward', CurveSettle, ...
InstrumentTypes, Instruments,'InterpMethod','pchip');

To create the plot for the bootstrapped market data: 

PlottingDates = (datenum('08/11/2007'):30:CurveSettle+365*25)';
plot(PlottingDates, getParYields(bootModel, PlottingDates),'r')
ylim([0 .06])
datetick

Open Live Script

In this bootstrapping example, InstrumentTypes, Instruments, and a Settle date are defined: 

CurveSettle = datenum('8-Mar-2010');

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

Instruments = [datenum('8-Mar-2010'),datenum('8-Apr-2010'),.003; ...
    datenum('8-Mar-2010'),datenum('8-Jun-2010'),.005; ...
    datenum('8-Mar-2010'),datenum('8-Sep-2010'),.007; ...
    datenum('8-Mar-2010'),datenum('8-Mar-2011'),.009; ...
    datenum('8-Mar-2010'),datenum('18-Jun-2011'),9840; ...
    datenum('8-Mar-2010'),datenum('17-Sep-2011'),9820; ...
    datenum('8-Mar-2010'),datenum('17-Dec-2011'),9810; ...
    datenum('8-Mar-2010'),datenum('18-Mar-2012'),9800; ...
    datenum('8-Mar-2010'),datenum('8-Mar-2015'),.025; ...
    datenum('8-Mar-2010'),datenum('8-Mar-2020'),.035; ...
    datenum('8-Mar-2010'),datenum('8-Mar-2030'),99; ...
    datenum('8-Mar-2010'),datenum('8-Mar-2040'),101];

When bonds are used, InstrumentCouponRate must be specified: 

InstrumentCouponRate = [zeros(10,1);.045;.05];

Note, for parameters that are only applicable to bonds (InstrumentFirstCouponDate, InstrumentLastCouponDate, InstrumentIssueDate, InstrumentFace) the entries for non-bond instruments (deposits and futures) are ignored.

Use the bootstrap method to create an IRDataCurve object. 

bootModel = IRDataCurve.bootstrap('Forward', CurveSettle, ...
InstrumentTypes, Instruments,'InterpMethod','pchip',...
'InstrumentCouponRate',InstrumentCouponRate);

Create the plot for the bootstrapped market data. 

PlottingDates = datemnth(CurveSettle,1:30*12);
plot(PlottingDates, getParYields(bootModel, PlottingDates),'r')
ylim([0 .06])
datetick

Open Live Script

Use the IRBootstrapOptionsObj optional argument with the bootstrap method to allow for negative zero rates when solving for the swap zero points. 

Settle = datenum('15-Mar-2015'); 
InstrumentTypes = {'Deposit';'Deposit';'Swap';'Swap';'Swap';'Swap';}; 

Instruments = [Settle,datenum('15-Jun-2015'),.001; ... 
Settle,datenum('15-Dec-2015'),.0005; ... 
Settle,datenum('15-Mar-2016'),-.001; ... 
Settle,datenum('15-Mar-2017'),-0.0005; ... 
Settle,datenum('15-Mar-2018'),.0017; ... 
Settle,datenum('15-Mar-2020'),.0019]; 

irbo = IRBootstrapOptions('LowerBound',-1); 

bootModel = IRDataCurve.bootstrap('zero', Settle, InstrumentTypes,... 
    Instruments,'IRBootstrapOptions',irbo); 

bootModel.getZeroRates(datemnth(Settle,1:60))
ans = 60×1

    0.0012
    0.0011
    0.0010
    0.0009
    0.0008
    0.0008
    0.0007
    0.0006
    0.0005
   -0.0000
      ⋮

Note that optional argument for LowerBound is set to -1 for negative zero rates when solving the swap zero points.

See Also

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Topics

Introduced in R2008b

Financial Instruments Toolbox Documentation

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