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bootstrap

Bootstrap interest-rate curve from market data

Description

example

DCurve = IRDataCurve.bootstrap(Type,Settle,InstrumentTypes,Instruments) bootstraps an interest-rate curve from market data. The dates of the bootstrapped curve correspond to the maturity dates of the input instruments.

example

DCurve = IRDataCurve.bootstrap(___,Name,Value) adds optional name-value pair arguments.

Examples

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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

Figure contains an axes object. The axes object contains an object of type line.

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

Figure contains an axes object. The axes object contains an object of type line.

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.

Input Arguments

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Type of interest-rate curve bootstrapped from market instruments, specified by using a scalar character vector.

When using the bootstrap, 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” functions (for example, getForwardRates).

Data Types: char

Settle date of interest-rate curve, specified using a scalar date character vector or serial date number.

Data Types: double | char

Instrument types, specified using an 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'.

Data Types: char | cell

Instruments, specified as an 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 (for example, 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.

Data Types: double

Name-Value 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 quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: DCurve = IRDataCurve.bootstrap('Forward',CurveSettle,InstrumentTypes,Instruments,'InterpMethod','pchip')
Name-Value Pair Arguments for All Bond Instruments

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Compounding frequency per-year for the IRDataCurve object, specified as the comma-separated pair consisting of 'Compounding' and a scalar numeric using one of the supported values:

  • −1 = Continuous compounding

  • 0 = Simple interest (no compounding)

  • 1 = Annual compounding

  • 2 = Semiannual compounding

  • 3 = Compounding three times per year

  • 4 = Quarterly compounding

  • 6 = Bimonthly compounding

  • 12 = Monthly compounding

Data Types: double

Day count basis of the interest-rate curve, specified as the comma-separated pair consisting of 'Basis' and a scalar integer.

  • 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

Interpolation method, specified as the comma-separated pair consisting of 'InterpMethod' and a scalar character vector. For more information on interpolation methods, see interp1.

Data Types: char

IRBootstrapOptions object, specified as the comma-separated pair consisting of 'IRBootstrapOptionsObj' and an IRBootstrapOptions object previously created using IRBootStrapOptions.

Data Types: object

RateSpec for curve used to discount cash flows, specified as the comma-separated pair consisting of 'DiscountCurve' and a RateSpec object previously created using intenvset or toRateSpec.

Data Types: object

Name-Value Pair Arguments for Each Bond Instrument

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Annual percentage rate to determine the coupons payable on an instrument, specified as the comma-separated pair consisting of 'InstrumentCouponRate' and a scalar decimal value.

Data Types: double

Coupons per year for the instrument, specified as the comma-separated pair consisting of 'InstrumentPeriod' and a scalar numeric value.

Data Types: double

Day count basis of the instrument, specified as the comma-separated pair consisting of 'InstrumentBasis' and a scalar integer.

  • 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

Note

InstrumentBasis distinguishes a bond instrument's Basis value from the interest-rate curve's Basis value.

For more information, see Basis.

Data Types: double

End-of-month rule, specified as the comma-separated pair consisting of 'InstrumentEndMonthRule' and a logical value. 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's coupon payment date is always the same numerical day of the month.

  • 1 = set rule on (default), meaning that a bond's coupon payment date is always the last actual day of the month.

Data Types: logical

Instrument issue date, specified as the comma-separated pair consisting of 'InstrumentIssueDate' and a scalar date character vector or serial date number.

Data Types: char | double

Date when a bond makes its first coupon payment (used when bond has an irregular first coupon period), specified as the comma-separated pair consisting of 'InstrumentFirstCouponDate' and a scalar date character vector or serial date number. When InstrumentFirstCouponDate and InstrumentLastCouponDate are both specified, InstrumentFirstCouponDate takes precedence in determining the coupon payment structure. If you do not specify a InstrumentFirstCouponDate, the cash flow payment dates are determined from other inputs.

Data Types: char | double

Last coupon date of a bond before the maturity date (used when bond has an irregular last coupon period), specified as the comma-separated pair consisting of 'InstrumentLastCouponDate' and a scalar date character vector or serial date number. In the absence of a specified InstrumentFirstCouponDate, a specified InstrumentLastCouponDate determines the coupon structure of the bond. The coupon structure of a bond is truncated at the InstrumentLastCouponDate, regardless of where it falls, and is followed only by the bond's maturity cash flow date. If you do not specify a InstrumentLastCouponDate, the cash flow payment dates are determined from other inputs.

Data Types: char | double

Face or par value, specified as the comma-separated pair consisting of 'InstrumentFace' and a scalar numeric.

Data Types: double

Note

When using Instrument name-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).

Output Arguments

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Interest-rate curve from market data, returned as a structure.

Introduced in R2008b