bootstrap

Bootstrap interest-rate curve from market data

Syntax

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

DCurve = IRDataCurve.bootstrap(___,Name,Value)

Description

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.

Note

The ratecurve object and associated methods were introduced in R2020a as part of a new object-based framework in the Financial Instruments Toolbox™ which supports end-to-end workflows in instrument modeling and analysis. For more information, see irbootstrap and Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments.

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

Examples

Use the bootstrap Method to Create an IRDataCurve Object

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

Use the bootstrap Method to Create an IRDataCurve Object That Includes Bonds

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

Use IRBootstrapOptionsObj with bootstrap for Negative Zero Interest-Rates

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
   -0.0005
   -0.0010
   -0.0010
   -0.0009
   -0.0009
      ⋮

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

Input Arguments

Type — Type of interest-rate curve bootstrapped from market instruments

character vector with value of 'zero', 'discount', or 'forward'

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 — Settle date of interest-rate curve

serial date number | character vector

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

Data Types: double | char

InstrumentTypes — Instrument types

cell array of character vectors with values of 'deposit', 'futures', 'swap', 'bond', and 'fra'

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 — Instruments

matrix

Instruments, specified as an N-by-3 data matrix for Instruments where the first column is Settle date using a serial date number, the second column is Maturity using a serial date number, and the third column is the market quote. 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 pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: DCurve = IRDataCurve.bootstrap('Forward',CurveSettle,InstrumentTypes,Instruments,'InterpMethod','pchip')

Name-Value Pair Arguments for All Bond Instruments

Compounding — Compounding frequency per-year for IRDataCurve object

CurveObj.Compounding (default) | possible values include: –1, 0, 1, 2, 3, 4, 6, 12.

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

Basis — Day count basis of the interest-rate curve

0 (actual/actual) (default) | integer from 0 to 13

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

InterpMethod — Interpolation method

'linear' (default) | character vector with values of 'linear', 'cubic', 'pchip', or 'spline'

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

IRBootstrapOptionsObj — IRBootstrapOptions object

[] (default) | IRBootstrapOptions object

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

Data Types: object

DiscountCurve — RateSpec for curve used to discount cash flows

[] (default) | RateSpec 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

InstrumentCouponRate — Annual percentage rate to determine the coupons payable on an instrument

[] (default) | decimal

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

InstrumentPeriod — Coupons per year for the instrument

2 (default) | numeric with value of 0, 1, 2, 3, 4, 6, and 12

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

Data Types: double

InstrumentBasis — Day-count basis of the instrument

0 (actual/actual) (default) | integer from 0 to 13

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

InstrumentEndMonthRule — End-of-month rule

1 (default) | logical with value 0 or 1

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

InstrumentIssueDate — Instrument issue date

[] (default) | string scalar | date character vector | serial date number

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

Data Types: char | double | string

InstrumentFirstCouponDate — Date when a bond makes its first coupon payment

cash flow payment dates are determined from other inputs (default) | string scalar | date character vector | serial date number

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 string, 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 | string

InstrumentLastCouponDate — Last coupon date of a bond before the maturity date

cash flow payment dates are determined from other inputs (default) | string scalar | date character vector | serial date number

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 string, 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 | string | datetime

InstrumentFace — Face or par value

100 (default) | numeric

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

DCurve — Interest-rate curve from market data

structure

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

Version History

Introduced in R2008b