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bootstrap - Bootstrap interest-rate curve from market data

Class

@IRDataCurve

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. Acceptable values are: discount, forward, or zero.

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, and bond.

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).

    Note   The market quote represents the following for each instrument:

    • deposit: rate

    • futures: price (e.g., 9628.54)

    • swap: rate

    • bond: clean price

Compounding

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

  • -1 =  Continuous compounding

  • 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/actual (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.

Instrument Parameters

For each of the supported InstrumentTypes, you can specify the following additional instrument parameters as parameter/value pairs by prepending the word Instrument to the parameter field. For example, prepending InstrumentBasis distinguishes an instrument's Basis value from the curve's Basis value.

CouponRate

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

Period

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

Basis

(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/actual (ISDA)

  • 13 = BUS/252

For more information, see basis.

EndMonthRule

(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.

IssueDate

(Optional) Date when an instrument was issued.

FirstCouponDate

(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.

LastCouponDate

(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.

Face

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

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, and IRBootstrapOptionsObj as parameter/value pairs.

Examples

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')

bootModel = 

	IRDataCurve

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

To create the plot for the bootstrapped market data:

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

For an example of bootstrapping using instrument parameters support for prepending the word Instrument to the parameter field, see Using IRDataCurve bootstrap Method for Bootstrapping Based on Market Instruments.

How To

  

 

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