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irbootstrap

Bootstrap interest-rate curve from market data

Description

example

outCurve = irbootstrap(BootInstruments,Settle) creates a data structure for storing interest-rate term structure data. The outCurve output is a ratecurve object.

example

outCurve = irbootstrap(___,Name,Value) specifies options using one or more name-value pair arguments in addition to any of the input argument combinations in the previous syntax. For example, OutCurve = irbootstrap(Settle,BootInstruments,'Type',"zero",'Compounding',2,'Basis',5,'InterpMethod',"cubic") bootstraps a zero curve from BootInstruments.

Examples

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Define Deposit and Swap Parameters

Settle = datetime(2018,3,21);
DepRates = [.0050769 .0054934 .0061432 .0072388 .0093263]';
DepTimes = [1 2 3 6 12]';
DepDates = datemnth(Settle,DepTimes);
nDeposits = length(DepTimes);
 
SwapRates = [.0112597 0;.0128489 0;.0138917 0;.0146135 0;.0151175 0;...
      .0155184 0;.0158536 0;.0161435 0];
SwapTimes = (2:9)';
SwapDates = datemnth(Settle,12*SwapTimes);
nSwaps = length(SwapTimes);
 
nInst = nDeposits + nSwaps;

Create a Vector of Market Swap Instruments

Use fininstrument to create a vector of market Deposit and Swap instrument objects.

 BootInstruments(nInst,1) = fininstrument.FinInstrument;
 for ii=1:length(DepDates)
      BootInstruments(ii) = fininstrument("deposit",'Maturity',DepDates(ii),'Rate',DepRates(ii));
 end
 
 for ii=1:length(SwapDates)
      BootInstruments(ii+nDeposits) = fininstrument("swap",'Maturity',SwapDates(ii),'LegRate',[SwapRates(ii) 0]);
 end

Create ratecurve Object for Zero-Rate Curve

Use irbootstrap to create a ratecurve object for the zero-rate curve.

ZeroCurve = irbootstrap(BootInstruments,Settle)
ZeroCurve = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 0
                Dates: [13x1 datetime]
                Rates: [13x1 double]
               Settle: 21-Mar-2018
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

This example shows how to create a ratecurve object using irbootstrap with Deposit and Swap instruments and a DiscountCurve for discounting cash flows.

Settle = datetime(2021,4,15); 
crvDates = Settle + [calmonths([1 2 3 6]) calyears([1 2 3 5 7 10 20 30])]';
crvRates = [0.0004 0.0004 0.0005 0.0006 0.0008 0.0018 0.0037 0.0088 0.013 0.0165 0.022 0.0233]';
DiscountCurve = ratecurve("zero",Settle,crvDates,crvRates);

DepRates = [0.002 0.0021 0.0023 0.0024 .0028]';
DepDates = Settle + calmonths([1 2 3 6 12]');

SwapRates = [0.0041 0;0.0057 0;0.017 0;0.0193 0;0.024 0;0.027 0];
SwapTimes = [2 3 5 10 20 30]';
SwapDates = datemnth(Settle,12*SwapTimes);

BootInstruments = [fininstrument("deposit","Maturity",DepDates,"Rate",DepRates); ...
    fininstrument("swap","Maturity",SwapDates,"LegRate",SwapRates)];

ZeroCurve = irbootstrap(BootInstruments,Settle,'DiscountCurve',DiscountCurve)
ZeroCurve = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 0
                Dates: [11x1 datetime]
                Rates: [11x1 double]
               Settle: 15-Apr-2021
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create a BootInstruments variable as an input argument to irbootstrap to create a ratecurve object. The BootInstruments variable has OISFuture instrument objects for one-month SOFR Futures and three-month SOFR Futures, and an OvernightIndexedSwap instrument object.

Create Instruments

Use fininstrument to create an OISFuture instrument object for one-month SOFR Futures.

Settle = datetime(2021,3,4);
HFDates = datetime(2021,3,1) + caldays(0:3)';
HistFixing = timetable(HFDates,[0.02;0.04;0.04;0.02]);

% Data from the following: https://www.cmegroup.com/trading/interest-rates/stir/one-month-sofr_quotes_globex.html
Prices_1M = [99.97 99.96 99.95]';
Maturity_1M = lbusdate(2021,[3 4 5]',[],[],'datetime');
StartDate_1M = fbusdate(2021,[3 4 5]',[],[],'datetime');
FutInstruments_1M = fininstrument("OISFuture","Maturity",Maturity_1M ,"QuotedPrice",Prices_1M,"StartDate",StartDate_1M,"Method","Average",...
    'HistoricalFixing',HistFixing,'Name',"1MonthSOFRFuture")
FutInstruments_1M=3×1 object
  3x1 OISFuture array with properties:

    QuotedPrice
    Method
    Basis
    StartDate
    Maturity
    Notional
    BusinessDayConvention
    Holidays
    ProjectionCurve
    HistoricalFixing
    Name

Use fininstrument to create an OISFuture instrument object for three-month SOFR Futures.

% Data from the following: https://www.cmegroup.com/trading/interest-rates/stir/three-month-sofr_quotes_globex.html
Prices_3M = [99.92 99.895 99.84 99.74]';
Dates_3M_Maturity = thirdwednesday([6 9 12 3]',[2021 2021 2021 2022]','datetime');
Dates_3M_Start = thirdwednesday([3 6 9 12]',2021,'datetime');
FutInstruments_3M = fininstrument("OISFuture","Maturity",Dates_3M_Maturity,...
    "QuotedPrice",Prices_3M,"StartDate",Dates_3M_Start,'HistoricalFixing',HistFixing,'Name',"3MonthSOFRFuture");

Use fininstrument to create an OvernightIndexedSwap instrument object.

SOFRSwapRates = [.0023 0;.0064 0;.013 0;.017 0;.0175 0];
SOFRSwapTimes = [3 5 10 20 30];
SOFRSwapDates = datemnth(Settle,12*SOFRSwapTimes)';
SOFRSwapInstruments = fininstrument("OvernightIndexedSwap","Maturity",SOFRSwapDates,"LegRate",SOFRSwapRates,'Name',"overnight_swap_instrument")
SOFRSwapInstruments=5×1 object
  5x1 OvernightIndexedSwap array with properties:

    LegRate
    LegType
    Reset
    Basis
    Notional
    HistoricalFixing
    ResetOffset
    ProjectionCurve
    BusinessDayConvention
    Holidays
    EndMonthRule
    StartDate
    Maturity
    Name

Define BootInstruments for the three types of instruments.

BootInstruments = [FutInstruments_1M;FutInstruments_3M;SOFRSwapInstruments]
BootInstruments=12×1 object
  12x1 heterogeneous FinInstrument (OISFuture, OvernightIndexedSwap) array with properties:

    Name

Create ratecurve Object

Use irbootstrap to create a ratecurve object.

SOFRCurve = irbootstrap(BootInstruments,Settle)
SOFRCurve = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 0
                Dates: [12x1 datetime]
                Rates: [12x1 double]
               Settle: 04-Mar-2021
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create BootInstruments for multiple Deposit, STIRFuture, and Swap instruments and then use irbootstrap to create and display a ratecurve object.

Create Instruments

Use fininstrument to create a Deposit instrument object.

Settle = datetime(2021,6,15); 
DepRates = [0.0016 0.0017 .00175]';
DepDates = Settle + calmonths([1 2 3]');

Deposits = fininstrument("Deposit","Maturity",DepDates,"Rate",DepRates,'Name',"deposit_instrument")
Deposits=3×1 object
  3x1 Deposit array with properties:

    Rate
    Period
    Basis
    Maturity
    Principal
    BusinessDayConvention
    Holidays
    Name

Use fininstrument to create a STIRFuture instrument object.

FutureRates = [0.002 0.0025 0.0035]';
FutMat = [datetime(2021,9,15) datetime(2021,12,15) datetime(2022,3,16)]';
FutEndDates = [datetime(2021,12,15) datetime(2022,3,15) datetime(2022,6,15)]';

Futures = fininstrument("STIRFuture","Maturity",FutMat,"RateEndDate",FutEndDates,"QuotedPrice",100 - 100*FutureRates,'Name',"stir_future_instrument")
Futures=3×1 object
  3x1 STIRFuture array with properties:

    QuotedPrice
    Basis
    RateEndDate
    Maturity
    Notional
    BusinessDayConvention
    Holidays
    ProjectionCurve
    Name

Use fininstrument to create a Swap instrument object.

SwapRates = [.0063 0;.0108 0;.013 0;.015 0;0.017 0;.018 0;0.019 0];
SwapTimes = [2 5 7 10 15 20 30]';
SwapDates = datemnth(Settle,12*SwapTimes);

Swaps = fininstrument("Swap","Maturity",SwapDates,"LegRate",SwapRates,'Name',"swap_instrument")
Swaps=7×1 object
  7x1 Swap array with properties:

    LegRate
    LegType
    Reset
    Basis
    Notional
    LatestFloatingRate
    ResetOffset
    DaycountAdjustedCashFlow
    ProjectionCurve
    BusinessDayConvention
    Holidays
    EndMonthRule
    StartDate
    Maturity
    Name

Define BootInstruments for the three instruments.

BootInstruments = [Deposits;Futures;Swaps];

Create ratecurve Object Using irbootstrap

Use irbootstrap to create a ratecurve object.

ConvexityAdj = (1:3)'/10000;
ZeroCurve = irbootstrap(BootInstruments,Settle,'ConvexityAdjustment',ConvexityAdj,'InterpMethod','pchip')
ZeroCurve = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 0
                Dates: [13x1 datetime]
                Rates: [13x1 double]
               Settle: 15-Jun-2021
         InterpMethod: "pchip"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Plot Bootstrapped Curve

PlottingDates = Settle + calmonths(1:360);
plot(PlottingDates,zerorates(ZeroCurve,PlottingDates))
xlabel('Maturity (Years)') 
ylabel('Zero Rate')
title('Bootstrapped Curve')

Figure contains an axes object. The axes object with title Bootstrapped Curve contains an object of type line.

Input Arguments

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Collection of instruments, specified as an array of instrument objects. The collection of instruments can include Deposit, Swap, FRA, STIRFuture, OISFuture, and OvernightIndexedSwap instruments.

Data Types: object

Settlement date, specified as a scalar datetime, serial date number, date character vector, or date string.

Data Types: double | char | string | datetime

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: OutCurve = irbootstrap(Settle,BootInstruments,'Type',"zero",'Compounding',2,'Basis',5,'InterpMethod',"cubic")

Type of interest-rate curve, specified as the comma-separated pair consisting of 'Type' and a scalar string or character vector.

Note

When you use irbootstrap, the value you specify for Type can impact the curve construction because it affects the type of data that is interpolated on (that is, forward rates, zero rates, or discount factors) during the bootstrapping process.

Data Types: char | string

Compounding frequency, specified as the comma-separated pair consisting of 'Compounding' and a scalar numeric using the supported values: –1, 0, 1, 2, 3, 4, 6, or 12.

Data Types: double

Day-count basis, 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 string or character vector using a supported value. For more information on interpolation methods, see interp1.

Data Types: char | string

Extrapolation method for data before first data, specified as the comma-separated pair consisting of 'ShortExtrapMethod' and a scalar string or character vector using a supported value. For more information on interpolation methods, see interp1.

Data Types: char | string

Extrapolation method for data after last data, specified as the comma-separated pair consisting of 'LongExtrapMethod' and a scalar string or character vector using a supported value. For more information on interpolation methods, see interp1.

Data Types: char | string

ratecurve object for discounting cash flows, specified as the comma-separated pair consisting of 'DiscountCurve' and the name of a previously created ratecurve object.

Data Types: object

Convexity adjustment for one or more STIRFuture instruments, specified as the comma-separated pair consisting of 'ConvexityAdjustment' and an NFutures-by-1 vector of numeric values.

Note

You can only use ConvexityAdjustment when using irbootstrap with a STIRFuture instrument. Also, the length of the ConvexityAdjustment vector must match the number of STIRFuture instruments.

Data Types: double

Output Arguments

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Rate curve, returned as a ratecurve object. The object has the following properties:

  • Type

  • Settle

  • Compounding

  • Basis

  • Dates

  • Rates

  • InterpMethod

  • ShortExtrapMethod

  • LongExtrapMethod

Introduced in R2020a